Patent Publication Number: US-10770087-B2

Title: Selecting codebooks for coding vectors decomposed from higher-order ambisonic audio signals

Description:
This application claims the benefit of the following U.S. Provisional Applications: 
     U.S. Provisional Application No. 61/994,794, filed May 16, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” 
     U.S. Provisional Application No. 62/004,128, filed May 28, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” 
     U.S. Provisional Application No. 62/019,663, filed Jul. 1, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” 
     U.S. Provisional Application No. 62/027,702, filed Jul. 22, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” 
     U.S. Provisional Application No. 62/028,282, filed Jul. 23, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” 
     U.S. Provisional Application No. 62/032,440, filed Aug. 1, 2014, entitled “CODING V-VECTORS OF A DECOMPOSED HIGHER ORDER AMBISONICS (HOA) AUDIO SIGNAL;” each of foregoing listed U.S. Provisional Applications is incorporated by reference as if set forth in their respective entirety herein. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to audio data and, more specifically, coding of higher-order ambisonic audio data. 
     BACKGROUND 
     A higher-order ambisonics (HOA) signal (often represented by a plurality of spherical harmonic coefficients (SHC) or other hierarchical elements) is a three-dimensional representation of a soundfield. The HOA or SHC representation may represent the soundfield in a manner that is independent of the local speaker geometry used to playback a multi-channel audio signal rendered from the SHC signal. The SHC signal may also facilitate backwards compatibility as the SHC signal may be rendered to well-known and highly adopted multi-channel formats, such as a 5.1 audio channel format or a 7.1 audio channel format. The SHC representation may therefore enable a better representation of a soundfield that also accommodates backward compatibility. 
     SUMMARY 
     In general, techniques are described for efficiently representing v-vectors (which may represent spatial information, such as width, shape, direction and location, of an associated audio object) of a decomposed higher order ambisonics (HOA) audio signal based on a set of code vectors. The techniques may involve decomposing the v-vector into a weighted sum of code vectors, selecting a subset of a plurality of weights and corresponding code vectors, quantizing the selected subset of the weights, and indexing the selected subset of code vectors. The techniques may provide improved bit-rates for coding HOA audio signals. 
     In one aspect, a method of obtaining a plurality of higher order ambisonic (HOA) coefficients, the method comprises obtaining from a bitstream data indicative of a plurality of weight values that represent a vector that is included in decomposed version of the plurality of HOA coefficients. Each of the weight values correspond to a respective one of a plurality of weights in a weighted sum of code vectors that represents the vector that includes a set of code vectors. The method further comprising reconstructing the vector based on the weight values and the code vectors. 
     In another aspect, a device configured to obtain a plurality of higher order ambisonic (HOA) coefficients, the device comprises one or more processors configured to obtain from a bitstream data indicative of a plurality of weight values that represent a vector that is included in a decomposed version of the plurality of HOA coefficients. Each of the weight values correspond to a respective one of a plurality of weights in a weighted sum of code vectors that represents the vector and that includes a set of code vectors. The one or more processors further configured to reconstruct the vector based on the weight values and the code vectors. The device also comprising a memory configured to store the reconstructed vector. 
     In another aspect, a device configured to obtain a plurality of higher order ambisonic (HOA) coefficients, the device comprises means for obtaining from a bitstream data indicative of a plurality of weight values that represent a vector that is included in decomposed version of the plurality of HOA coefficients, each of the weight values corresponding to a respective one of a plurality of weights in a weighted sum of code vectors that represents the vector that includes a set of code vectors, and means for reconstructing the vector based on the weight values and the code vectors. 
     In another aspect, a non-transitory computer-readable storage medium has stored thereon instructions that, when executed, cause one or more processors to obtaining from a bitstream data indicative of a plurality of weight values that represent a vector that is included in decomposed version of a plurality of higher order ambisonic (HOA) coefficients, each of the weight values corresponding to a respective one of a plurality of weights in a weighted sum of code vectors that represents the vector that includes a set of code vectors, and reconstruct the vector based on the weight values and the code vectors. 
     In another aspect, a method comprises determining, based on a set of code vectors, one or more weight values that represent a vector that is included in a decomposed version of a plurality of higher order ambisonic (HOA) coefficients, each of the weight values corresponding to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     In another aspect, a device comprises a memory configured to store a set of code vectors, and one or more processors configured to determine, based on the set of code vectors, one or more weight values that represent a vector that is included in a decomposed version of a plurality of higher order ambisonic (HOA) coefficients, each of the weight values corresponding to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     In another aspect, an apparatus comprises means for performing a decomposition with respect to a plurality of higher order ambisonic (HOA) coefficients to generate a decomposed version of the HOA coefficients. The apparatus further comprises means for determining, based on a set of code vectors, one or more weight values that represent a vector that is included in the decomposed version of the HOA coefficients, each of the weight values corresponding to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     In another aspect, a non-transitory computer-readable storage medium has stored thereon instructions that, when executed, cause one or more processors to determine, based on a set of code vectors, one or more weight values that represent a vector that is included in a decomposed version of a plurality of higher order ambisonic (HOA) coefficients, each of the weight values corresponding to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     In another aspect, a method of decoding audio data indicative of a plurality of higher-order ambisonic (HOA) coefficients, the method comprises determining whether to perform vector dequantization or scalar dequantization with respect to a decomposed version of the plurality of HOA coefficients. 
     In another aspect, a device configured to decode audio data indicative of a plurality of higher-order ambisonic (HOA) coefficients, the device comprises a memory configured to store the audio data, and one or more processors configured to determine whether to perform vector dequantization or scalar dequantization with respect to a decomposed version of the plurality of HOA coefficients. 
     In another aspect, a method of encoding audio data, the method comprises determining whether to perform vector quantization or scalar quantization with respect to a decomposed version of a plurality of higher order ambisonic (HOA) coefficients. 
     In another aspect, a method of decoding audio data, the method comprises selecting one of a plurality of codebooks to use when performing vector dequantization with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients. 
     In another aspect, a device comprises a memory configured to store a plurality of codebooks to use when performing vector dequantization with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients, and one or more processors configured to select one of the plurality of codebooks. 
     In another aspect, a device comprises means for storing a plurality of codebooks to use when performing vector dequantization with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients, and means for selecting one of the plurality of codebooks. 
     In another aspect, a non-transitory computer-readable storage medium has stored thereon instructions that, when executed, cause one or more processors to select one of a plurality of codebooks to use when performing vector dequantization with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients. 
     In another aspect, a method of encoding audio data, the method comprises selecting one of a plurality of codebooks to use when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients. 
     In another aspect, a device comprises a memory configured to store a plurality of codebooks to use when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients. The device also comprises one or more processors configured to select one of the plurality of codebooks. 
     In another aspect, a device comprises means for storing a plurality of codebooks to use when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients, and means for selecting one of the plurality of codebooks. 
     In another aspect, a non-transitory computer-readable storage medium has stored thereon instructions that, when executed, cause one or more processors to select one of a plurality of codebooks to use when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients. 
     The details of one or more aspects of the techniques are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the techniques will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram illustrating spherical harmonic basis functions of various orders and sub-orders. 
         FIG. 2  is a diagram illustrating a system that may perform various aspects of the techniques described in this disclosure. 
         FIGS. 3A and 3B  are block diagrams illustrating, in more detail, different examples of the audio encoding device shown in the example of  FIG. 2  that may perform various aspects of the techniques described in this disclosure. 
         FIGS. 4A and 4B  are block diagrams illustrating different versions of the audio decoding device of  FIG. 2  in more detail. 
         FIG. 5  is a flowchart illustrating exemplary operation of an audio encoding device in performing various aspects of the vector-based synthesis techniques described in this disclosure. 
         FIG. 6  is a flowchart illustrating exemplary operation of an audio decoding device in performing various aspects of the techniques described in this disclosure. 
         FIGS. 7 and 8  are diagrams illustrating different versions of the V-vector coding unit of the audio encoding device of  FIG. 3A  or  FIG. 3B  in more detail. 
         FIG. 9  is a conceptual diagram illustrating a sound field generated from a v-vector. 
         FIG. 10  is a conceptual diagram illustrating a sound field generated from a 25th order model of the v-vector described above with respect to  FIG. 60 . 
         FIG. 11  is a conceptual diagram illustrating the weighting of each order for the 25th order model shown in  FIG. 10 . 
         FIG. 12  is a conceptual diagram illustrating a 5th order model of the v-vector described above with respect to  FIG. 9 . 
         FIG. 13  is a conceptual diagram illustrating the weighting of each order for the 5th order model shown in  FIG. 12 . 
         FIG. 14  is a conceptual diagram illustrating example dimensions of example matrices used to perform singular value decomposition. 
         FIG. 15  is a chart illustrating example performance improvements that may be obtained by using the v-vector coding techniques of this disclosure. 
         FIG. 16  is a number of diagrams showing an example of the V-vector coding when performed in accordance with the techniques described in this disclosure. 
         FIG. 17  is a conceptual diagram illustrating an example code vector-based decomposition of a V-vector according to this disclosure. 
         FIG. 18  is a diagram illustrating different ways by which the 16 different code vectors may be employed by the V-vector coding unit shown in the example of either or both of  FIGS. 10 and 11 . 
         FIGS. 19A and 19B  are diagrams illustrating codebooks with 256 rows with each row having 10 values and 16 values respectively that may be used in accordance with various aspects of the techniques described in this disclosure. 
         FIG. 20  is a diagram illustrating an example graph showing a threshold error used to select X* number of code vectors in accordance with various aspects of the techniques described in this disclosure. 
         FIG. 21  is a block diagram illustrating an example vector quantization unit  520  according to this disclosure. 
         FIGS. 22, 24, and 26  are flowcharts illustrating exemplary operation of the vector quantization unit in performing various aspects of the techniques described in this disclosure. 
         FIGS. 23, 25, and 27  are flowcharts illustrating exemplary operation of the V-vector reconstruction unit in performing various aspects of the techniques described in this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In general, techniques are described for efficiently representing v-vectors (which may represent spatial information, such as width, shape, direction and location, of an associated audio object) of a decomposed higher order ambisonics (HOA) audio signal based on a set of code vectors. The techniques may involve decomposing the v-vector into a weighted sum of code vectors, selecting a subset of a plurality of weights and corresponding code vectors, quantizing the selected subset of the weights, and indexing the selected subset of code vectors. The techniques may provide improved bit-rates for coding HOA audio signals. 
     The evolution of surround sound has made available many output formats for entertainment nowadays. Examples of such consumer surround sound formats are mostly ‘channel’ based in that they implicitly specify feeds to loudspeakers in certain geometrical coordinates. The consumer surround sound formats include the popular 5.1 format (which includes the following six channels: front left (FL), front right (FR), center or front center, back left or surround left, back right or surround right, and low frequency effects (LFE)), the growing 7.1 format, various formats that includes height speakers such as the 7.1.4 format and the 22.2 format (e.g., for use with the Ultra High Definition Television standard). Non-consumer formats can span any number of speakers (in symmetric and non-symmetric geometries) often termed ‘surround arrays’. One example of such an array includes 32 loudspeakers positioned on coordinates on the corners of a truncated icosahedron. 
     The input to a future MPEG encoder is optionally one of three possible formats: (i) traditional channel-based audio (as discussed above), which is meant to be played through loudspeakers at pre-specified positions; (ii) object-based audio, which involves discrete pulse-code-modulation (PCM) data for single audio objects with associated metadata containing their location coordinates (amongst other information); and (iii) scene-based audio, which involves representing the soundfield using coefficients of spherical harmonic basis functions (also called “spherical harmonic coefficients” or SHC, “Higher-order Ambisonics” or HOA, and “HOA coefficients”). The future MPEG encoder may be described in more detail in a document entitled “Call for Proposals for 3D Audio,” by the International Organization for Standardization/International Electrotechnical Commission (ISO)/(IEC) JTC1/SC29/WG11/N13411, released January 2013 in Geneva, Switzerland, and available at http://mpeg.chiariglione.org/sites/default/files/files/standards/parts/docs/w13411.zip. 
     There are various ‘surround-sound’ channel-based formats in the market. They range, for example, from the 5.1 home theatre system (which has been the most successful in terms of making inroads into living rooms beyond stereo) to the 22.2 system developed by NHK (Nippon Hoso Kyokai or Japan Broadcasting Corporation). Content creators (e.g., Hollywood studios) would like to produce the soundtrack for a movie once, and not spend effort to remix it for each speaker configuration. Recently, Standards Developing Organizations have been considering ways in which to provide an encoding into a standardized bitstream and a subsequent decoding that is adaptable and agnostic to the speaker geometry (and number) and acoustic conditions at the location of the playback (involving a renderer). 
     To provide such flexibility for content creators, a hierarchical set of elements may be used to represent a soundfield. The hierarchical set of elements may refer to a set of elements in which the elements are ordered such that a basic set of lower-ordered elements provides a full representation of the modeled soundfield. As the set is extended to include higher-order elements, the representation becomes more detailed, increasing resolution. 
     One example of a hierarchical set of elements is a set of spherical harmonic coefficients (SHC). The following expression demonstrates a description or representation of a soundfield using SHC: 
     
       
         
           
             
               
                 
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     The expression shows that the pressure p i  at any point {r r , θ r , φ r } of the soundfield, at time t, can be represented uniquely by the SHC, A n   m (k). Here, 
               k   =     ω   c       ,   c         
is the speed of sound (˜343 m/s), {r r , θ r , φ r } is a point of reference (or observation point), j n (·) is the spherical Bessel function of order n, and Y n   m  (θ r , φ r ) are the spherical harmonic basis functions of order n and suborder m. It can be recognized that the term in square brackets is a frequency-domain representation of the signal (i.e., S(ω, r r , θ r , φ r )) which can be approximated by various time-frequency transformations, such as the discrete Fourier transform (DFT), the discrete cosine transform (DCT), or a wavelet transform. Other examples of hierarchical sets include sets of wavelet transform coefficients and other sets of coefficients of multiresolution basis functions.
 
       FIG. 1  is a diagram illustrating spherical harmonic basis functions from the zero order (n=0) to the fourth order (n=4). As can be seen, for each order, there is an expansion of suborders m which are shown but not explicitly noted in the example of  FIG. 1  for ease of illustration purposes. 
     The SHC A n   m (k) can either be physically acquired (e.g., recorded) by various microphone array configurations or, alternatively, they can be derived from channel-based or object-based descriptions of the soundfield. The SHC represent scene-based audio, where the SHC may be input to an audio encoder to obtain encoded SHC that may promote more efficient transmission or storage. For example, a fourth-order representation involving (1+4) 2  (25, and hence fourth order) coefficients may be used. 
     As noted above, the SHC may be derived from a microphone recording using a microphone array. Various examples of how SHC may be derived from microphone arrays are described in Poletti, M., “Three-Dimensional Surround Sound Systems Based on Spherical Harmonics,” J. Audio Eng. Soc., Vol. 53, No. 11, 2005 November, pp. 1004-1025. 
     To illustrate how the SHCs may be derived from an object-based description, consider the following equation. The coefficients A n   m  (k) for the soundfield corresponding to an individual audio object may be expressed as:
 
 A   n   m ( k )= g (ω)(−4π ik ) h   n   (2) ( kr   s ) Y   n   m (θ s ,φ s ),
 
where i is √{square root over (−1)}, h n   (2) (·) is the spherical Hankel function (of the second kind) of order n, and {r s , θ s , φ s } is the location of the object. Knowing the object source energy g (ω) as a function of frequency (e.g., using time-frequency analysis techniques, such as performing a fast Fourier transform on the PCM stream) allows us to convert each PCM object and the corresponding location into the SHC A n   m  (k). Further, it can be shown (since the above is a linear and orthogonal decomposition) that the A n   m (k) coefficients for each object are additive. In this manner, a multitude of PCM objects can be represented by the A n   m (k) coefficients (e.g., as a sum of the coefficient vectors for the individual objects). Essentially, the coefficients contain information about the soundfield (the pressure as a function of 3D coordinates), and the above represents the transformation from individual objects to a representation of the overall soundfield, in the vicinity of the observation point {r r , θ r , φ r }. The remaining figures are described below in the context of object-based and SHC-based audio coding.
 
       FIG. 2  is a diagram illustrating a system  10  that may perform various aspects of the techniques described in this disclosure. As shown in the example of  FIG. 2 , the system  10  includes a content creator device  12  and a content consumer device  14 . While described in the context of the content creator device  12  and the content consumer device  14 , the techniques may be implemented in any context in which SHCs (which may also be referred to as HOA coefficients) or any other hierarchical representation of a soundfield are encoded to form a bitstream representative of the audio data. Moreover, the content creator device  12  may represent any form of computing device capable of implementing the techniques described in this disclosure, including a handset (or cellular phone), a tablet computer, a smart phone, or a desktop computer to provide a few examples. Likewise, the content consumer device  14  may represent any form of computing device capable of implementing the techniques described in this disclosure, including a handset (or cellular phone), a tablet computer, a smart phone, a set-top box, or a desktop computer to provide a few examples. 
     The content creator device  12  may be operated by a movie studio or other entity that may generate multi-channel audio content for consumption by operators of content consumer devices, such as the content consumer device  14 . In some examples, the content creator device  12  may be operated by an individual user who would like to compress HOA coefficients  11 . Often, the content creator generates audio content in conjunction with video content. The content consumer device  14  may be operated by an individual. The content consumer device  14  may include an audio playback system  16 , which may refer to any form of audio playback system capable of rendering SHC for play back as multi-channel audio content. 
     The content creator device  12  includes an audio editing system  18 . The content creator device  12  obtain live recordings  7  in various formats (including directly as HOA coefficients) and audio objects  9 , which the content creator device  12  may edit using audio editing system  18 . A microphone  5  may capture the live recordings  7 . The content creator may, during the editing process, render HOA coefficients  11  from audio objects  9 , listening to the rendered speaker feeds in an attempt to identify various aspects of the soundfield that require further editing. The content creator device  12  may then edit HOA coefficients  11  (potentially indirectly through manipulation of different ones of the audio objects  9  from which the source HOA coefficients may be derived in the manner described above). The content creator device  12  may employ the audio editing system  18  to generate the HOA coefficients  11 . The audio editing system  18  represents any system capable of editing audio data and outputting the audio data as one or more source spherical harmonic coefficients. 
     When the editing process is complete, the content creator device  12  may generate a bitstream  21  based on the HOA coefficients  11 . That is, the content creator device  12  includes an audio encoding device  20  that represents a device configured to encode or otherwise compress HOA coefficients  11  in accordance with various aspects of the techniques described in this disclosure to generate the bitstream  21 . The audio encoding device  20  may generate the bitstream  21  for transmission, as one example, across a transmission channel, which may be a wired or wireless channel, a data storage device, or the like. The bitstream  21  may represent an encoded version of the HOA coefficients  11  and may include a primary bitstream and another side bitstream, which may be referred to as side channel information. 
     While shown in  FIG. 2  as being directly transmitted to the content consumer device  14 , the content creator device  12  may output the bitstream  21  to an intermediate device positioned between the content creator device  12  and the content consumer device  14 . The intermediate device may store the bitstream  21  for later delivery to the content consumer device  14 , which may request the bitstream. The intermediate device may comprise a file server, a web server, a desktop computer, a laptop computer, a tablet computer, a mobile phone, a smart phone, or any other device capable of storing the bitstream  21  for later retrieval by an audio decoder. The intermediate device may reside in a content delivery network capable of streaming the bitstream  21  (and possibly in conjunction with transmitting a corresponding video data bitstream) to subscribers, such as the content consumer device  14 , requesting the bitstream  21 . 
     Alternatively, the content creator device  12  may store the bitstream  21  to a storage medium, such as a compact disc, a digital video disc, a high definition video disc or other storage media, most of which are capable of being read by a computer and therefore may be referred to as computer-readable storage media or non-transitory computer-readable storage media. In this context, the transmission channel may refer to the channels by which content stored to the mediums are transmitted (and may include retail stores and other store-based delivery mechanism). In any event, the techniques of this disclosure should not therefore be limited in this respect to the example of  FIG. 2 . 
     As further shown in the example of  FIG. 2 , the content consumer device  14  includes the audio playback system  16 . The audio playback system  16  may represent any audio playback system capable of playing back multi-channel audio data. The audio playback system  16  may include a number of different renderers  22 . The renderers  22  may each provide for a different form of rendering, where the different forms of rendering may include one or more of the various ways of performing vector-base amplitude panning (VBAP), and/or one or more of the various ways of performing soundfield synthesis. As used herein, “A and/or B” means “A or B”, or both “A and B”. 
     The audio playback system  16  may further include an audio decoding device  24 . The audio decoding device  24  may represent a device configured to decode HOA coefficients  11 ′ from the bitstream  21 , where the HOA coefficients  11 ′ may be similar to the HOA coefficients  11  but differ due to lossy operations (e.g., quantization) and/or transmission via the transmission channel. The audio playback system  16  may, after decoding the bitstream  21  to obtain the HOA coefficients  11 ′ and render the HOA coefficients  11 ′ to output loudspeaker feeds  25 . The loudspeaker feeds  25  may drive one or more loudspeakers (which are not shown in the example of  FIG. 2  for ease of illustration purposes). 
     To select the appropriate renderer or, in some instances, generate an appropriate renderer, the audio playback system  16  may obtain loudspeaker information  13  indicative of a number of loudspeakers and/or a spatial geometry of the loudspeakers. In some instances, the audio playback system  16  may obtain the loudspeaker information  13  using a reference microphone and driving the loudspeakers in such a manner as to dynamically determine the loudspeaker information  13 . In other instances or in conjunction with the dynamic determination of the loudspeaker information  13 , the audio playback system  16  may prompt a user to interface with the audio playback system  16  and input the loudspeaker information  13 . 
     The audio playback system  16  may then select one of the audio renderers  22  based on the loudspeaker information  13 . In some instances, the audio playback system  16  may, when none of the audio renderers  22  are within some threshold similarity measure (in terms of the loudspeaker geometry) to the loudspeaker geometry specified in the loudspeaker information  13 , generate the one of audio renderers  22  based on the loudspeaker information  13 . The audio playback system  16  may, in some instances, generate one of the audio renderers  22  based on the loudspeaker information  13  without first attempting to select an existing one of the audio renderers  22 . One or more speakers  3  may then playback the rendered loudspeaker feeds  25 . 
       FIG. 3A  is a block diagram illustrating, in more detail, one example of the audio encoding device  20  shown in the example of  FIG. 2  that may perform various aspects of the techniques described in this disclosure. The audio encoding device  20  includes a content analysis unit  26 , a vector-based decomposition unit  27  and a directional-based decomposition unit  28 . Although described briefly below, more information regarding the audio encoding device  20  and the various aspects of compressing or otherwise encoding HOA coefficients is available in International Patent Application Publication No. WO 2014/194099, entitled “INTERPOLATION FOR DECOMPOSED REPRESENTATIONS OF A SOUND FIELD,” filed 29 May, 2014. 
     The content analysis unit  26  represents a unit configured to analyze the content of the HOA coefficients  11  to identify whether the HOA coefficients  11  represent content generated from a live recording or an audio object. The content analysis unit  26  may determine whether the HOA coefficients  11  were generated from a recording of an actual soundfield or from an artificial audio object. In some instances, when the framed HOA coefficients  11  were generated from a recording, the content analysis unit  26  passes the HOA coefficients  11  to the vector-based decomposition unit  27 . In some instances, when the framed HOA coefficients  11  were generated from a synthetic audio object, the content analysis unit  26  passes the HOA coefficients  11  to the directional-based synthesis unit  28 . The directional-based synthesis unit  28  may represent a unit configured to perform a directional-based synthesis of the HOA coefficients  11  to generate a directional-based bitstream  21 . 
     As shown in the example of  FIG. 3A , the vector-based decomposition unit  27  may include a linear invertible transform (LIT) unit  30 , a parameter calculation unit  32 , a reorder unit  34 , a foreground selection unit  36 , an energy compensation unit  38 , a psychoacoustic audio coder unit  40 , a bitstream generation unit  42 , a soundfield analysis unit  44 , a coefficient reduction unit  46 , a background (BG) selection unit  48 , a spatio-temporal interpolation unit  50 , and a V-vector coding unit  52 . 
     The linear invertible transform (LIT) unit  30  receives the HOA coefficients  11  in the form of HOA channels, each channel representative of a block or frame of a coefficient associated with a given order, sub-order of the spherical basis functions (which may be denoted as HOA[k], where k may denote the current frame or block of samples). The matrix of HOA coefficients  11  may have dimensions D: M×(N+1) 2 . 
     The LIT unit  30  may represent a unit configured to perform a form of analysis referred to as singular value decomposition. While described with respect to SVD, the techniques described in this disclosure may be performed with respect to any similar transformation or decomposition that provides for sets of linearly uncorrelated, energy compacted output. Also, reference to “sets” in this disclosure is generally intended to refer to non-zero sets unless specifically stated to the contrary and is not intended to refer to the classical mathematical definition of sets that includes the so-called “empty set.” An alternative transformation may comprise a principal component analysis, which is often referred to as “PCA.” Depending on the context, PCA may be referred to by a number of different names, such as discrete Karhunen-Loeve transform, the Hotelling transform, proper orthogonal decomposition (POD), and eigenvalue decomposition (EVD) to name a few examples. Properties of such operations that are conducive to the underlying goal of compressing audio data are ‘energy compaction’ and ‘decorrelation’ of the multichannel audio data. 
     In any event, assuming the LIT unit  30  performs a singular value decomposition (which, again, may be referred to as “SVD”) for purposes of example, the LIT unit  30  may transform the HOA coefficients  11  into two or more sets of transformed HOA coefficients. The “sets” of transformed HOA coefficients may include vectors of transformed HOA coefficients. In the example of  FIG. 3A , the LIT unit  30  may perform the SVD with respect to the HOA coefficients  11  to generate a so-called V matrix, an S matrix, and a U matrix. SVD, in linear algebra, may represent a factorization of a y-by-z real or complex matrix X (where X may represent multi-channel audio data, such as the HOA coefficients  11 ) in the following form:
 
 X=USV*  
 
U may represent a y-by-y real or complex unitary matrix, where the y columns of U are known as the left-singular vectors of the multi-channel audio data. S may represent a y-by-z rectangular diagonal matrix with non-negative real numbers on the diagonal, where the diagonal values of S are known as the singular values of the multi-channel audio data. V* (which may denote a conjugate transpose of V) may represent a z-by-z real or complex unitary matrix, where the z columns of V* are known as the right-singular vectors of the multi-channel audio data.
 
     In some examples, the V* matrix in the SVD mathematical expression referenced above is denoted as the conjugate transpose of the V matrix to reflect that SVD may be applied to matrices comprising complex numbers. When applied to matrices comprising only real-numbers, the complex conjugate of the V matrix (or, in other words, the V* matrix) may be considered to be the transpose of the V matrix. Below it is assumed, for ease of illustration purposes, that the HOA coefficients  11  comprise real-numbers with the result that the V matrix is output through SVD rather than the V* matrix. Moreover, while denoted as the V matrix in this disclosure, reference to the V matrix should be understood to refer to the transpose of the V matrix where appropriate. While assumed to be the V matrix, the techniques may be applied in a similar fashion to HOA coefficients  11  having complex coefficients, where the output of the SVD is the V* matrix. Accordingly, the techniques should not be limited in this respect to only provide for application of SVD to generate a V matrix, but may include application of SVD to HOA coefficients  11  having complex components to generate a V* matrix. 
     In this way, the LIT unit  30  may perform SVD with respect to the HOA coefficients  11  to output US[k] vectors  33  (which may represent a combined version of the S vectors and the U vectors) having dimensions D: M×(N+1) 2 , and V[k] vectors  35  having dimensions D: (N+1) 2 ×(N+1) 2 . Individual vector elements in the US[k] matrix may also be termed X PS (k) while individual vectors of the V[k] matrix may also be termed v(k). 
     An analysis of the U, S and V matrices may reveal that the matrices carry or represent spatial and temporal characteristics of the underlying soundfield represented above by X. Each of the N vectors in U (of length M samples) may represent normalized separated audio signals as a function of time (for the time period represented by M samples), that are orthogonal to each other and that have been decoupled from any spatial characteristics (which may also be referred to as directional information). The spatial characteristics, representing spatial shape and position (r, theta, phi) may instead be represented by individual i th  vectors, v (i) (k), in the V matrix (each of length (N+1) 2 ). The individual elements of each of v (i) (k) vectors may represent an HOA coefficient describing the shape (including width) and position of the soundfield for an associated audio object. Both the vectors in the U matrix and the V matrix are normalized such that their root-mean-square energies are equal to unity. The energy of the audio signals in U are thus represented by the diagonal elements in S. Multiplying U and S to form US[k] (with individual vector elements X PS  (k)), thus represent the audio signal with energies. The ability of the SVD decomposition to decouple the audio time-signals (in U), their energies (in S) and their spatial characteristics (in V) may support various aspects of the techniques described in this disclosure. Further, the model of synthesizing the underlying HOA[k] coefficients, X, by a vector multiplication of US[k] and V[k] gives rise the term “vector-based decomposition,” which is used throughout this document. 
     Although described as being performed directly with respect to the HOA coefficients  11 , the LIT unit  30  may apply the linear invertible transform to derivatives of the HOA coefficients  11 . For example, the LIT unit  30  may apply SVD with respect to a power spectral density matrix derived from the HOA coefficients  11 . By performing SVD with respect to the power spectral density (PSD) of the HOA coefficients rather than the coefficients themselves, the LIT unit  30  may potentially reduce the computational complexity of performing the SVD in terms of one or more of processor cycles and storage space, while achieving the same source audio encoding efficiency as if the SVD were applied directly to the HOA coefficients. 
     The parameter calculation unit  32  represents a unit configured to calculate various parameters, such as a correlation parameter (R), directional properties parameters (θ, φ, r), and an energy property (e). Each of the parameters for the current frame may be denoted as R[k], θ[k], φ[k], r[k] and e[k]. The parameter calculation unit  32  may perform an energy analysis and/or correlation (or so-called cross-correlation) with respect to the US[k] vectors  33  to identify the parameters. The parameter calculation unit  32  may also determine the parameters for the previous frame, where the previous frame parameters may be denoted R[k−1], θ[k−1], φ[k−1], r[k−1] and e[k−1], based on the previous frame of US[k−1] vector and V[k−1] vectors. The parameter calculation unit  32  may output the current parameters  37  and the previous parameters  39  to reorder unit  34 . 
     The parameters calculated by the parameter calculation unit  32  may be used by the reorder unit  34  to re-order the audio objects to represent their natural evaluation or continuity over time. The reorder unit  34  may compare each of the parameters  37  from the first US[k] vectors  33  turn-wise against each of the parameters  39  for the second US[k−1] vectors  33 . The reorder unit  34  may reorder (using, as one example, a Hungarian algorithm) the various vectors within the US[k] matrix  33  and the V[k] matrix  35  based on the current parameters  37  and the previous parameters  39  to output a reordered US[k] matrix  33 ′ (which may be denoted mathematically as  US [k]) and a reordered V[k] matrix  35 ′ (which may be denoted mathematically as  V [k]) to a foreground sound (or predominant sound—PS) selection unit  36  (“foreground selection unit  36 ”) and an energy compensation unit  38 . 
     The soundfield analysis unit  44  may represent a unit configured to perform a soundfield analysis with respect to the HOA coefficients  11  so as to potentially achieve a target bitrate  41 . The soundfield analysis unit  44  may, based on the analysis and/or on a received target bitrate  41 , determine the total number of psychoacoustic coder instantiations (which may be a function of the total number of ambient or background channels (BG TOT ) and the number of foreground channels or, in other words, predominant channels. The total number of psychoacoustic coder instantiations can be denoted as numHOATransportChannels. 
     The soundfield analysis unit  44  may also determine, again to potentially achieve the target bitrate  41 , the total number of foreground channels (nFG)  45 , the minimum order of the background (or, in other words, ambient) soundfield (N BG  or, alternatively, MinAmbHOAorder), the corresponding number of actual channels representative of the minimum order of background soundfield (nBGa=(MinAmbHOAorder+1) 2 ), and indices (i) of additional BG HOA channels to send (which may collectively be denoted as background channel information  43  in the example of  FIG. 3A ). The background channel information  42  may also be referred to as ambient channel information  43 . Each of the channels that remains from numHOATransportChannels—nBGa, may either be an “additional background/ambient channel”, an “active vector-based predominant channel”, an “active directional based predominant signal” or “completely inactive”. In one aspect, the channel types may be indicated (as a “ChannelType”) syntax element by two bits (e.g. 00: directional based signal; 01: vector-based predominant signal; 10: additional ambient signal; 11: inactive signal). The total number of background or ambient signals, nBGa, may be given by (MinAmbHOAorder+1) 2 +the number of times the index 10 (in the above example) appears as a channel type in the bitstream for that frame. 
     The soundfield analysis unit  44  may select the number of background (or, in other words, ambient) channels and the number of foreground (or, in other words, predominant) channels based on the target bitrate  41 , selecting more background and/or foreground channels when the target bitrate  41  is relatively higher (e.g., when the target bitrate  41  equals or is greater than 512 Kbps). In one aspect, the numHOATransportChannels may be set to 8 while the MinAmbHOAorder may be set to 1 in the header section of the bitstream. In this scenario, at every frame, four channels may be dedicated to represent the background or ambient portion of the soundfield while the other 4 channels can, on a frame-by-frame basis vary on the type of channel—e.g., either used as an additional background/ambient channel or a foreground/predominant channel. The foreground/predominant signals can be one of either vector-based or directional based signals, as described above. 
     In some instances, the total number of vector-based predominant signals for a frame, may be given by the number of times the ChannelType index is 01 in the bitstream of that frame. In the above aspect, for every additional background/ambient channel (e.g., corresponding to a ChannelType of 10), corresponding information of which of the possible HOA coefficients (beyond the first four) may be represented in that channel. The information, for fourth order HOA content, may be an index to indicate the HOA coefficients 5-25. The first four ambient HOA coefficients 1-4 may be sent all the time when minAmbHOAorder is set to 1, hence the audio encoding device may only need to indicate one of the additional ambient HOA coefficient having an index of 5-25. The information could thus be sent using a 5 bits syntax element (for 4 th  order content), which may be denoted as “CodedAmbCoeffIdx.” In any event, the soundfield analysis unit  44  outputs the background channel information  43  and the HOA coefficients  11  to the background (BG) selection unit  36 , the background channel information  43  to coefficient reduction unit  46  and the bitstream generation unit  42 , and the nFG  45  to a foreground selection unit  36 . 
     The background selection unit  48  may represent a unit configured to determine background or ambient HOA coefficients  47  based on the background channel information (e.g., the background soundfield (N BG ) and the number (nBGa) and the indices (i) of additional BG HOA channels to send). For example, when N BG  equals one, the background selection unit  48  may select the HOA coefficients  11  for each sample of the audio frame having an order equal to or less than one. The background selection unit  48  may, in this example, then select the HOA coefficients  11  having an index identified by one of the indices (i) as additional BG HOA coefficients, where the nBGa is provided to the bitstream generation unit  42  to be specified in the bitstream  21  so as to enable the audio decoding device, such as the audio decoding device  24  shown in the example of  FIGS. 4A and 4B , to parse the background HOA coefficients  47  from the bitstream  21 . The background selection unit  48  may then output the ambient HOA coefficients  47  to the energy compensation unit  38 . The ambient HOA coefficients  47  may have dimensions D: M×[(N BG +1) 2 +nBGa]. The ambient HOA coefficients  47  may also be referred to as “ambient HOA coefficients  47 ,” where each of the ambient HOA coefficients  47  corresponds to a separate ambient HOA channel  47  to be encoded by the psychoacoustic audio coder unit  40 . 
     The foreground selection unit  36  may represent a unit configured to select the reordered US[k] matrix  33 ′ and the reordered V[k] matrix  35 ′ that represent foreground or distinct components of the soundfield based on nFG  45  (which may represent a one or more indices identifying the foreground vectors). The foreground selection unit  36  may output nFG signals  49  (which may be denoted as a reordered US[k] 1, . . . , nFG   49 , FG 1, . . . , nfG [k]  49 , or X PS   (1 . . . nFG) (k)  49 ) to the psychoacoustic audio coder unit  40 , where the nFG signals  49  may have dimensions D: M×nFG and each represent mono-audio objects. The foreground selection unit  36  may also output the reordered V[k] matrix  35 ′ (or v (1 . . . nFG) (k)  35 ′) corresponding to foreground components of the soundfield to the spatio-temporal interpolation unit  50 , where a subset of the reordered V[k] matrix  35 ′ corresponding to the foreground components may be denoted as foreground V[k] matrix  51   k  (which may be mathematically denoted as  V   1, . . . ,nFG [k]) having dimensions D: (N+1) 2 ×nFG. 
     The energy compensation unit  38  may represent a unit configured to perform energy compensation with respect to the ambient HOA coefficients  47  to compensate for energy loss due to removal of various ones of the HOA channels by the background selection unit  48 . The energy compensation unit  38  may perform an energy analysis with respect to one or more of the reordered US[k] matrix  33 ′, the reordered V[k] matrix  35 ′, the nFG signals  49 , the foreground V[k] vectors  51   k  and the ambient HOA coefficients  47  and then perform energy compensation based on the energy analysis to generate energy compensated ambient HOA coefficients  47 ′. The energy compensation unit  38  may output the energy compensated ambient HOA coefficients  47 ′ to the psychoacoustic audio coder unit  40 . 
     The spatio-temporal interpolation unit  50  may represent a unit configured to receive the foreground V[k] vectors  51   k  for the k th  frame and the foreground V[k−1] vectors  51   k-1  for the previous frame (hence the k−1 notation) and perform spatio-temporal interpolation to generate interpolated foreground V[k] vectors. The spatio-temporal interpolation unit  50  may recombine the nFG signals  49  with the foreground V[k] vectors  51   k  to recover reordered foreground HOA coefficients. The spatio-temporal interpolation unit  50  may then divide the reordered foreground HOA coefficients by the interpolated V[k] vectors to generate interpolated nFG signals  49 ′. The spatio-temporal interpolation unit  50  may also output the foreground V[k] vectors  51   k  that were used to generate the interpolated foreground V[k] vectors so that an audio decoding device, such as the audio decoding device  24 , may generate the interpolated foreground V[k] vectors and thereby recover the foreground V[k] vectors  51   k . The foreground V[k] vectors  51   k  used to generate the interpolated foreground V[k] vectors are denoted as the remaining foreground V[k] vectors  53 . In order to ensure that the same V[k] and V[k−1] are used at the encoder and decoder (to create the interpolated vectors V[k]) quantized/dequantized versions of the vectors may be used at the encoder and decoder. The spatio-temporal interpolation unit  50  may output the interpolated nFG signals  49 ′ to the psychoacoustic audio coder unit  46  and the interpolated foreground V[k] vectors  51   k  to the coefficient reduction unit  46 . 
     The coefficient reduction unit  46  may represent a unit configured to perform coefficient reduction with respect to the remaining foreground V[k] vectors  53  based on the background channel information  43  to output reduced foreground V[k] vectors  55  to the V-vector coding unit  52 . The reduced foreground V[k] vectors  55  may have dimensions D: [(N+1) 2 −(N BG +1) 2 −BG TOT ]×nFG. The coefficient reduction unit  46  may, in this respect, represent a unit configured to reduce the number of coefficients in the remaining foreground V[k] vectors  53 . In other words, coefficient reduction unit  46  may represent a unit configured to eliminate the coefficients in the foreground V[k] vectors (that form the remaining foreground V[k] vectors  53 ) having little to no directional information. In some examples, the coefficients of the distinct or, in other words, foreground V[k] vectors corresponding to a first and zero order basis functions (which may be denoted as N BG ) provide little directional information and therefore can be removed from the foreground V-vectors (through a process that may be referred to as “coefficient reduction”). In this example, greater flexibility may be provided to not only identify the coefficients that correspond N BG  but to identify additional HOA channels (which may be denoted by the variable TotalOfAddAmbHOAChan) from the set of [(N BG +1) 2 +1, (N+1) 2 ]. 
     The V-vector coding unit  52  may represent a unit configured to perform any form of quantization to compress the reduced foreground V[k] vectors  55  to generate coded foreground V[k] vectors  57 , outputting the coded foreground V[k] vectors  57  to the bitstream generation unit  42 . In operation, the V-vector coding unit  52  may represent a unit configured to compress a spatial component of the soundfield, i.e., one or more of the reduced foreground V[k] vectors  55  in this example. The V-vector coding unit  52  may perform any one of the following 12 quantization modes, as indicated by a quantization mode syntax element denoted “NbitsQ”: 
     NbitsQ value Type of Quantization Mode 
     0-3: Reserved 
     4: Vector Quantization 
     5: Scalar Quantization without Huffman Coding 
     6: 6-bit Scalar Quantization with Huffman Coding 
     7: 7-bit Scalar Quantization with Huffman Coding 
     8: 8-bit Scalar Quantization with Huffman Coding 
     16: 16-bit Scalar Quantization with Huffman Coding 
     The V-vector coding unit  52  may also perform predicted versions of any of the foregoing types of quantization modes, where a difference is determined between an element of (or a weight when vector quantization is performed) of the V-vector of a previous frame and the element (or weight when vector quantization is performed) of the V-vector of a current frame is determined. The V-vector coding unit  52  may then quantize the difference between the elements or weights of the current frame and previous frame rather than the value of the element of the V-vector of the current frame itself. 
     The V-vector coding unit  52  may perform multiple forms of quantization with respect to each of the reduced foreground V[k] vectors  55  to obtain multiple coded versions of the reduced foreground V[k] vectors  55 . The V-vector coding unit  52  may select the one of the coded versions of the reduced foreground V[k] vectors  55  as the coded foreground V[k] vector  57 . The V-vector coding unit  52  may, in other words, select one of the non-predicted vector-quantized V-vector, predicted vector-quantized V-vector, the non-Huffman-coded scalar-quantized V-vector, and the Huffman-coded scalar-quantized V-vector to use as the output switched-quantized V-vector based on any combination of the criteria discussed in this disclosure. 
     In some examples, the V-vector coding unit  52  may select a quantization mode from a set of quantization modes that includes a vector quantization mode and one or more scalar quantization modes, and quantize an input V-vector based on (or according to) the selected mode. The V-vector coding unit  52  may then provide the selected one of the non-predicted vector-quantized V-vector (e.g., in terms of weight values or bits indicative thereof), predicted vector-quantized V-vector (e.g., in terms of error values or bits indicative thereof), the non-Huffman-coded scalar-quantized V-vector and the Huffman-coded scalar-quantized V-vector to the bitstream generation unit  52  as the coded foreground V[k] vectors  57 . The V-vector coding unit  52  may also provide the syntax elements indicative of the quantization mode (e.g., the NbitsQ syntax element) and any other syntax elements used to dequantize or otherwise reconstruct the V-vector. 
     With regard to vector quantization, the v-vector coding unit  52  may code the reduced foreground V[k] vectors  55  based on the code vectors  63  to generate coded V[k] vectors. As shown in  FIG. 3A , the v-vector coding unit  52  may in some examples, output coded weights  57  and indices  73 . The coded weights  57  and the indices  73 , in such examples, may together represent the coded V[k] vectors. The indices  73  may represent which code vectors in a weighted sum of coding vectors corresponds to each of the weights in the coded weights  57 . 
     To code the reduced foreground V[k] vectors  55 , the v-vector coding unit  52  may, in some examples, decompose each of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors based on the code vectors  63 . The weighted sum of code vectors may include a plurality of weights and a plurality of code vectors, and may represent the sum of the products of each of the weights may be multiplied by a respective one of the code vectors. The plurality of code vectors included in the weighted sum of the code vectors may correspond to the code vectors  63  received by the v-vector coding unit  52 . Decomposing one of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors may involve determining weight values for one or more of the weights included in the weighted sum of code vectors. 
     After determining the weight values that correspond to the weights included in the weighted sum of code vectors, the v-vector coding unit  52  may code one or more of the weight values to generate the coded weights  57 . In some examples, coding the weight values may include quantizing the weight values. In further examples, coding the weight values may include quantizing the weight values and performing Huffman coding with respect to the quantized weight values. In additional examples, coding the weight values may include coding one or more of the weight values, data indicative of the weight values, the quantized weight values, data indicative of the quantized weight values using any coding technique. 
     In some examples, the code vectors  63  may be a set of orthonormal vectors. In further examples, the code vectors  63  may be a set of pseudo-orthonormal vectors. In additional examples, the code vectors  63  may be one or more of the following: a set of directional vectors, a set of orthogonal directional vectors, a set of orthonormal directional vectors, a set of pseudo-orthonormal directional vectors, a set of pseudo-orthogonal directional vectors, a set of directional basis vectors, a set of orthogonal vectors, a set of pseudo-orthogonal vectors, a set of spherical harmonic basis vectors, a set of normalized vectors, and a set of basis vectors. In examples where the code vectors  63  include directional vectors, each of the directional vectors may have a directionality that corresponds to a direction or directional radiation pattern in 2D or 3D space. 
     In some examples, the code vectors  63  may be a predefined and/or predetermined set of code vectors  63 . In additional examples, the code vectors may be independent of the underlying HOA soundfield coefficients and/or not be generated based on the underlying HOA soundfield coefficients. In further examples, the code vectors  63  may be the same when coding different frames of HOA coefficients. In additional examples, the code vectors  63  may be different when coding different frames of HOA coefficients. In additional examples, the code vectors  63  may be alternatively referred to as codebook vectors and/or candidate code vectors. 
     In some examples, to determine the weight values corresponding to one of the reduced foreground V[k] vectors  55 , the v-vector coding unit  52  may, for each of the weight values in the weighted sum of code vectors, multiply the reduced foreground V[k] vector by a respective one of the code vectors  63  to determine the respective weight value. In some cases, to multiply the reduced foreground V[k] vector by the code vector, the v-vector coding unit  52  may multiply the reduced foreground V[k] vector by a transpose of the respective one of the code vectors  63  to determine the respective weight value. 
     To quantize the weights, the v-vector coding unit  52  may perform any type of quantization. For example, the v-vector coding unit  52  may perform scalar quantization, vector quantization, or matrix quantization with respect to the weight values. 
     In some examples, instead of coding all of the weight values to generate the coded weights  57 , the v-vector coding unit  52  may code a subset of the weight values included in the weighted sum of code vectors to generate the coded weights  57 . For example, the v-vector coding unit  52  may quantize a set of the weight values included in the weighted sum of code vectors. A subset of the weight values included in the weighted sum of code vectors may refer to a set of weight values that has a number of weight values that is less than the number of weight values in the entire set of weight values included in the weighted sum of code vectors. 
     In some example, the v-vector coding unit  52  may select a subset of the weight values included in the weighted sum of code vectors to code and/or quantize based on various criteria. In one example, the integer N may represent the total number of weight values included in the weighted sum of code vectors, and the v-vector coding unit  52  may select the M greatest weight values (i.e., maxima weight values) from the set of N weight values to form the subset of the weight values where M is an integer less than N. In this way, the contributions of code vectors that contribute a relatively large amount to the decomposed v-vector may be preserved, while the contributions of code vectors that contribute a relatively small amount to the decomposed v-vector may be discarded to increase coding efficiency. Other criteria may also be used to select the subset of the weight values for coding and/or quantization. 
     In some examples, the M greatest weight values may be the M weight values from the set of N weight values that have the greatest value. In further examples, the M greatest weight values may be the M weight values from the set of N weight values that have the greatest absolute value. 
     In examples where the v-vector coding unit  52  codes and/or quantizes a subset of the weight values, the coded weights  57  may include data indicative of which of the weight values were selected for quantizing and/or coding in addition to quantized data indicative of the weight values. In some examples, the data indicative of which of the weight values were selected for quantizing and/or coding may include one or more indices from a set of indices that correspond to the code vectors in the weighted sum of code vectors. In such examples, for each of the weights that were selected for coding and/or quantization, an index value of the code vector that corresponds to the weight value in the weighted sum of code vectors may be included in the bitstream. 
     In some examples, each of the reduced foreground V[k] vectors  55  may be represented based on the following expression: 
                     V   FG     ≈       ∑     j   =   1     25     ⁢           ⁢       ω   j     ⁢     Ω   j                 (   1   )               
where Ω j  represents the jth code vector in a set of code vectors ({Ω j }), ω j  represents the jth weight in a set of weights ({ω j }), and V FG  corresponds to the v-vector that is being represented, decomposed, and/or coded by the v-vector coding unit  52 . The right hand side of expression (1) may represent a weighted sum of code vectors that includes a set of weights ({ω j }) and a set of code vectors ({Ω j }).
 
     In some examples, the v-vector coding unit  52  may determine the weight values based on the following equation:
 
ω k=V   FG Ω k   T   (2)
 
where Ω k   T  represents a transpose of the kth code vector in a set of code vectors ({Ω k }), V FG  corresponds to the v-vector that is being represented, decomposed, and/or coded by the v-vector coding unit  52 , and ω k  represents the jth weight in a set of weights ({ω k }).
 
     In examples where the set of code vectors ({Ω j }) is orthonormal, the following expression may apply: 
     
       
         
           
             
               
                 
                   
                     
                       Ω 
                       j 
                     
                     ⁢ 
                     
                       Ω 
                       k 
                       T 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               for 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               j 
                             
                             = 
                             k 
                           
                         
                       
                       
                         
                           
                             
                               0 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               for 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               j 
                             
                             ≠ 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In such examples, the right-hand side of equation (2) may simplify as follows: 
                         V   FG     ⁢     Ω   k   T       ≈       (       ∑     j   =   1     25     ⁢           ⁢       ω   j     ⁢     Ω   j         )     ⁢     Ω   k   T         =     ω   k             (   4   )               
where ω k  corresponds to the kth weight in the weighted sum of code vectors.
 
     For the example weighted sum of code vectors used in equation (1), the v-vector coding unit  52  may calculate the weight values for each of the weights in the weighted sum of code vectors using equation (2) and the resulting weights may be represented as:
 
{ω k } k=1, . . . ,25   (5)
 
Consider an example where the v-vector coding unit  52  selects the five maxima weight values (i.e., weights with greatest values or absolute values). The subset of the weight values to be quantized may be represented as:
 
{ ω   k } k=1, . . . ,5   (6)
 
The subset of the weight values together with their corresponding code vectors may be used to form a weighted sum of code vectors that estimates the v-vector, as shown in the following expression:
 
                       V   _     FG     ≈       ∑     j   =   1     5     ⁢           ⁢         ω   _     j     ⁢     Ω   j                 (   7   )               
where Ω j  represents the jth code vector in a subset of the code vectors ({Ω j }),  ω   j  represents the jth weight in a subset of weights ({ ω   j }), and  V   FG  corresponds to an estimated v-vector that corresponds to the v-vector being decomposed and/or coded by the v-vector coding unit  52 . The right hand side of expression (1) may represent a weighted sum of code vectors that includes a set of weights ({ ω   j }) and a set of code vectors ({Ω j }).
 
     The v-vector coding unit  52  may quantize the subset of the weight values to generate quantized weight values that may be represented as:
 
{{circumflex over (ω)} k } k=1, . . . ,5   (8)
 
     The quantized weight values together with their corresponding code vectors may be used to form a weighted sum of code vectors that represents a quantized version of the estimated v-vector, as shown in the following expression: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       ^ 
                     
                     FG 
                   
                   ≈ 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       5 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           ω 
                           ^ 
                         
                         j 
                       
                       ⁢ 
                       
                         Ω 
                         j 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     where Ω j  represents the jth code vector in a subset of the code vectors ({Ω j }), {circumflex over (ω)} j  represents the jth weight in a subset of weights ({{circumflex over (ω)} j }), and {circumflex over (V)} FG  corresponds to an estimated v-vector that corresponds to the v-vector being decomposed and/or coded by the v-vector coding unit  52 . The right hand side of expression (1) may represent a weighted sum of a subset of the code vectors that includes a set of weights ({{circumflex over (ω)} j }) and a set of code vectors ({Ω j }). 
     An alternative restatement of the foregoing (which is largly equivalent to that described above) may be as follows. The V-vectors may be coded based on a predefined set of code vectors. To code the V-vectors, each V-vector is decomposed into a weighted sum of code vectors. The weighted sum of code vectors consists of k pairs of predefined code vectors and associated weights: 
             V   ≈       ∑     j   =   0     k     ⁢           ⁢       ω   j     ⁢     Ω   j               
where Ω j  represents the jth code vector in a set of predefined code vectors ({Ω j }), ω j  represents the jth real-valued weight in a set of predefined weights ({ω j }), k corresponds to the index of addends, which can be up to 7, and V corresponds to the V-vector that is being coded. The choice of k depends on the encoder. If the encoder chooses a weighted sum of two or more code vectors, the total number of predefined code vectors the encoder can chose of is (N+1) 2 , where predefined code vectors are derived as HOA expansion coefficients from, in some examples, the tables F.2 to F.11. Reference to tables denoted by F followed by a period and a number refer to tables specified in Annex F of the MPEG-H 3D Audio Standard, entitled “Information Technology—High efficiency coding and media delivery in heterogeneous environments—Part 3: 3D Audio,” ISO/IEC JTC1/SC 29, dated 2015 Feb. 20 (Feb. 20, 2015), ISO/IEC 23008-3:2015(E), ISO/IEC JTC 1/SC 29/WG 11 (filename: ISO_IEC_23008-3(E)-Word_document_v33.doc).
 
     When N is 4, the table in Annex F. 6  with 32 predefined directions is used. In all cases the absolute values of the weights ω are vector-quantized with respect to the predefined weighting values {circumflex over (ω)} found in the first k+1 columns of the table in table F. 12  shown below and signaled with the associated row number index. 
     The number signs of the weights ω are separately coded as 
     
       
         
           
             
               
                 
                   
                     s 
                     j 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               , 
                               
                                 
                                   ω 
                                   j 
                                 
                                 ≥ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               0 
                               , 
                               
                                 
                                   ω 
                                   j 
                                 
                                 &lt; 
                                 0 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In other words, after signaling the value k, a V-vector is encoded with k+1 indices that point to the k+1 predefined code vectors {Ω j }, one index that points to the k quantized weights {{circumflex over (ω)} k } in the predefined weighting codebook, and k+1 number sign values s j : 
                     V   ^     ≈       ∑     j   =   0     k     ⁢       (       2   ⁢     s   j       -   1     )     ⁢           ⁢       ω   ^     j     ⁢       Ω   j     .                 (   13   )               
If the encoder selects a weighted sum of one code vector, a codebook derived from table F.8 is used in combination with the absolute weighting values {circumflex over (ω)} in the table of table F.11, where both of these tables are shown below. Also, the number sign of the weighting value ω may be separately coded.
 
     In this respect, the techniques may enable the audio encoding device  20  to select one of a plurality of codebooks to use when performing vector quantizaion with respect to a spatial component of a soundfield, the spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients. 
     Moreover, the techniques may enable the audio encoding device  20  to select between a plurality of paired codebooks to be used when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients. 
     In some examples, the V-vector coding unit  52  may determine, based on a set of code vectors, one or more weight values that represent a vector that is included in a decomposed version of a plurality of higher order ambisonic (HOA) coefficients. Each of the weight values may correspond to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     In such examples, the V-vector coding unit  52  may, in some examples, quantize the data indicative of the weight values. In such examples, to quantize the data indicative of the weight values the V-vector coding unit  52  may, in some examples, select a subset of the weight values to quantize, and quantize data indicative of the selected subset of the weight values. In such examples, the V-vector coding unit  52  may, in some examples, not quantize data indicative of weight values that are not included in the selected subset of the weight values. 
     In some examples, the V-vector coding unit  52  may determine a set of N weight values. In such examples, the V-vector coding unit  52  may select the M greatest weight values from the set of N weight values to form the subset of the weight values where M is less than N. 
     To quantize the data indicative of the weight values, the V-vector coding unit  52  may perform at least one of scalar quantization, vector quantization, and matrix quantization with respect to the data indicative of the weight values. Other quantization techniques in addition to or lieu of the above-mentioned quantization techniques may also be performed. 
     To determine the weight values, the V-vector coding unit  52  may, for each of the weight values, determine the respective weight value based on a respective one of the code vectors  63 . For example, the V-vector coding unit  52  may multiply the vector by a respective one of the code vectors  63  to determine the respective weight value. In some cases, the V-vector coding unit  52  may involve multiply the vector by a transpose of the respective one of the code vectors  63  to determine the respective weight value. 
     In some examples, the decomposed version of the HOA coefficients may be a singular value decomposed version of the HOA coefficients. In further examples, the decomposed version of the HOA coefficients may be at least one of a principal component analyzed (PCA) version of the HOA coefficients, a Karhunen-Loeve transformed version of the HOA coefficients, a Hotelling transformed version of the HOA coefficients, a proper orthogonal decomposed (POD) version of the HOA coefficients, and an eigenvalue decomposed (EVD) version of the HOA coefficients. 
     In further examples, the set of code vectors  63  may include at least one of a set of directional vectors, a set of orthogonal directional vectors, a set of orthonormal directional vectors, a set of pseudo-orthonormal directional vectors, a set of pseudo-orthogonal directional vectors, a set of directional basis vectors, a set of orthogonal vectors, a set of orthonormal vectors, a set of pseudo-orthonormal vectors, a set of pseudo-orthogonal vectors, a set of spherical harmonic basis vectors, a set of normalized vectors, and a set of basis vectors. 
     In some examples, the V-vector coding unit  52  may use a decomposition codebook to determine the weights that are used to represent a V-vector (e.g., a reduced foreground V[k] vector). For example, the V-vector coding unit  52  may select a decomposition codebook from a set of candidate decomposition codebooks, and determine the weights that represent the V-vector based on the selected decomposition codebook. 
     In some examples, each of the candidate decomposition codebooks may correspond to a set of code vectors  63  that may be used to decompose a V-vector and/or to determine the weights that correspond to the V-vector. In other words, each different decomposition codebook corresponds to a different set of code vectors  63  that may be used to decompose a V-vector. Each entry in the decomposition codebook corresponds to one of the vectors in the set of code vectors. 
     The set of code vectors in a decomposition codebook may correspond to all code vectors included in a weighted sum of code vectors that is used to decompose a V-vector. For example, the set of code vectors may correspond to the set of code vectors  63  ({Ω j }) included in the weighted sum of code vectors shown on the right-hand side of expression (1). In this example, each one of the code vectors  63  (i.e., Ω j ) may correspond to an entry in the decomposition codebook. 
     Different decomposition codebooks may have a same number of code vectors  63  in some examples. In further examples, different decomposition codebooks may have a different number of code vectors  63 . 
     For example, at least two of the candidate decomposition codebooks may have a different number of entries (i.e., code vectors  63  in this example). As another example, all of the candidate decomposition codebooks may have a different number of entries  63 . As a further example, at least two of the candidate decomposition codebooks may have a same number of entries  63 . As an additional example, all of the candidate decomposition codebooks may have the same number of entries  63 . 
     The V-vector coding unit  52  may select a decomposition codebook from the set of candidate decomposition codebooks based on one or more various criteria. For example, the V-vector coding unit  52  may select a decomposition codebook based on the weights corresponding to each decomposition codebook. For instance, the V-vector coding unit  52  may perform an analysis of the weights corresponding to each decomposition codebook (from the corresponding weighted sum that represents the V-vector) to determine how many weights are required to represent the V-vector within some margin of accuracy (as defined for example by a threshold error). The V-vector coding unit  52  may select the decomposition codebook which requires the least number of weights. In additional examples, the V-vector coding unit  52  may select a decomposition codebook based on the characteristics of the underlying soundfield (e.g., artificially created, naturally recorded, highly diffuse, etc.). 
     To determine the weights (i.e., weight values) based on a selected codebook, the V-vector coding unit  52  may, for each of the weights, select a codebook entry (i.e., code vector) that corresponds to the respective weight (as identified for example by the “WeightIdx” syntax element), and determine the weight value for the respective weight based on the selected codebook entry. To determine the weight value based on the selected codebook entry, the V-vector coding unit  52  may, in some examples, multiply the V-vector by the code vector  63  that is specified by the selected codebook entry to generate the weight value. For example, the V-vector coding unit  52  may multiply the V-vector by the transpose of the code vector  63  that is specified by the selected codebook entry to generate a scalar weight value. As another example, equation (2) may be used to determine the weight values. 
     In some examples, each of the decomposition codebooks may correspond to a respective one of a plurality of quantization codebooks. In such examples, when the V-vector coding unit  52  selects a decomposition codebook, the V-vector coding unit  52  may also select a quantization codebook that corresponds to the decomposition codebook. 
     The V-vector coding unit  52  may provide to the bitstream generation unit  42  data indicative of which decomposition codebook was selected (e.g., the CodebkIdx syntax element) for coding one or more of the reduced foreground V[k] vectors  55  so that the bitstream generation unit  42  may include such data in the resulting bitstream. In some examples, the V-vector coding unit  52  may select a decomposition codebook to use for each frame of HOA coefficients to be coded. In such examples, the V-vector coding unit  52  may provide data indicative of which decomposition codebook was selected for coding each frame (e.g., the CodebkIdx syntax element) to the bitstream generation unit  42 . In some examples, the data indicative of which decomposition codebook was selected may be a codebook index and/or an identification value that corresponds to the selected codebook. 
     In some examples, the V-vector coding unit  52  may select a number indicative of how many weights are to be used to estimate a V-vector (e.g., a reduced foreground V[k] vector). The number indicative of how many weights are to be used to estimate a V-vector may also be indicative of the number of weights to be quantized and/or coded by the V-vector coding unit  52  and/or the audio encoding device  20 . The number indicative of how many weights are to be used to estimate a V-vector may also be referred to as the number of weights to be quantized and/or coded. This number indicative of how many weights may alternatively be represented as the number of code vectors  63  to which these weights correspond. This number may therefore also be denoted as the number of code vectors  63  used to dequantize a vector-quantized V-vector, and may be denoted by a NumVecIndices syntax element. 
     In some examples, the V-vector coding unit  52  may select the number of weights to be quantized and/or coded for a particular V-vector based on the weight values that were determined for that particular V-vector. In additional examples, the V-vector coding unit  52  may select the number of weights to be quantized and/or coded for a particular V-vector based on an error associated with estimating the V-vector using one or more particular numbers of weights. 
     For example, the V-vector coding unit  52  may determine a maximum error threshold for an error associated with estimating a V-vector, and may determine how many weights are needed to make the error between an estimated V-vector that is estimated with that number of weights and the V-vector less than or equal to the maximum error threshold. The estimated vector may correspond to weighted sum of code vectors where less than all of the code vectors from the codebook are used in the weighted sum. 
     In some examples, the V-vector coding unit  52  may determine how many weights are needed to make the error below a threshold based on the following equation: 
                   error   =              V   FG     -       ∑     i   =   1     X     ⁢           ⁢     (       ω   i     *     Ω   i       )              α             (   14   )               
where Ω i  represents the ith code vector, ω i  represents the ith weight, V FG  corresponds to the V-vector that is being decomposed, quantized and/or coded by the V-vector coding unit  52 , and |x| α  is a norm of the value x, where α is a value indicative of which type of norm is used. For example, α=1 represents an L1 norm and α=2 represents an L2 norm.  FIG. 20  is a diagram illustrating an example graph  700  showing a threshold error used to select X* number of code vectors in accordance with various aspects of the techniques described in this disclosure. The graph  700  includes a line  702  illustrating how the error decreases as the number of code vectors increases.
 
     In the above-mentioned example, the indices, i, may, in some examples, index the weights in an order sequence such that larger magnitude (e.g., larger absolute value) weights occur prior to lower magnitude (e.g., lower absolute value) weights in the ordered sequence. In other words, ω 1  may represent the largest weight value, ω 2  may represent the next largest weight value, and so on. Similarly, ω x  may represent the lowest weight value. 
     The V-vector coding unit  52  may provide to the bitstream generation unit  42  data indicative of how many weights were selected for coding one or more of the reduced foreground V[k] vectors  55  so that the bitstream generation unit  42  may include such data in the resulting bitstream. In some examples, the V-vector coding unit  52  may select a number of weights to use for coding a V-vector for each frame of HOA coefficients to be coded. In such examples, the V-vector coding unit  52  may provide to the bitstream generation unit  42  data indicative of how many weights were selected for coding selected each frame to the bitstream generation unit  42 . In some examples, the data indicative of how many weights were selected may be a number indicative of how many weights were selected for coding and/or quantization. 
     In some examples, the V-vector coding unit  52  may use a quantization codebook to quantize the set of weights that are used to represent and/or estimate a V-vector (e.g., a reduced foreground V[k] vector). For example, the V-vector coding unit  52  may select a quantization codebook from a set of candidate quantization codebooks, and quantize the V-vector based on the selected quantization codebook. 
     In some examples, each of the candidate quantization codebooks may correspond to a set of candidate quantization vectors that may be used to quantize a set of weights. The set of weights may form a vector of weights that are to be quantized using these quantization codebooks. In other words, each different quantization codebook corresponds to a different set of quantization vectors from a which a single quantization vector may be selected to quantize the V-vector. 
     Each entry in the codebook may correspond to a candidate quantization vector. The number of components in each of the candidate quantization vectors may, in some examples, be equal to number of weights to be quantized. 
     In some examples, different quantization codebooks may have same number of candidate quantization vectors. In further examples, different quantization codebooks may have a different number of candidate quantization vectors. 
     For example, at least two of the candidate quantization codebooks may have a different number of candidate quantization vectors. As another example, all of the candidate quantization codebooks may have a different number of candidate quantization vectors. As a further example, at least two of the candidate quantization codebooks may have a same number of candidate quantization vectors. As an additional example, all of the candidate quantization codebooks may have the same number of candidate quantization vectors. 
     The V-vector coding unit  52  may select a quantization codebook from the set of candidate quantization codebooks based on one or more various criteria. For example, the V-vector coding unit  52  may select a quantization codebook for a V-vector based on a decomposition codebook that was used to determine the weights for the V-vector. As another example, the V-vector coding unit  52  may select the quantization codebook for a V-vector based on a probability distribution of the weight values to be quantized. In other examples, the V-vector coding unit  52  may select the quantization codebook for a V-vector based on a combination of the selection of the decomposition codebook that was used to determine the weights for the V-vector as well as the number of weights that were deemed necessary to represent the V-vector within some error threshold (e.g., as per Equation 14). 
     To quantize the weights based on the selected quantization codebook, the V-vector coding unit  52  may, in some examples, determine a quantization vector to use for quantizing the V-vector based on the selected quantization codebook. For example, the V-vector coding unit  52  may perform vector quantization (VQ) to determine the quantization vector to use for quantizing the V-vector. 
     In additional examples, to quantize the weights based on the selected quantization codebook, the V-vector coding unit  52  may, for each V-vector, select a quantization vector from the selected quantization codebook based on a quantization error associated with using one or more of the quantization vectors to represent the V-vector. For example, the V-vector coding unit  52  may select a candidate quantization vector from the selected quantization codebook that minimizes a quantization error (e.g., minimizes a least squares error). 
     In some examples, each of the quantization codebooks may correspond to a respective one of a plurality of decomposition codebooks. In such examples, the V-vector coding unit  52  may also select a quantization codebook for quantizing the set of weights associated with a V-vector based on the decomposition codebook that was used to determine the weights for the V-vector. For example, the V-vector coding unit  52  may select a quantization codebook that corresponds to the decomposition codebook that was used to determine the weights for the V-vector. 
     The V-vector coding unit  52  may provide to the bitstream generation unit  42  data indicative of which quantization codebook was selected for quantizing the weights corresponding to one or more of the reduced foreground V[k] vectors  55  so that the bitstream generation unit  42  may include such data in the resulting bitstream. In some examples, the V-vector coding unit  52  may select a quantization codebook to use for each frame of HOA coefficients to be coded. In such examples, the V-vector coding unit  52  may provide data indicative of which quantization codebook was selected for quantizing weights in each frame to the bitstream generation unit  42 . In some examples, the data indicative of which quantization codebook was selected may be a codebook index and/or identification value that corresponds to the selected codebook. 
     The psychoacoustic audio coder unit  40  included within the audio encoding device  20  may represent multiple instances of a psychoacoustic audio coder, each of which is used to encode a different audio object or HOA channel of each of the energy compensated ambient HOA coefficients  47 ′ and the interpolated nFG signals  49 ′ to generate encoded ambient HOA coefficients  59  and encoded nFG signals  61 . The psychoacoustic audio coder unit  40  may output the encoded ambient HOA coefficients  59  and the encoded nFG signals  61  to the bitstream generation unit  42 . 
     The bitstream generation unit  42  included within the audio encoding device  20  represents a unit that formats data to conform to a known format (which may refer to a format known by a decoding device), thereby generating the vector-based bitstream  21 . The bitstream  21  may, in other words, represent encoded audio data, having been encoded in the manner described above. The bitstream generation unit  42  may represent a multiplexer in some examples, which may receive the coded foreground V[k] vectors  57 , the encoded ambient HOA coefficients  59 , the encoded nFG signals  61  and the background channel information  43 . The bitstream generation unit  42  may then generate a bitstream  21  based on the coded foreground V[k] vectors  57 , the encoded ambient HOA coefficients  59 , the encoded nFG signals  61  and the background channel information  43 . In this way, the bitstream generation unit  42  may thereby specify the vectors  57  in the bitstream  21  to obtain the bitstream  21 . The bitstream  21  may include a primary or main bitstream and one or more side channel bitstreams. 
     Although not shown in the example of  FIG. 3A , the audio encoding device  20  may also include a bitstream output unit that switches the bitstream output from the audio encoding device  20  (e.g., between the directional-based bitstream  21  and the vector-based bitstream  21 ) based on whether a current frame is to be encoded using the directional-based synthesis or the vector-based synthesis. The bitstream output unit may perform the switch based on the syntax element output by the content analysis unit  26  indicating whether a directional-based synthesis was performed (as a result of detecting that the HOA coefficients  11  were generated from a synthetic audio object) or a vector-based synthesis was performed (as a result of detecting that the HOA coefficients were recorded). The bitstream output unit may specify the correct header syntax to indicate the switch or current encoding used for the current frame along with the respective one of the bitstreams  21 . 
     Moreover, as noted above, the soundfield analysis unit  44  may identify BG TOT  ambient HOA coefficients  47 , which may change on a frame-by-frame basis (although at times BG TOT  may remain constant or the same across two or more adjacent (in time) frames). The change in BG TOT  may result in changes to the coefficients expressed in the reduced foreground V[k] vectors  55 . The change in BG TOT  may result in background HOA coefficients (which may also be referred to as “ambient HOA coefficients”) that change on a frame-by-frame basis (although, again, at times BG TOT  may remain constant or the same across two or more adjacent (in time) frames). The changes often result in a change of energy for the aspects of the sound field represented by the addition or removal of the additional ambient HOA coefficients and the corresponding removal of coefficients from or addition of coefficients to the reduced foreground V[k] vectors  55 . 
     As a result, the soundfield analysis unit  44  may further determine when the ambient HOA coefficients change from frame to frame and generate a flag or other syntax element indicative of the change to the ambient HOA coefficient in terms of being used to represent the ambient components of the sound field (where the change may also be referred to as a “transition” of the ambient HOA coefficient or as a “transition” of the ambient HOA coefficient). In particular, the coefficient reduction unit  46  may generate the flag (which may be denoted as an AmbCoeffTransition flag or an AmbCoeffIdxTransition flag), providing the flag to the bitstream generation unit  42  so that the flag may be included in the bitstream  21  (possibly as part of side channel information). 
     The coefficient reduction unit  46  may, in addition to specifying the ambient coefficient transition flag, also modify how the reduced foreground V[k] vectors  55  are generated. In one example, upon determining that one of the ambient HOA ambient coefficients is in transition during the current frame, the coefficient reduction unit  46  may specify, a vector coefficient (which may also be referred to as a “vector element” or “element”) for each of the V-vectors of the reduced foreground V[k] vectors  55  that corresponds to the ambient HOA coefficient in transition. Again, the ambient HOA coefficient in transition may add or remove from the BG TOT  total number of background coefficients. Therefore, the resulting change in the total number of background coefficients affects whether the ambient HOA coefficient is included or not included in the bitstream, and whether the corresponding element of the V-vectors are included for the V-vectors specified in the bitstream in the second and third configuration modes described above. More information regarding how the coefficient reduction unit  46  may specify the reduced foreground V[k] vectors  55  to overcome the changes in energy is provided in U.S. application Ser. No. 14/594,533, entitled “TRANSITIONING OF AMBIENT HIGHER_ORDER AMBISONIC COEFFICIENTS,” filed Jan. 12, 2015. 
       FIG. 3B  is a block diagram illustrating, in more detail, another example of the audio encoding device  420  shown in the example of  FIG. 3  that may perform various aspects of the techniques described in this disclosure. The audio encoding device  420  shown in  FIG. 3B  is similar to the audio encoding device  20  except that the v-vector coding unit  52  in the audio encoding device  420  also provides weight value information  71  to the reorder unit  34 . 
     In some examples, the weight value information  71  may include one or more of the weight values calculated by the v-vector coding unit  52 . In further examples, the weight value information  71  may include information indicative of which weights were selected for quantization and/or coding by the v-vector coding unit  52 . In additional examples, the weight value information  71  may include information indicative of which weights were not selected for quantization and/or coding by the v-vector coding unit  52 . The weight value information  71  may include any combination of any of the above-mentioned information items as well as other items in addition to or in lieu of the above-mentioned information items. 
     In some examples, the reorder unit  34  may reorder the vectors based on the weight value information  71  (e.g., based on the weight values). In examples where the v-vector coding unit  52  selects a subset of the weight values to quantize and/or code, the reorder unit  34  may, in some examples, reorder the vectors based on which of the weight values were selected for quantizing or coding (which may be indicated by the weight value information  71 ). 
       FIG. 4A  is a block diagram illustrating the audio decoding device  24  of  FIG. 2  in more detail. As shown in the example of  FIG. 4A  the audio decoding device  24  may include an extraction unit  72 , a directionality-based reconstruction unit  90  and a vector-based reconstruction unit  92 . Although described below, more information regarding the audio decoding device  24  and the various aspects of decompressing or otherwise decoding HOA coefficients is available in International Patent Application Publication No. WO 2014/194099, entitled “INTERPOLATION FOR DECOMPOSED REPRESENTATIONS OF A SOUND FIELD,” filed 29 May, 2014. 
     The extraction unit  72  may represent a unit configured to receive the bitstream  21  and extract the various encoded versions (e.g., a directional-based encoded version or a vector-based encoded version) of the HOA coefficients  11 . The extraction unit  72  may determine from the above noted syntax element indicative of whether the HOA coefficients  11  were encoded via the various direction-based or vector-based versions. When a directional-based encoding was performed, the extraction unit  72  may extract the directional-based version of the HOA coefficients  11  and the syntax elements associated with the encoded version (which is denoted as directional-based information  91  in the example of  FIG. 4A ), passing the directional based information  91  to the directional-based reconstruction unit  90 . The directional-based reconstruction unit  90  may represent a unit configured to reconstruct the HOA coefficients in the form of HOA coefficients  11 ′ based on the directional-based information  91 . 
     When the syntax element indicates that the HOA coefficients  11  were encoded using a vector-based synthesis, the extraction unit  72  may extract the coded foreground V[k] vectors (which may include coded weights  57  and/or indices  73 ), the encoded ambient HOA coefficients  59  and the encoded nFG signals  59 . The extraction unit  72  may pass the coded weights  57  to the quantization unit  74  and the encoded ambient HOA coefficients  59  along with the encoded nFG signals  61  to the psychoacoustic decoding unit  80 . 
     To extract the coded weights  57 , the encoded ambient HOA coefficients  59  and the encoded nFG signals  59 , the extraction unit  72  may obtain an HOADecoderConfig container that includes, which includes the syntax element denoted CodedVVecLength. The extraction unit  72  may parse the CodedVVecLength from the HOADecoderConfig container. The extraction unit  72  may be configured to operate in any one of the above described configuration modes based on the CodedVVecLength syntax element. 
     In some examples, the extraction unit  72  may operate in accordance with the switch statement presented in the following pseudo-code with the syntax presented in the following syntax table (where strikethorughs indicate removal of the struckthrough subject matter and underlines indicate addition of the underlined subject matter relative to previous versions of the syntax table) for VVectorData as understood in view of the accompanying semantics: 
     
       
         
           
               
             
               
                   
               
             
            
               
                 switch CodedVVecLength{ 
               
            
           
           
               
               
            
               
                   
                 case 0: 
               
            
           
           
               
               
            
               
                   
                 VVecLength = NumOfHoaCoeffs; 
               
               
                   
                 for (m=0; m&lt;VVecLength; ++m){ 
               
            
           
           
               
               
            
               
                   
                 VVecCoeffId[m] = m; 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 break; 
               
            
           
           
               
               
            
               
                   
                 case 1: 
               
            
           
           
               
               
            
               
                   
                 VVecLength = NumOfHoaCoeffs − 
               
               
                   
                 MinNumOfCoeffsForAmbHOA − 
               
            
           
           
               
            
               
                 NumOfContAddHoaChans; 
               
            
           
           
               
               
            
               
                   
                 CoeffIdx = MinNumOfCoeffsForAmbHOA+1; 
               
               
                   
                 for (m=0; m&lt;VVecLength; ++m){ 
               
            
           
           
               
               
            
               
                   
                 bIsInArray = isMemberOf(CoeffIdx, ContAddHoaCoeff, 
               
            
           
           
               
            
               
                 NumOfContAddHoaChans); 
               
            
           
           
               
               
            
               
                   
                 while(bIsInArray){ 
               
            
           
           
               
               
            
               
                   
                 CoeffIdx++; 
               
               
                   
                 bIsInArray = isMemberOf(CoeffIdx, 
               
               
                   
                 ContAddHoaCoeff, 
               
            
           
           
               
            
               
                 NumOfContAddHoaChans); 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 VVecCoeffId[m] = CoeffIdx−1; 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 break; 
               
            
           
           
               
               
            
               
                   
                 case 2: 
               
            
           
           
               
               
            
               
                   
                 VVecLength = NumOfHoaCoeffs − 
               
               
                   
                 MinNumOfCoeffsForAmbHOA; 
               
               
                   
                 for (m=0; m&lt; VVecLength; ++m){ 
               
            
           
           
               
               
            
               
                   
                 VVecCoeffId[m] = m + MinNumOfCoeffsForAmbHOA; 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                   
               
            
           
         
       
     
                                     Syntax   No. of bits   Mnemonic                                    VVectorData(i)       {                         if (NbitsQ(k)[i] == 4){                         If CodebkIdx(k)[i] == 0 {                         nbitsW = 3;           nbitsIdx = 10;                         } else {                         nbitsW = 8;           nbitsIdx = ceil(log2(NumOfHoaCoeffs));                         }           NumVecIndices = CodebkIdx(k)[i] +1;                                   WeightIdx ;     nbitsW       uimsbf                           for (j=0; j&lt; NumVecIndiecies; ++j) {                                 VecIdx[j] = VecIdx + 1;   nbitsIdx   uimsbf                                     WeightVal[j] = ((SgnVal*2)−1) *   1   uimsbf                 WeightValCdbk[CodebkIdx(k)[i]][WeightIdx][j];                         }                         }           elseif (NbitsQ(k)[i] == 5){                         for (m=0; m&lt; VVecLength; ++m){                                 aVal[i][m] = (VecVal / 128.0)− 1.0;   8   uimsbf                         }           elseif(NbitsQ(k)[i] &gt;= 6){                         for (m=0; m&lt; VVecLength; ++m){                                 huffIdx = huffSelect(VVecCoeffId[m], PFlag[i], CbFlag[i]);                   cid = huffDecode(NbitsQ[i], huffIdx, huffVal);   dynamic   huffDecode           aVal[i][m] = 0.0;           if ( cid &gt; 0 ) {                                 aVal[i][m] = sgn = (sgnVal * 2) − 1;   1   bslbf           if (cid &gt; 1) {                                 aVal[i][m] = sgn * (2.0{circumflex over ( )}(cid −1 ) + intAddVal);   cid − 1   uimsbf                         }                         }                         }                         }                 }               NOTE:       See section 11.4.1.9.1 for computation of VVecLength            
VVectorData(VecSigChannelIds(i))
 
This structure contains the coded V-Vector data used for the vector-based signal synthesis.
     VVec(k)[i] This is the V-Vector for the k-th HOAframe( ) for the i-th channel.   VVecLength This variable indicates the number of vector elements to read out.   VVecCoeffId This vector contains the indices of the transmitted V-Vector coefficients.   VecVal An integer value between 0 and 255.   aVal A temporary variable used during decoding of the VVectorData.   huffVal A Huffman code word, to be Huffman-decoded.   sgnVal This is the coded sign value used during decoding.   intAddVal This is additional integer value used during decoding.   NumVecIndices The number of vectors used to dequantise a vector-quantised V-vector.   WeightIdx The index in WeightValCdbk used to dequantise a vector-quantised V-vector.   nbitsW Field size for reading WeightIdx to decode a vector-quantised V-vector.   WeightValCdbk Codebook which contains a vector of positive real-valued weighting coefficients. If NumVecIndices is set to 1, the WeightValCdbk with 16 entries is used, otherwise the WeightValCdbk with 256 entries is used.   VvecIdx An index for VecDict, used to dequantise a vector-quantised V-vector.   nbitsIdx Field size for reading individual VvecIdxs to decode a vector-quantised V-vector.   WeightVal A real-valued weighting coefficient to decode a vector-quantised V-vector.   

     In the foregoing syntax table, the first switch statement with the four cases (case 0-3) provides for a way by which to determine the V T   DIST  vector length in terms of the number (VVecLength) and indices of coefficients (VVecCoeffId). The first case, case 0, indicates that all of the coefficients for the V T   DIST  vectors (NumOfHoaCoeffs) are specified. The second case, case 1, indicates that only those coefficients of the V T   DIST  vector corresponding to the number greater than a MinNumOfCoeffsForAmbHOA are specified, which may denote what is referred to as (N DIST +1) 2 −(N BG +1) 2  above. Further those NumOfContAddAmbHoaChan coefficients identified in ContAddAmbHoaChan are substracted. The list ContAddAmbHoaChan specifies additional channels (where “channels” refer to a particular coefficient corresponding to a certain order, sub-order combination) corresponding to an order that exceeds the order MinAmbHoaOrder. The third case, case 2, indicates that those coefficients of the V T   DIST  vector corresponding to the number greater than a MinNumOfCoeffsForAmbHOA are specified, which may denote what is referred to as (N DIST +1) 2 −(N BG +1) 2  above. Both the VVecLength as well as the VVecCoeffId list is valid for all VVectors within on HOAFrame. 
     After this switch statement, the decision of whether to perform vector quantization, or uniform scalar dequantization may be controlled by NbitsQ (or, as denoted above, nbits). Previously, only scalar quantization was proposed to quantize the Vvectors (e.g., when NbitsQ equals 4). While scalar quantization is still provided when NBitsQ equals 5, a vector quantization may be performed in accordance with the techniques described in this disclosure when, as one example, NbitsQ equals 4. 
     In other words, an HOA signal that has strong directionality is represented by a foreground audio signal and the corresponding spatial information, i.e., a V-vector in the examples of this disclosure. In the V-vector coding techniques described in this disclosure, each V-vector is represented by a weighted summation of pre-defined directional vectors as given by the following equation: 
             V   ≈       ∑     i   =   1     I     ⁢           ⁢       ω   i     ⁢     Ω   i               
where ω i  and Ω i  are an i-th weighting value and the corresponding directional vector, respectively.
 
     An example of the V-vector coding is illustrated in  FIG. 16 . As shown in  FIG. 16 ( a ) , an original V-vector may be represented by a mixture of the several directional vectors. The original V-vector may then be estimated by a weighted sum as shown in  FIG. 16 ( b )  where a weighting vector is shown in  FIG. 16 ( e ) .  FIGS. 16 ( c ) and ( f )  illustrate the cases that only I S (I S ≤I) highest weighting values are selected. Vector quantization (VQ) may then be performed for the selected weighting values and the result is illustrated in  FIGS. 16( d ) and ( g ) . 
     The computational complexity of this v-vector coding scheme may be determined as follows:
 
0.06 MOPS (HOA order=6)/0.05 MOPS (HOA order=5); and
 
0.03 MOPS (HOA order=4)/0.02 MOPS (HOA order=3).
 
The ROM complexity may be determined as 16.29 kbytes (for HOA orders 3, 4, 5 and 6), while the algorithmic delay is determined to be 0 samples.
 
     The required modification to the current version of the 3D audio coding standard referenced above may be denoted within the VVectorData syntax table shown above by the use of underlines. That is, in the CD of the above referenced MPEG-H 3D Audio proposed standard, V-vector coding was performed with scalar quantization (SQ) or SQ followed by the Huffman coding. Required bits of the proposed vector quantization (VQ) method may be lower than the conventional SQ coding methods. For the 12 reference test items, the required bits in average are as follows:
         SQ+Huffman: 16.25 kbps   Proposed VQ: 5.25 kbps
 
The saved bits may be repurposed for use for perceptual audio coding.
       

     The v-vector reconstruction unit  74  may, in other words, operate in accordance with the following pseudocode to reconstruct the V-vectors: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 for (m=0; m&lt; VVecLength; ++m){ 
               
            
           
           
               
               
            
               
                   
                 if (NbitsQ(k)[i] == 4){ 
               
            
           
           
               
               
            
               
                   
                 idx = VVecCoeffID[m]; 
               
               
                   
                 v (i)   VVecCoeffId[m] (k) = 0.0; 
               
               
                   
                 if (NumVvecIndicies == 1){ 
               
            
           
           
               
               
            
               
                   
                 cdbLen = 900; 
               
            
           
           
               
               
            
               
                   
                 } else { 
               
            
           
           
               
               
            
               
                   
                 cdbLen = 0; 
               
               
                   
                 if (N==4) 
               
            
           
           
               
               
            
               
                   
                 cdbLen = 32; 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 for (j=0; j&lt; NumVvecIndecies; ++j){ 
               
            
           
           
               
               
            
               
                   
                 v (i)   VVecCoeffId[m] (k) +=    WeightVal[j] * 
               
            
           
           
               
               
            
               
                   
                 VecDict[cdbLen].[VecIdx[j]][idx]; 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 elseif (NbitsQ(k)[i] == 5){ 
               
               
                   
                 v (i)   VVecCoeffId[m] (k) = (N+1)*aVal[i][m]; 
               
               
                   
                 } 
               
               
                   
                 elseif (NbitsQ(k)[i] &gt;= 6){ 
               
            
           
           
               
               
            
               
                   
                 v (i)   VVecCoeffId[m] (k) = (N+1)*(2{circumflex over ( )}(16 − 
               
               
                   
                 NbitsQ(k)[i])*aVal[i][m])/2{circumflex over ( )}15; 
               
               
                   
                 if (PFlag(k)[i] == 1) { 
               
            
           
           
               
               
            
               
                   
                 v (i)   VVecCoeffId[m] (k) += v (i)   VVecCoeffId[m] (k − 1); 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                   
               
            
           
         
       
     
     According to the foregoing psuedocode (with strikethroughs indicating removal of the struckthrough subject matter), the v-vector reconstruction unit  74  may determine VVecLength per the pseudocode for the switch statement based on the value of CodedVVecLength. Based on this VVecLength, the v-vector reconstruction unit  74  may iterate through the subsequent if/elseif statements, which consider the NbitsQ value. When the i th  NbitsQ value for the k th  frame equals 4, the v-vector reconstruction unit  74  determines that vector dequantization is to be performed. 
     The cdbLen syntax element indicates the number of entries in the dictionary or codebook of code vectors (where this dictionary is denoted as “VecDict” in the foregoing psuedocode and represents a codebook with cdbLen codebook entries containing vectors of HOA expansion coefficients, used to decode a vector quantized V-vector), which is derived based on the NumVveclndicies and the HOA order. When the value of NumVveclndicies is equal to one, the Vector codebook HOA expansion coefficients derrived from the above table F.8 in conjungtion with a codebook of 8×1 weighting values shown in the above table F.11. When the value of NumVveclndicies is larger than one, the Vector codebook with 0 vector is used in combination with 256×8 weighting values shown in the above table F.12. 
     Although described above as using a codebook of size 256×8, different codebooks may be used having different numbers of values. That is, instead of val 0  -val 7 , a codebook with 256 rows may be used with each row being indexed by a different index value (index  0 -index  255 ) and having a different number of values, such as val  0  -val  9  (for a total of ten values) or val  0 -val  15  (for a total of 16 values).  FIGS. 19A and 19B  are diagrams illustrating codebooks with 256 rows with each row having 10 values and 16 values respectively that may be used in accordance with various aspects of the techniques described in this disclosure. 
     The v-vector reconstruction unit  74  may derive the weight value for each corresponding code vector used to reconstruct the V-vector based on a weight value codebook (denoted as “WeightValCdbk,” which may represent a multideminsional table indexed based on one or more of a codebook index (denoted “CodebkIdx” in the foregoing VVectorData(i) syntax table) and a weight index (denoted “WeightIdx” in the foregoing VVectorData(i) syntax table)). This CodebkIdx syntax element may be defined in a portion of the side channel information, as shown in the following ChannelSideInfoData(i) syntax table. 
     
       
         
           
               
             
               
                 TABLE 
               
             
            
               
                   
               
               
                 Syntax of ChannelSideInfoData(i) 
               
            
           
           
               
               
               
            
               
                 Syntax 
                 No. of bits 
                 Mnemonic 
               
               
                   
               
            
           
           
               
            
               
                 ChannelSideInfoData(i) 
               
               
                 { 
               
            
           
           
               
               
               
               
            
               
                   
                 ChannelType[i] 
                 2 
                 uimsbf 
               
               
                   
                 switch ChannelType[i] 
               
               
                   
                 { 
               
            
           
           
               
               
            
               
                   
                 case 0: 
               
            
           
           
               
               
               
               
            
               
                   
                 ActiveDirsIds[i]; 
                 10  
                 uimsbf 
               
               
                   
                 break; 
               
            
           
           
               
               
            
               
                   
                 case 1: 
               
            
           
           
               
               
            
               
                   
                 if(hoaIndependencyFlag){ 
               
            
           
           
               
               
               
               
            
               
                   
                 NbitsQ(k)[i] 
                 4 
                 uimsbf 
               
               
                   
                 
                   if (NbitsQ(k)[i] == 4) { 
                 
               
            
           
           
               
               
               
               
            
               
                   
                 
                   CodebkIdx(k)[i]; 
                 
                 
                   3 
                 
                 
                   uimsbf 
                 
               
            
           
           
               
               
            
               
                   
                 
                   } 
                 
               
               
                   
                   else if (NbitsQ(k)[i] &gt;= 6) { 
               
            
           
           
               
               
               
               
            
               
                   
                 PFlag(k)[i] = 0; 
                   
                   
               
               
                   
                 CbFlag(k)[i]; 
                 1 
                 bslbf 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 else{ 
               
            
           
           
               
               
               
               
            
               
                   
                 bA; 
                 1 
                 bslbf 
               
               
                   
                 bB; 
                 1 
                 bslbf 
               
               
                   
                 if ((bA + bB) == 0) { 
               
            
           
           
               
               
            
               
                   
                 NbitsQ(k)[i] = NbitsQ(k−1)[i]; 
               
               
                   
                 PFlag(k)[i] = PFlag(k−1)[i]; 
               
               
                   
                 CbFlag(k)[i] = CbFlag(k−1)[i]; 
               
               
                   
                 
                   CodebkIdx(k)[i] = CodebkIdx(k−1)[i]; 
                 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 else{ 
               
            
           
           
               
               
               
               
            
               
                   
                 NbitsQ(k)[i] = (8*bA)+(4*bB)+uintC; 
                 2 
                 uimsbf 
               
               
                   
                 
                   if (NbitsQ(k)[i] == 4) { 
                 
               
            
           
           
               
               
               
               
            
               
                   
                 
                   CodebkIdx(k)[i]; 
                 
                 
                   3 
                 
                 
                   uimsbf 
                 
               
            
           
           
               
               
               
               
            
               
                   
                 
                   } 
                 
                   
                   
               
               
                   
                   else if (NbitsQ(k)[i] &gt;= 6) { 
                   
                   
               
               
                   
                 PFlag(k)[i]; 
                 1 
                 bslbf 
               
               
                   
                 CbFlag(k)[i]; 
                 1 
                 bslbf 
               
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                 break; 
               
            
           
           
               
               
            
               
                   
                 case 2: 
               
            
           
           
               
               
            
               
                   
                 AddAmbHoaInfoChannel(i); 
               
               
                   
                 break; 
               
            
           
           
               
               
            
               
                   
                 default: 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
            
               
                 } 
               
               
                   
               
               
                 NOTE: 
               
            
           
         
       
     
     Underlines in the foregoing table denote changes to the existing syntax table to accommodate the addition of the CodebkIdx. The semantics for the foregoing table are as follows. 
     This payload holds the side information for the i-th channel. The size and the data of the payload depend on the type of the channel. 
     
         
         ChannelType[i] This element stores the type of the i-th channel which is defined in Table 95. 
         ActiveDirsIds[i] This element indicates the direction of the active directional signal using an index of the 900 predefined, uniformly distributed points from Annex F.7. The code word 0 is used for signaling the end of a directional signal. 
         PFlag[i] The prediction flag used for the Huffman decoding of the scalar-quantised V-vector associated with the Vector-based signal of the i-th channel. 
         CbFlag[i] The codebook flag used for the Huffman decoding of the scalar-quantised V-vector associated with the Vector-based signal of the i-th channel. 
         CodebkIdx[i] Signals the specific codebook used to dequantise the vector-quantized V-vector associated with the Vector-based signal of the i-th channel. 
         NbitsQ[i] This index determines the Huffman table used for the Huffman decoding of the data associated with the Vector-based signal of the i-th channel. The code word 5 determines the use of a uniform 8 bit dequantizer. The two MSBs 00 determines reusing the NbitsQ[i], PFlag[i] and CbFlag[i] data of the previous frame (k−1). 
         bA, bB The msb (bA) and second msb (bB) of the NbitsQ[i] field. 
         uintC The code word of the remaining two bits of the NbitsQ[i] field. 
         AddAmbHoaInfoChannel(i) This payload holds the information for additional ambient HOA coefficients. 
       
    
     Per the VVectorData syntax table semantics the nbitsW syntax element represents a field size for reading WeightIdx to decode a vector-quantised V-vector, while the WeightValCdbk syntax element represents a Codebook which contains a vector of positive real-valued weighting coefficients. If NumVecIndices is set to 1, the WeightValCdbk with 8 entries is used, otherwise the WeightValCdbk with 256 entries is used. Per the VVectorData syntax table, when the CodebkIdx equals zero, the v-vector reconstruction unit  74  determines that nbitsW equals 3 and the WeightIdx can have a value in the range of 0-7. In this instance, the code vector dictionary VecDict has a relatively large number of entries (e.g., 900) and is paired with a weight codebook having only 8 entries. When the CodebkIdx does not equal zero, the v-vector reconstruction unit  74  determines that nbitsW equals 8 and the WeightIdx can have a value in the range of 0-255. In this instance, the VecDict has a relatively smaller number of entries (e.g., 25 or 32 entires) and a relatively larger number of weights are required (e.g., 256) in the weight codebook to ensure an acceptable error. In this manner, the techniques may provide for paired codebooks (referring to the paired VecDict used and the weight codebooks). The weight value (denoted “WeightVal” in the foregoing VVectorData syntax table) may then be computed as follows:
 
|WeightVal[ j ]=((SgnVar*2)−1)*WeightValCdbk[CodebkIdx( k )[ i ]][WeightIdx][ j ];
 
This WeightVal may then be applied per the above psuedocode to a corresponding code vector to de-vector quantize the v-vector.
 
     In this respect, the techniques may enable an audio decoding device, e.g., the audio decoding device  24 , to select one of a plurality of codebooks to use when performing vector dequantizaion with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients. 
     Moreover, the techniques may enable the audio decoding device  24  to select between a plurality of paired codebooks to be used when performing vector dequantization with respect to a vector quantized spatial component of a soundfield, the vector quantized spatial component obtained through application of a vector-based synthesis to a plurality of higher order ambisonic coefficients. 
     When NbitsQ equals 5, a uniform 8 bit scalar dequantization is performed. In contrast, an NbitsQ value of greater or equals 6 may result in application of Huffman decoding. The cid value referred to above may be equal to the two least significant bits of the NbitsQ value. The prediction mode discussed above is denoted as the PFlag in the above syntax table, while the HT info bit is denoted as the CbFlag in the above syntax table. The remaining syntax specifies how the decoding occurs in a manner substantially similar to that described above. 
     The vector-based reconstruction unit  92  represents a unit configured to perform operations reciprocal to those described above with respect to the vector-based synthesis unit  27  so as to reconstruct the HOA coefficients  11 ′. The vector based reconstruction unit  92  may include a v-vector reconstruction unit  74 , a spatio-temporal interpolation unit  76 , a foreground formulation unit  78 , a psychoacoustic decoding unit  80 , a HOA coefficient formulation unit  82  and a reorder unit  84 . 
     The v-vector reconstruction unit  74  may receive coded weights  57  and generate reduced foreground V[k] vectors  55   k . The v-vector reconstruction unit  74  may forward the reduced foreground V[k] vectors  55   k  to the reorder unit  84 . 
     For example, the v-vector reconstruction unit  74  may obtain the coded weights  57  from the bitstream  21  via the extraction unit  72 , and reconstruct the reduced foreground V[k] vectors  55   k  based on the coded weights  57  and one or more code vectors. In some examples, the coded weights  57  may include weight values corresponding to all code vectors in a set of code vectors that is used to represent the reduced foreground V[k] vectors  55   k . In such examples, the v-vector reconstruction unit  74  may reconstruct the reduced foreground V[k] vectors  55   k  based on the entire set of code vectors. 
     The coded weights  57  may include weight values corresponding to a subset of a set of code vectors that is used to represent the reduced foreground V[k] vectors  55   k . In such examples, the coded weights  57  may further include data indicative of which of a plurality of code vectors to use for reconstructing the reduced foreground V[k] vectors  55   k , and the v-vector reconstruction unit  74  may use a subset of the code vectors indicated by such data to reconstruct the reduced foreground V[k] vectors  55   k . In some examples, the data indicative of which of a plurality of code vectors to use for reconstructing the reduced foreground V[k] vectors  55   k  may correspond to indices  57 . 
     In some examples, the v-vector reconstruction unit  74  may obtain from a bitstream data indicative of a plurality of weight values that represent a vector that is included in a decomposed version of a plurality of HOA coefficients, and reconstruct the vector based on the weight values and the code vectors. Each of the weight values may correspond to a respective one of a plurality of weights in a weighted sum of code vectors that represents the vector. 
     In some examples, to reconstruct the vector, the v-vector reconstruction unit  74  may determine a weighted sum of the code vectors where the code vectors are weighted by the weight values. In further examples, to reconstruct the vector, the v-vector reconstruction unit  74  may, for each of the weight values, multiply the weight value by a respective one of the code vectors to generate a respective weighted code vector included in a plurality of weighted code vectors, and sum the plurality of weighted code vectors to determine the vector. 
     In some examples, v-vector reconstruction unit  74  may obtain, from the bitstream, data indicative of which of a plurality of code vectors to use for reconstructing the vector, and reconstruct the vector based on the weight values (e.g., the WeightVal element derived from the WeightValCdbk based on the CodebkIdx and WeightIdx syntax elements), the code vectors, and the data indicative of which of a plurality of code vectors (as identified for example by the VVecIdx syntax element in addition with the NumVecIndices) to use for reconstructing the vector. In such examples, to reconstruct the vector, the v-vector reconstruction unit  74  may, in some examples, select a subset of the code vectors based on the data indicative of which of a plurality of code vectors to use for reconstructing the vector, and reconstruct the vector based on the weight values and the selected subset of the code vectors. 
     In such examples, to reconstruct the vector based on the weight values and the selected subset of the code vectors, the v-vector reconstruction unit  74  may, for each of the weight values, multiply the weight value by a respective one of the code vectors in the subset of code vectors to generate a respective weighted code vector, and sum the plurality of weighted code vectors to determine the vector. 
     The psychoacoustic decoding unit  80  may operate in a manner reciprocal to the psychoacoustic audio coding unit  40  shown in the example of  FIG. 4A  so as to decode the encoded ambient HOA coefficients  59  and the encoded nFG signals  61  and thereby generate energy compensated ambient HOA coefficients  47 ′ and the interpolated nFG signals  49 ′ (which may also be referred to as interpolated nFG audio objects  49 ′). Although shown as being separate from one another, the encoded ambient HOA coefficients  59  and the encoded nFG signals  61  may not be separate from one another and instead may be specified as encoded channels, as described below with respect to  FIG. 4B . The psychoacoustic decoding unit  80  may, when the encoded ambient HOA coefficients  59  and the encoded nFG signals  61  are specified together as the encoded channels, may decode the encoded channels to obtain decoded channels and then perform a form of channel reassignment with respect to the decoded channels to obtain the energy compensated ambient HOA coefficients  47 ′ and the interpolated nFG signals  49 ′. 
     In other words, the psychoacoustic decoding unit  80  may obtain the interpolated nFG signals  49 ′ of all the predominant sound signals, which may be denoted as the frame X ps (k), the energy compensated ambient HOA coefficients  47 ′ representative of the intermediate representation of the ambient HOA component, which may be denoted as the frame C I,AMB (k). The psychoacoustic decoding unit  80  may perform this channel reassignment based on syntax elements specified in the bitstream  21  or  29 , which may include an assignment vector specifying, for each transport channel, the index of a possibly contained coefficient sequence of the ambient HOA component and other syntax elements indicative of a set of active V vectors. In any event, the psychoacoustic decoding unit  80  may pass the energy compensated ambient HOA coefficients  47 ′ to HOA coefficient formulation unit  82  and the nFG signals  49 ′ to the reorder  84 . 
     In other words, the psychoacoustic decoding unit  80  may obtain the interpolated nFG signals  49 ′ of all the predominant sound signals, which may be denoted as the frame X ps (k), the energy compensated ambient HOA coefficients  47 ′ representative of the intermediate representation of the ambient HOA component, which may be denoted as the frame C I,AMB (k). The psychoacoustic decoding unit  80  may perform this channel reassignment based on syntax elements specified in the bitstream  21  or  29 , which may include an assignment vector specifying, for each transport channel, the index of a possibly contained coefficient sequence of the ambient HOA component and other syntax elements indicative of a set of active V vectors. In any event, the psychoacoustic decoding unit  80  may pass the energy compensated ambient HOA coefficients  47 ′ to HOA coefficient formulation unit  82  and the nFG signals  49 ′ to the reorder  84 . 
     To restate the foregoing, the HOA coefficients may be reformulated from the vector-based signals in the manner described above. Scalar dequantization may first be performed with respect to each V-vector to generate M VEC (k), where the i th  individual vectors of the current frame may be denoted as v i   (i) (k). The V-vectors may have been decomposed from the HOA coefficients using a linear invertible transform (such as a singular value decomposition, a principle component analysis, a Karhunen-Loeve transform, a Hotelling transform, proper orthogonal decomoposition, or an eigenvalue decomposition), as described above. The decomposition also outputs, in the case of a singular value decomposition, S[k] and U[k] vectors, which may be combined to form US[k]. Individual vector elements in the US[k] matrix may be denoted as X PS (k,l). 
     Spatio-temporal interpolation may be performed with respect to the M VEC (k) and M VEC (k−1) (which denotes V-vectors from a previous frame with individual vectors of M VEC (k−1) denoted as v o   (i)  (k)). The spatial interpolation method is, as one example, controlled by w VEC (l). Following interpolation, the i th  interpolated V-vector ( v (t) (k,l) ) are then multiplied by the i th  US[k] (which is denoted as X PS,i (k,l)) to output the i th  column of the HOA representation (c VEC   (i) (k,l)). The column vectors may then be summed to formulate the HOA representation of the vector-based signals. In this way, the decomposed interpolated representation of the HOA coefficients are obtained for a frame by performing an interpolation with respect to v I   (i) (k) and v o   (i)  (k), as described in further detail below. 
       FIG. 4B  is a block diagram illustrating another example of the audio decoding device  24  in more detail. The example shown in  FIG. 4B  of the audio decoding device  24  is denoted as the audio decoding device  24 ′. The audio decoding device  24 ′ is substantially similar to the audio decoding device  24  shown in the example of  FIG. 4A  except that the psychoacoustic decoding unit  902  of the audio decoding device  24 ′ does not perform the channel reassignment described above. Instead, the audio encoding device  24 ′ includes a separate channel reassignment unit  904  that performs the channel reassignment described above. In the example of  FIG. 4B , the psychoacoustic decoding unit  902  receives encoded channels  900  and performs psychoacoustic decoding with respect to the encoded channels  900  to obtain decoded channels  901 . The psychoacoustic decoding unit  902  may output the decoded channel  901  to the channel reassignment unit  904 . The channel reassignment unit  904  may then perform the above described channel reassignment with respect to the decoded channel  901  to obtain the energy compensated ambient HOA coefficients  47 ′ and the interpolated nFG signals  49 ′. 
     The spatio-temporal interpolation unit  76  may operate in a manner similar to that described above with respect to the spatio-temporal interpolation unit  50 . The spatio-temporal interpolation unit  76  may receive the reduced foreground V[k] vectors  55   k  and perform the spatio-temporal interpolation with respect to the foreground V[k] vectors  55   k  and the reduced foreground V[k−1] vectors  55   k-1  to generate interpolated foreground V[k] vectors  55   k ″. The spatio-temporal interpolation unit  76  may forward the interpolated foreground V[k] vectors  55   k ″ to the fade unit  770 . 
     The extraction unit  72  may also output a signal  757  indicative of when one of the ambient HOA coefficients is in transition to fade unit  770 , which may then determine which of the SHC BG    47 ′ (where the SHC BG    47 ′ may also be denoted as “ambient HOA channels  47 ” or “ambient HOA coefficients  47 ′) and the elements of the interpolated foreground V[k] vectors  55   k ” are to be either faded-in or faded-out. In some examples, the fade unit  770  may operate opposite with respect to each of the ambient HOA coefficients  47 ′ and the elements of the interpolated foreground V[k] vectors  55   k ″. That is, the fade unit  770  may perform a fade-in or fade-out, or both a fade-in or fade-out with respect to corresponding one of the ambient HOA coefficients  47 ′, while performing a fade-in or fade-out or both a fade-in and a fade-out, with respect to the corresponding one of the elements of the interpolated foreground V[k] vectors  55   k ″. The fade unit  770  may output adjusted ambient HOA coefficients  47 ″ to the HOA coefficient formulation unit  82  and adjusted foreground V[k] vectors  55   k ′″ to the foreground formulation unit  78 . In this respect, the fade unit  770  represents a unit configured to perform a fade operation with respect to various aspects of the HOA coefficients or derivatives thereof, e.g., in the form of the ambient HOA coefficients  47 ′ and the elements of the interpolated foreground V[k] vectors  55   k ″. 
     The foreground formulation unit  78  may represent a unit configured to perform matrix multiplication with respect to the adjusted foreground V[k] vectors  55   k ′″ and the interpolated nFG signals  49 ′ to generate the foreground HOA coefficients  65 . In this respect, the foreground formulation unit  78  may combine the audio objects  49 ′ (which is another way by which to denote the interpolated nFG signals  49 ′) with the vectors  55   k ′″ to reconstruct the foreground or, in other words, predominant aspects of the HOA coefficients  11 ′. The foreground formulation unit  78  may perform a matrix multiplication of the interpolated nFG signals  49 ′ by the adjusted foreground V[k] vectors  55   k ′″. 
     The HOA coefficient formulation unit  82  may represent a unit configured to combine the foreground HOA coefficients  65  to the adjusted ambient HOA coefficients  47 ″ so as to obtain the HOA coefficients  11 ′. The prime notation reflects that the HOA coefficients  11 ′ may be similar to but not the same as the HOA coefficients  11 . The differences between the HOA coefficients  11  and  11 ′ may result from loss due to transmission over a lossy transmission medium, quantization or other lossy operations. 
       FIG. 5  is a flowchart illustrating exemplary operation of an audio encoding device, such as the audio encoding device  20  shown in the example of  FIG. 3A , in performing various aspects of the vector-based synthesis techniques described in this disclosure. Initially, the audio encoding device  20  receives the HOA coefficients  11  ( 106 ). The audio encoding device  20  may invoke the LIT unit  30 , which may apply a LIT with respect to the HOA coefficients to output transformed HOA coefficients (e.g., in the case of SVD, the transformed HOA coefficients may comprise the US[k] vectors  33  and the V[k] vectors  35 ) ( 107 ). 
     The audio encoding device  20  may next invoke the parameter calculation unit  32  to perform the above described analysis with respect to any combination of the US[k] vectors  33 , US[k−1] vectors  33 , the V[k] and/or V[k−1] vectors  35  to identify various parameters in the manner described above. That is, the parameter calculation unit  32  may determine at least one parameter based on an analysis of the transformed HOA coefficients  33 / 35  ( 108 ). 
     The audio encoding device  20  may then invoke the reorder unit  34 , which may reorder the transformed HOA coefficients (which, again in the context of SVD, may refer to the US[k] vectors  33  and the V[k] vectors  35 ) based on the parameter to generate reordered transformed HOA coefficients  33 ′/ 35 ′ (or, in other words, the US[k] vectors  33 ′ and the V[k] vectors  35 ′), as described above (109). The audio encoding device  20  may, during any of the foregoing operations or subsequent operations, also invoke the soundfield analysis unit  44 . The soundfield analysis unit  44  may, as described above, perform a soundfield analysis with respect to the HOA coefficients  11  and/or the transformed HOA coefficients  33 / 35  to determine the total number of foreground channels (nFG)  45 , the order of the background soundfield (N BG ) and the number (nBGa) and indices (i) of additional BG HOA channels to send (which may collectively be denoted as background channel information  43  in the example of  FIG. 3A ) ( 109 ). 
     The audio encoding device  20  may also invoke the background selection unit  48 . The background selection unit  48  may determine background or ambient HOA coefficients  47  based on the background channel information  43  ( 110 ). The audio encoding device  20  may further invoke the foreground selection unit  36 , which may select the reordered US[k] vectors  33 ′ and the reordered V[k] vectors  35 ′ that represent foreground or distinct components of the soundfield based on nFG  45  (which may represent a one or more indices identifying the foreground vectors) ( 112 ). 
     The audio encoding device  20  may invoke the energy compensation unit  38 . The energy compensation unit  38  may perform energy compensation with respect to the ambient HOA coefficients  47  to compensate for energy loss due to removal of various ones of the HOA coefficients by the background selection unit  48  ( 114 ) and thereby generate energy compensated ambient HOA coefficients  47 ′. 
     The audio encoding device  20  may also invoke the spatio-temporal interpolation unit  50 . The spatio-temporal interpolation unit  50  may perform spatio-temporal interpolation with respect to the reordered transformed HOA coefficients  33 ′/ 35 ′ to obtain the interpolated foreground signals  49 ′ (which may also be referred to as the “interpolated nFG signals  49 ”) and the remaining foreground directional information  53  (which may also be referred to as the “V[k] vectors  53 ”) ( 116 ). The audio encoding device  20  may then invoke the coefficient reduction unit  46 . The coefficient reduction unit  46  may perform coefficient reduction with respect to the remaining foreground V[k] vectors  53  based on the background channel information  43  to obtain reduced foreground directional information  55  (which may also be referred to as the reduced foreground V[k] vectors  55 ) ( 118 ). 
     The audio encoding device  20  may then invoke the V-vector coding unit  52  to compress, in the manner described above, the reduced foreground V[k] vectors  55  and generate coded foreground V[k] vectors  57  ( 120 ). 
     The audio encoding device  20  may also invoke the psychoacoustic audio coder unit  40 . The psychoacoustic audio coder unit  40  may psychoacoustic code each vector of the energy compensated ambient HOA coefficients  47 ′ and the interpolated nFG signals  49 ′ to generate encoded ambient HOA coefficients  59  and encoded nFG signals  61 . The audio encoding device may then invoke the bitstream generation unit  42 . The bitstream generation unit  42  may generate the bitstream  21  based on the coded foreground directional information  57 , the coded ambient HOA coefficients  59 , the coded nFG signals  61  and the background channel information  43 . 
       FIG. 6  is a flowchart illustrating exemplary operation of an audio decoding device, such as the audio decoding device  24  shown in  FIG. 4A , in performing various aspects of the techniques described in this disclosure. Initially, the audio decoding device  24  may receive the bitstream  21  ( 130 ). Upon receiving the bitstream, the audio decoding device  24  may invoke the extraction unit  72 . Assuming for purposes of discussion that the bitstream  21  indicates that vector-based reconstruction is to be performed, the extraction unit  72  may parse the bitstream to retrieve the above noted information, passing the information to the vector-based reconstruction unit  92 . 
     In other words, the extraction unit  72  may extract the coded foreground directional information  57  (which, again, may also be referred to as the coded foreground V[k] vectors  57 ), the coded ambient HOA coefficients  59  and the coded foreground signals (which may also be referred to as the coded foreground nFG signals  59  or the coded foreground audio objects  59 ) from the bitstream  21  in the manner described above (132). 
     The audio decoding device  24  may further invoke the dequantization unit  74 . The dequantization unit  74  may entropy decode and dequantize the coded foreground directional information  57  to obtain reduced foreground directional information  55   k  ( 136 ). The audio decoding device  24  may also invoke the psychoacoustic decoding unit  80 . The psychoacoustic audio decoding unit  80  may decode the encoded ambient HOA coefficients  59  and the encoded foreground signals  61  to obtain energy compensated ambient HOA coefficients  47 ′ and the interpolated foreground signals  49 ′ ( 138 ). The psychoacoustic decoding unit  80  may pass the energy compensated ambient HOA coefficients  47 ′ to the fade unit  770  and the nFG signals  49 ′ to the foreground formulation unit  78 . 
     The audio decoding device  24  may next invoke the spatio-temporal interpolation unit  76 . The spatio-temporal interpolation unit  76  may receive the reordered foreground directional information  55   k ′ and perform the spatio-temporal interpolation with respect to the reduced foreground directional information  55   k /55 k-1  to generate the interpolated foreground directional information  55   k ″ ( 140 ). The spatio-temporal interpolation unit  76  may forward the interpolated foreground V[k] vectors  55   k ″ to the fade unit  770 . 
     The audio decoding device  24  may invoke the fade unit  770 . The fade unit  770  may receive or otherwise obtain syntax elements (e.g., from the extraction unit  72 ) indicative of when the energy compensated ambient HOA coefficients  47 ′ are in transition (e.g., the AmbCoeffTransition syntax element). The fade unit  770  may, based on the transition syntax elements and the maintained transition state information, fade-in or fade-out the energy compensated ambient HOA coefficients  47 ′ outputting adjusted ambient HOA coefficients  47 ″ to the HOA coefficient formulation unit  82 . The fade unit  770  may also, based on the syntax elements and the maintained transition state information, and fade-out or fade-in the corresponding one or more elements of the interpolated foreground V[k] vectors  55   k ″ outputting the adjusted foreground V[k] vectors  55   k ′″ to the foreground formulation unit  78  ( 142 ). 
     The audio decoding device  24  may invoke the foreground formulation unit  78 . The foreground formulation unit  78  may perform matrix multiplication the nFG signals  49 ′ by the adjusted foreground directional information  55   k ′″ to obtain the foreground HOA coefficients  65  ( 144 ). The audio decoding device  24  may also invoke the HOA coefficient formulation unit  82 . The HOA coefficient formulation unit  82  may add the foreground HOA coefficients  65  to adjusted ambient HOA coefficients  47 ″ so as to obtain the HOA coefficients  11 ′ ( 146 ). 
       FIG. 7  is a block diagram illustrating, in more detail, an example v-vector coding unit  52  that may be used in the audio encoding device  20  of  FIG. 3A . The v-vector coding unit  52  includes a decomposition unit  502  and a quantization unit  504 . The decomposition unit  502  may decompose each of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors based on the code vectors  63 . The decomposition unit  502  may generate weights  506  and provide the weights  506  to the quantization unit  504 . The quantization unit  504  may quantize the weights  506  to generate the coded weights  57 . 
       FIG. 8  is a block diagram illustrating, in more detail, an example v-vector coding unit  52  that may be used in the audio encoding device  20  of  FIG. 3A . The v-vector coding unit  52  includes a decomposition unit  502 , a weight selection unit  510 , and a quantization unit  504 . The decomposition unit  502  may decompose each of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors based on the code vectors  63 . The decomposition unit  502  may generate weights  514  and provide the weights  514  to the weight selection unit  510 . The weight selection unit  510  may select a subset of the weights  514  to generate a selected subset of weights  516 , and provide the selected subset of weights  516  to the quantization unit  504 . The quantization unit  504  may quantize the selected subset of weights  516  to generate the coded weights  57 . 
       FIG. 9  is a conceptual diagram illustrating a sound field generated from a v-vector.  FIG. 10  is a conceptual diagram illustrating a sound field generated from a 25th order model of the v-vector described above with respect to  FIG. 9 .  FIG. 11  is a conceptual diagram illustrating the weighting of each order for the 25th order model shown in  FIG. 10 .  FIG. 12  is a conceptual diagram illustrating a 5th order model of the v-vector described above with respect to  FIG. 9 .  FIG. 13  is a conceptual diagram illustrating the weighting of each order for the 5th order model shown in  FIG. 12 . 
       FIG. 14  is a conceptual diagram illustrating example dimensions of example matrices used to perform singular value decomposition. As shown in  FIG. 14 , a U FG  matrix is included in a U matrix, an S FG  matrix is included in an S matrix, and a V FG   T  matrix is included in a V T  matrix. 
     In the example matrixes of  FIG. 14 , the U FG  matrix has dimensions 1280 by 2 where 1280 corresponds to the number of samples, and 2 corresponds to the number of foreground vectors selected for foreground coding. The U matrix has dimensions of 1280 by 25 where 1280 corresponds to the number of samples, and 25 corresponds to the number of channels in the HOA audio signal. The number of channels may be equal to (N+1) 2  where N is equal to the order of the HOA audio signal. 
     The S FG  matrix has dimensions 2 by 2 where each 2 corresponds to the number of foreground vectors selected for foreground coding. The S matrix has dimensions of 25 by 25 where each 25 corresponds to the number of channels in the HOA audio signal. 
     The V FG   T  matrix has dimensions 25 by 2 where 25 corresponds to the number of channels in the HOA audio signal, and 2 corresponds to the number of foreground vectors selected for foreground coding. The V T  matrix has dimensions of 25 by 25 where each 25 corresponds to the number of channels in the HOA audio signal. 
     As shown in  FIG. 14 , the U FG  matrix, the S FG  matrix, and the V FG   T  matrix may be multiplied together to generate an H FG  matrix. The H FG  matrix has dimensions of 1280 by 25 where 1280 corresponds to the number of samples, and 25 corresponds to the number of channels in the HOA audio signal. 
       FIG. 15  is a chart illustrating example performance improvements that may be obtained by using the v-vector coding techniques of this disclosure. Each row represents a test item, and the columns indicate from left-to-right, the test item number, the test item name, the bits-per-frame associated with the test item, the bit-rate using one or more of the example v-vector coding techniques of this disclosure, and the bit-rate obtained using other v-vector coding techniques (e.g., scalar quantizing the v-vector components without decomposing the v-vector). As shown in  FIG. 15 , the techniques of this disclosure may, in some examples, provide significant improvements in bit-rate relative to other techniques that do not decompose v-vectors into weights and/or select a subset of the weights to quantize. 
     In some examples, the techniques of this disclosure may perform V-vector quantization based on a set of directional vectors. A V-vector may be represented by a weighted sum of directional vectors. In some examples, for a given set of directional vectors that are orthonormal to each other, the v-vector coding unit  52  may calculate the weighting value for each directional vector. The v-vector coding unit  52  may select the N-maxima weighting values, {w_i}, and the corresponding directional vectors, {o_i}. The v-vector coding unit  52  may transmit indices {i} to the decoder that correspond to the selected weighting values and/or directional vectors. In some examples, when calculating maxima, the v-vector coding unit  52  may use absolute values (by neglecting sign information). The v-vector coding unit  52  may quantize the N-maxima weighting values, {w_i}, to generate quantized weighting values {w _i}. The v-vector coding unit  52  may transmit the quantization indices for {w{circumflex over ( )}_i} to the decoder. At the decoder, the quantized V-vector may be synthesized as sum_i (w{circumflex over ( )}_i*o_i) 
     In some examples, the techniques of this disclosure may provide a significant improvement in performance. For example, compared with using scalar quantization followed by Huffman coding, an approximately 85% bit-rate reduction may be obtained. For example, scalar quantization followed by Huffman coding may, in some examples, require a bit-rate of 16.26 kbps (kilo bits-per-second) while the techniques of this disclosure may, in some examples, be capable of coding at bit-rate of 2.75 kbsp. 
     Consider an example where X code vectors from a codebook (and X corresponding weights) are used to code a v-vector. In some examples, the bitstream generation unit  42  may generate the bitstream  21  such that each v-vector is represented by 3 categories of parameters: (1) X number of indices each pointing to a particular vector in a codebook of code vectors (e.g., a codebook of normalized directional vectors); (2) a corresponding (X) number of weights to go with the above indices; and (3) a sign bit for each of the above (X) number of weights. In some cases, the X number of weights may be further quantized using yet another vector quantization (VQ). 
     The decomposition codebook used for determining the weights in this example may be selected from a set of candidate codebooks. For example, the codebook may be 1 of 8 different codebooks. Each of these codebooks may have different lengths. So, for example, not only may a codebook of size 49 used to determine weights for 6th order HOA content, but the techniques of this disclosure may give the option of using any one of 8 different sized codebooks. 
     The quantization codebook used for the VQ of the weights may, in some examples, also have the same corresponding number of possible codebooks as the number of possible decomposition codebooks used to determine the weights. Thus, in some examples, there may be a variable number of different codebooks for determining the weights and a variable number of codebooks for quantizing the weights. 
     In some examples, the number of weights used to estimate a v-vector (i.e., the number of weights selected for quantization) may be variable. For example, a threshold error criterion may be set, and the number (X) of weights selected for quantization may depend on reaching the error threshold where the error threshold is defined above in equation (10). 
     In some examples, one or more of the above-mentioned concepts may be signaled in a bitstream. Consider an example where the maximum number of weights used to code v-vectors is set to 128 weights, and eight different quantization codebooks are used to quantize the weights. In such an example, the bitstream generation unit  42  may generate the bitstream  21  such that an Access Frame Unit in the bitstream  21  indicates the maximum number of indices that can be used on a frame-by-frame basis. In this example, the maximum number of indices is a number from 0-128, so the above-mentioned data may consume 7 bits in the Access Frame Unit. 
     In the above-mentioned example, on a frame-by-frame basis, the bitstream generation unit  42  may generate the bitstream  21  to include data indicative of: (1) which one of the 8 different codebooks was used to do the VQ (for every v-vector); and (2) the actual number of indices (X) used to code each v-vector. The data indicative of which one of the 8 different codebooks was used to do the VQ may consume 3 bits in this example. The data indicative of the actual number of indices (X) used to code each v-vector may be given by the maximum number of indices specified in the Access Frame Unit. This may vary from 0 bits to 7 bits in this example. 
     In some examples, the bitstream generation unit  42  may generate the bitstream  21  to include: (1) indices that indicate which directional vectors are selected and transmitted (according the calculated weighting values); and (2) weighting value(s) for each selected directional vector. In some examples, the this disclosure may provide techniques for the quantization of V-vectors using a decomposition on a codebook of normalized spherical harmonic code vectors. 
       FIG. 17  is a diagram illustrating 16 different code vectors  63 A- 63 P represented in a spatial domain that may be used by the V-vector coding unit  52  shown in the example of either or both of  FIGS. 7 and 8 . The code vectors  63 A- 63 P may represent one or more of the code vectors  63  discussed above. 
       FIG. 18  is a diagram illustrating different ways by which the 16 different code vectors  63 A- 63 P may be employed by the V-vector coding unit  52  shown in the example of either or both of  FIGS. 7 and 8 . The V-vector coding unit  52  may receive one of reduced foreground V[k] vectors  55 , which is shown after being rendered to the spatial domain and is denoted as V-vector  55 . The V-vector coding unit  52  may perform the vector quantization discussed above to produce three different coded versions of the V-vector  55 . The three different coded versions of the V-vector  55  are shown after being rendered to the spatial domain and are denoted coded V-vector  57 A, coded V-vector  57 B and coded V-vectors  57 C. The V-vector coding unit  52  may select one of the coded V-vectors  57 A- 57 C as one of the coded foreground V[k] vectors  57  corresponding to V-vector  55 . 
     The V-vector coding unit  52  may generate each of coded V-vectors  57 A- 57 C based on code vectors  63 A- 63 P (“code vectors  63 ”) shown in better detail in the example of  FIG. 17 . The V-vector coding unit  52  may generate the coded V-vector  57 A based on all 16 of the code vectors  63  as shown in graph  300 A where all 16 indexes are specified along with 16 weighting values. The V-vector coding unit  52  may generate the coded V-vector  57 A based on a non-zero subset of the code vectors  63  (e.g., the code vectors  63  enclosed in the square box and associated with the indexes  2 ,  6  and  7  as shown in graph  300 B given that the other indexes have a weighting of zero). The V-vector coding unit  52  may generate the coded V-vector  57 C using the same three code vectors  63  as that used when generating the coded V-vector  57 B except that the original V-vector  55  is first quantized. 
     Reviewing the renderings of the coded V-vectors  57 A- 57 C in comparison to the original V-vector  55  illustrates that vector quantization may provide a substantially similar representation of the original V-vector  55  (meaning that the error between each of the coded V-vectors  57 A- 57 C is likely small). Comparing the coded V-vectors  57 A- 57 C to one another also reveals that there are only minor or slight differences. As such, the one of the coded V-vectors  57 A- 57 C providing the best bit reduction is likely the one of the coded V-vectors  57 A- 57 C that the V-vector coding unit  52  may select. Given that the coded V-vector  57 C provides the smallest bit rate most likely (given that the coded V-vector  57 C utilizes a quantized version of the V-vector  55  while also using only three of the code vectors  63 ), the V-vector coding unit  52  may select the coded V-vector  57 C as the one of the coded foreground V[k] vectors  57  corresponding to V-vector  55 . 
       FIG. 21  is a block diagram illustrating an example vector quantization unit  520  according to this disclosure. In some examples, the vector quantization unit  520  may be an example of the V-vector coding unit  52  in the audio encoding device  20  of  FIG. 3A  or in the audio encoding device  20  of  FIG. 3B . The vector quantization unit  520  includes a decomposition unit  522 , a weight selection and ordering unit  524 , and a vector selection unit  526 . The decomposition unit  522  may decompose each of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors based on the code vectors  63 . The decomposition unit  522  may generate weight values  528  and provide the weight values  528  to the weight selection and ordering unit  524 . 
     The weight selection and ordering unit  524  may select a subset of the weight values  528  to generate a selected subset of weight values. For example, the weight selection and ordering unit  524  may select the M greatest-magnitude weight values from the set of weight values  528 . The weight selection and ordering unit  524  may further reorder the selected subset of weight values based on magnitudes of the weight values to generate a reordered selected subset of weight values  530 , and provide the reordered selected subset of weight values  530  to the vector selection unit  526 . 
     The vector selection unit  526  may select an M-component vector from a quantization codebook  532  to represent M weight values. In other words, the vector selection unit  526  may vector quantize M weight values. In some examples, M may correspond to the number of weight values selected by the weight selection and ordering unit  524  to represent a single V-vector. The vector selection unit  526  may generate data indicative of the M-component vector selected to represent the M weight values, and provide this data to the bitstream generation unit  42  as the coded weights  57 . In some examples, the quantization codebook  532  may include a plurality of M-component vectors that are indexed, and the data indicative of the M-component vector may be an index value into the quantization codebook  532  that points to the selected vector. In such examples, the decoder may include a similarly indexed quantization codebook to decode the index value. 
       FIG. 22  is a flowchart illustrating exemplary operation of the vector quantization unit in performing various aspects of the techniques described in this disclosure. As described above with respect to the example of  FIG. 21 , the vector quantization unit  520  includes a decomposition unit  522 , a weight selection and ordering unit  524 , and a vector selection unit  526 . The decomposition unit  522  may decompose each of the reduced foreground V[k] vectors  55  into a weighted sum of code vectors based on the code vectors  63  ( 750 ). The decomposition unit  522  may obtain weight values  528  and provide the weight values  528  to the weight selection and ordering unit  524  ( 752 ). 
     The weight selection and ordering unit  524  may select a subset of the weight values  528  to generate a selected subset of weight values ( 754 ). For example, the weight selection and ordering unit  524  may select the M greatest-magnitude weight values from the set of weight values  528 . The weight selection and ordering unit  524  may further reorder the selected subset of weight values based on magnitudes of the weight values to generate a reordered selected subset of weight values  530 , and provide the reordered selected subset of weight values  530  to the vector selection unit  526  ( 756 ). 
     The vector selection unit  526  may select an M-component vector from a quantization codebook  532  to represent M weight values. In other words, the vector selection unit  526  may vector quantize M weight values ( 758 ). In some examples, M may correspond to the number of weight values selected by the weight selection and ordering unit  524  to represent a single V-vector. The vector selection unit  526  may generate data indicative of the M-component vector selected to represent the M weight values, and provide this data to the bitstream generation unit  42  as the coded weights  57 . In some examples, the quantization codebook  532  may include a plurality of M-component vectors that are indexed, and the data indicative of the M-component vector may be an index value into the quantization codebook  532  that points to the selected vector. In such examples, the decoder may include a similarly indexed quantization codebook to decode the index value. 
       FIG. 23  is a flowchart illustrating exemplary operation of the V-vector reconstruction unit in performing various aspects of the techniques described in this disclosure. The V-vector reconstruction unit  74  of  FIG. 4A or 4B  may first obtain the weight values, e.g., from extraction unit  72  after being parsed from the bitstream  21  ( 760 ). The V-vector reconstruction unit  74  may also obtain code vectors, e.g., from a codebook using an index signaled in the bitstream  21  in the manner described above (762). The V-vector reconstruction unit  74  may then reconstruct the reduced foreground V[k] vectors (which may also be referred to as the V-vectors)  55  based on the weight values and the code vectors in one or more of the various ways described above (764). 
       FIG. 24  is a flowchart illustrating exemplary operation of the V-vector coding unit of  FIG. 3A or 3B  in performing various aspects of the techniques described in this disclosure. The V-vector coding unit  52  may obtain a target bitrate (which may also be referred to as a threshold bitrate)  41  ( 770 ). When the target bitrate  41  is greater than 256 Kbps (or any other specified, configured or determined bitrate) (“NO”  772 ), the V-vector coding unit  52  may determine to apply and then apply scalar quantization to the V-vectors  55  ( 774 ). When the target bitrate  41  is less than or equal to 256 Kbps (“YES”  772 ), the V-vector reconstruction unit  52  may determine to apply and then apply vector quantization to the V-vectors  55  ( 776 ). The V-vector coding unit  52  may also signal in the bitstream  21  that scalar or vector quantization was performed with respect to the V-vectors  55  ( 778 ). 
       FIG. 25  is a flowchart illustrating exemplary operation of the V-vector reconstruction unit in performing various aspects of the techniques described in this disclosure. The V-vector reconstruction unit  74  of  FIG. 4A or 4B  may first obtain an indication (such as a syntax element) of whether scalar or vector quantization was performed with respect to the V-vectors  55  ( 780 ). When the syntax element indicates scalar quantization was not performed (“NO”  782 ), the V-vector reconstruction unit  74  may perform vector dequantization to reconstruct the V-vectors  55  ( 784 ). When the syntax element indicates that scalar quantization was performed (“YES”  782 ), the V-vector reconstruction unit  74  may perform scalar dequantization to reconstruct the V-vectors  55  ( 786 ). 
       FIG. 26  is a flowchart illustrating exemplary operation of the V-vector coding unit of  FIG. 3A or 3B  in performing various aspects of the techniques described in this disclosure. The V-vector coding unit  52  may select one of a plurality (meaning, two or more) codebooks to use when vector quantizing the V-vectors  55  ( 790 ). The V-vector coding unit  52  may then perform vector quantization in the manner described above with respect to the V-vectors  55  using the selected one of the two or more codebooks ( 792 ). The V-vector coding unit  52  may then indicate or otherwise signal that one of the two or more codebooks was used in quantizing the V-vector  55  in the bitstream  21  ( 794 ). 
       FIG. 27  is a flowchart illustrating exemplary operation of the V-vector reconstruction unit in performing various aspects of the techniques described in this disclosure. The V-vector reconstruction unit  74  of  FIG. 4A or 4B  may first obtain an indication (such as a syntax element) of one of two or more codebooks used when vector quantizing a V-vector  55  ( 800 ). The V-vector reconstruction unit  74  may then perform vector dequantization to reconstruct the V-vector  55  using the selected one of the two or more codebooks in the manner described above (802). 
     Various aspects of the techniques may enable a device set forth in the following clauses: 
     Clause 1. A device comprising means for storing a plurality of codebooks to use when performing vector quantization with respect to a spatial component of a soundfield, the spatial component obtained through application of a decomposition to a plurality of higher order ambisonic coefficients, and means for selecting one of the plurality of codebooks. 
     Clause 2. The device of clause 1, further comprising means for specifying a syntax element in a bitstream that includes the vector quantized spatial component, the syntax element identifying an index into the selected one of the plurality of codebooks having a weight value used when performing the vector quantization of the spatial component. 
     Clause 3. The device of clause 1, further comprising means for specifying a syntax element in a bitstream that includes the vector quantized spatial component, the syntax element identifying an index into a vector dictionary having a code vector used when performing the vector quantization of the spatial component. 
     Clause 4. The method of clause 1, wherein the means for selecting one of a plurality of codebooks comprises means for selecting the one of the plurality of codebooks based on a number of code vectors used when performing the vector quantization. 
     Various aspects of the techniques may also enable a device set forth in the following clauses: 
     Clause 5. An apparatus comprising means for performing a decomposition with respect to a plurality of higher order ambisonic (HOA) coefficients to generate a decomposed version of the HOA coefficients, and means for determining, based on a set of code vectors, one or more weight values that represent a vector that is included in the decomposed version of the HOA coefficients, each of the weight values corresponding to a respective one of a plurality of weights included in a weighted sum of the code vectors that represents the vector. 
     Clause 6. The apparatus of clause 5, further comprising means for selecting a decomposition codebook from a set of candidate decomposition codebooks, wherein the means for determining, based on the set of code vectors, the one or more weight values comprises means for determining the weight values based on the set of code vectors specified by the selected decomposition codebook. 
     Clause 7. The apparatus of clause 6, wherein each of the candidate decomposition codebooks includes a plurality of code vectors, and wherein at least two of the candidate decomposition codebooks have a different number of code vectors. 
     Clause 8. The apparatus of claim  5 , further comprising means for generating a bitstream to include one or more indices that indicate which code vectors are used for determining the weights, and means for generating the bitstream to further include weighting values corresponding to each of the indices. 
     Any of the foregoing techniques may be performed with respect to any number of different contexts and audio ecosystems. A number of example contexts are described below, although the techniques should be limited to the example contexts. One example audio ecosystem may include audio content, movie studios, music studios, gaming audio studios, channel based audio content, coding engines, game audio stems, game audio coding/rendering engines, and delivery systems. 
     The movie studios, the music studios, and the gaming audio studios may receive audio content. In some examples, the audio content may represent the output of an acquisition. The movie studios may output channel based audio content (e.g., in 2.0, 5.1, and 7.1) such as by using a digital audio workstation (DAW). The music studios may output channel based audio content (e.g., in 2.0, and 5.1) such as by using a DAW. In either case, the coding engines may receive and encode the channel based audio content based one or more codecs (e.g., AAC, AC3, Dolby True HD, Dolby Digital Plus, and DTS Master Audio) for output by the delivery systems. The gaming audio studios may output one or more game audio stems, such as by using a DAW. The game audio coding/rendering engines may code and or render the audio stems into channel based audio content for output by the delivery systems. Another example context in which the techniques may be performed comprises an audio ecosystem that may include broadcast recording audio objects, professional audio systems, consumer on-device capture, HOA audio format, on-device rendering, consumer audio, TV, and accessories, and car audio systems. 
     The broadcast recording audio objects, the professional audio systems, and the consumer on-device capture may all code their output using HOA audio format. In this way, the audio content may be coded using the HOA audio format into a single representation that may be played back using the on-device rendering, the consumer audio, TV, and accessories, and the car audio systems. In other words, the single representation of the audio content may be played back at a generic audio playback system (i.e., as opposed to requiring a particular configuration such as 5.1, 7.1, etc.), such as audio playback system  16 . 
     Other examples of context in which the techniques may be performed include an audio ecosystem that may include acquisition elements, and playback elements. The acquisition elements may include wired and/or wireless acquisition devices (e.g., Eigen microphones), on-device surround sound capture, and mobile devices (e.g., smartphones and tablets). In some examples, wired and/or wireless acquisition devices may be coupled to mobile device via wired and/or wireless communication channel(s). 
     In accordance with one or more techniques of this disclosure, the mobile device may be used to acquire a soundfield. For instance, the mobile device may acquire a soundfield via the wired and/or wireless acquisition devices and/or the on-device surround sound capture (e.g., a plurality of microphones integrated into the mobile device). The mobile device may then code the acquired soundfield into the HOA coefficients for playback by one or more of the playback elements. For instance, a user of the mobile device may record (acquire a soundfield of) a live event (e.g., a meeting, a conference, a play, a concert, etc.), and code the recording into HOA coefficients. 
     The mobile device may also utilize one or more of the playback elements to playback the HOA coded soundfield. For instance, the mobile device may decode the HOA coded soundfield and output a signal to one or more of the playback elements that causes the one or more of the playback elements to recreate the soundfield. As one example, the mobile device may utilize the wireless and/or wireless communication channels to output the signal to one or more speakers (e.g., speaker arrays, sound bars, etc.). As another example, the mobile device may utilize docking solutions to output the signal to one or more docking stations and/or one or more docked speakers (e.g., sound systems in smart cars and/or homes). As another example, the mobile device may utilize headphone rendering to output the signal to a set of headphones, e.g., to create realistic binaural sound. 
     In some examples, a particular mobile device may both acquire a 3D soundfield and playback the same 3D soundfield at a later time. In some examples, the mobile device may acquire a 3D soundfield, encode the 3D soundfield into HOA, and transmit the encoded 3D soundfield to one or more other devices (e.g., other mobile devices and/or other non-mobile devices) for playback. 
     Yet another context in which the techniques may be performed includes an audio ecosystem that may include audio content, game studios, coded audio content, rendering engines, and delivery systems. In some examples, the game studios may include one or more DAWs which may support editing of HOA signals. For instance, the one or more DAWs may include HOA plugins and/or tools which may be configured to operate with (e.g., work with) one or more game audio systems. In some examples, the game studios may output new stem formats that support HOA. In any case, the game studios may output coded audio content to the rendering engines which may render a soundfield for playback by the delivery systems. 
     The techniques may also be performed with respect to exemplary audio acquisition devices. For example, the techniques may be performed with respect to an Eigen microphone which may include a plurality of microphones that are collectively configured to record a 3D soundfield. In some examples, the plurality of microphones of Eigen microphone may be located on the surface of a substantially spherical ball with a radius of approximately 4 cm. In some examples, the audio encoding device  20  may be integrated into the Eigen microphone so as to output a bitstream  21  directly from the microphone. 
     Another exemplary audio acquisition context may include a production truck which may be configured to receive a signal from one or more microphones, such as one or more Eigen microphones. The production truck may also include an audio encoder, such as audio encoder  20  of  FIG. 3A . 
     The mobile device may also, in some instances, include a plurality of microphones that are collectively configured to record a 3D soundfield. In other words, the plurality of microphone may have X, Y, Z diversity. In some examples, the mobile device may include a microphone which may be rotated to provide X, Y, Z diversity with respect to one or more other microphones of the mobile device. The mobile device may also include an audio encoder, such as audio encoder  20  of  FIG. 3A . 
     A ruggedized video capture device may further be configured to record a 3D soundfield. In some examples, the ruggedized video capture device may be attached to a helmet of a user engaged in an activity. For instance, the ruggedized video capture device may be attached to a helmet of a user whitewater rafting. In this way, the ruggedized video capture device may capture a 3D soundfield that represents the action all around the user (e.g., water crashing behind the user, another rafter speaking in front of the user, etc. . . . ). 
     The techniques may also be performed with respect to an accessory enhanced mobile device, which may be configured to record a 3D soundfield. In some examples, the mobile device may be similar to the mobile devices discussed above, with the addition of one or more accessories. For instance, an Eigen microphone may be attached to the above noted mobile device to form an accessory enhanced mobile device. In this way, the accessory enhanced mobile device may capture a higher quality version of the 3D soundfield than just using sound capture components integral to the accessory enhanced mobile device. 
     Example audio playback devices that may perform various aspects of the techniques described in this disclosure are further discussed below. In accordance with one or more techniques of this disclosure, speakers and/or sound bars may be arranged in any arbitrary configuration while still playing back a 3D soundfield. Moreover, in some examples, headphone playback devices may be coupled to a decoder  24  via either a wired or a wireless connection. In accordance with one or more techniques of this disclosure, a single generic representation of a soundfield may be utilized to render the soundfield on any combination of the speakers, the sound bars, and the headphone playback devices. 
     A number of different example audio playback environments may also be suitable for performing various aspects of the techniques described in this disclosure. For instance, a 5.1 speaker playback environment, a 2.0 (e.g., stereo) speaker playback environment, a 9.1 speaker playback environment with full height front loudspeakers, a 22.2 speaker playback environment, a 16.0 speaker playback environment, an automotive speaker playback environment, and a mobile device with ear bud playback environment may be suitable environments for performing various aspects of the techniques described in this disclosure. 
     In accordance with one or more techniques of this disclosure, a single generic representation of a soundfield may be utilized to render the soundfield on any of the foregoing playback environments. Additionally, the techniques of this disclosure enable a rendered to render a soundfield from a generic representation for playback on the playback environments other than that described above. For instance, if design considerations prohibit proper placement of speakers according to a 7.1 speaker playback environment (e.g., if it is not possible to place a right surround speaker), the techniques of this disclosure enable a render to compensate with the other 6 speakers such that playback may be achieved on a 6.1 speaker playback environment. 
     Moreover, a user may watch a sports game while wearing headphones. In accordance with one or more techniques of this disclosure, the 3D soundfield of the sports game may be acquired (e.g., one or more Eigen microphones may be placed in and/or around the baseball stadium), HOA coefficients corresponding to the 3D soundfield may be obtained and transmitted to a decoder, the decoder may reconstruct the 3D soundfield based on the HOA coefficients and output the reconstructed 3D soundfield to a renderer, the renderer may obtain an indication as to the type of playback environment (e.g., headphones), and render the reconstructed 3D soundfield into signals that cause the headphones to output a representation of the 3D soundfield of the sports game. 
     In each of the various instances described above, it should be understood that the audio encoding device  20  may perform a method or otherwise comprise means to perform each step of the method for which the audio encoding device  20  is configured to perform In some instances, the means may comprise one or more processors. In some instances, the one or more processors may represent a special purpose processor configured by way of instructions stored to a non-transitory computer-readable storage medium. In other words, various aspects of the techniques in each of the sets of encoding examples may provide for a non-transitory computer-readable storage medium having stored thereon instructions that, when executed, cause the one or more processors to perform the method for which the audio encoding device  20  has been configured to perform. 
     In one or more examples, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium and executed by a hardware-based processing unit. Computer-readable media may include computer-readable storage media, which corresponds to a tangible medium such as data storage media. Data storage media may be any available media that can be accessed by one or more computers or one or more processors to retrieve instructions, code and/or data structures for implementation of the techniques described in this disclosure. A computer program product may include a computer-readable medium. 
     Likewise, in each of the various instances described above, it should be understood that the audio decoding device  24  may perform a method or otherwise comprise means to perform each step of the method for which the audio decoding device  24  is configured to perform. In some instances, the means may comprise one or more processors. In some instances, the one or more processors may represent a special purpose processor configured by way of instructions stored to a non-transitory computer-readable storage medium. In other words, various aspects of the techniques in each of the sets of encoding examples may provide for a non-transitory computer-readable storage medium having stored thereon instructions that, when executed, cause the one or more processors to perform the method for which the audio decoding device  24  has been configured to perform. 
     By way of example, and not limitation, such computer-readable storage media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage, or other magnetic storage devices, flash memory, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer. It should be understood, however, that computer-readable storage media and data storage media do not include connections, carrier waves, signals, or other transitory media, but are instead directed to non-transitory, tangible storage media. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc, where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. 
     Instructions may be executed by one or more processors, such as one or more digital signal processors (DSPs), general purpose microprocessors, application specific integrated circuits (ASICs), field programmable logic arrays (FPGAs), or other equivalent integrated or discrete logic circuitry. Accordingly, the term “processor,” as used herein may refer to any of the foregoing structure or any other structure suitable for implementation of the techniques described herein. In addition, in some aspects, the functionality described herein may be provided within dedicated hardware and/or software modules configured for encoding and decoding, or incorporated in a combined codec. Also, the techniques could be fully implemented in one or more circuits or logic elements. 
     The techniques of this disclosure may be implemented in a wide variety of devices or apparatuses, including a wireless handset, an integrated circuit (IC) or a set of ICs (e.g., a chip set). Various components, modules, or units are described in this disclosure to emphasize functional aspects of devices configured to perform the disclosed techniques, but do not necessarily require realization by different hardware units. Rather, as described above, various units may be combined in a codec hardware unit or provided by a collection of interoperative hardware units, including one or more processors as described above, in conjunction with suitable software and/or firmware. 
     Various aspects of the techniques have been described. These and other aspects of the techniques are within the scope of the following claims.