Abstract:
Higher Order Ambisonics represents three-dimensional sound independent of a specific loudspeaker set-up. However, transmission of an HOA representation results in a very high bit rate. Therefore compression with a fixed number of channels is used, in which directional and ambient signal components are processed differently. For coding, portions of the original HOA representation are predicted from the directional signal components. This prediction provides side information which is required for a corresponding decoding. By using some additional specific purpose bits, a known side information coding processing is improved in that the required number of bits for coding that side information is reduced on average.

Description:
TECHNICAL FIELD 
       [0001]    The invention relates to a method and to an apparatus for improving the coding of side information required for coding a Higher Order Ambisonics representation of a sound field. 
       BACKGROUND 
       [0002]    Higher Order Ambisonics (HOA) offers one possibility to represent three-dimensional sound among other techniques like wave field synthesis (WFS) or channel based approaches like the 22.2 multichannel audio format. In contrast to channel based methods, the HOA representation offers the advantage of being independent of a specific loudspeaker set-up. This flexibility, however, is at the expense of a decoding process which is required for the playback of the HOA representation on a particular loudspeaker set-up. Compared to the WFS approach, where the number of required loudspeakers is usually very large, HOA signals may also be rendered to set-ups consisting of only few loudspeakers. A further advantage of HOA is that the same representation can also be employed without any modification for binaural rendering to head-phones. 
         [0003]    HOA is based on the representation of the spatial density of complex harmonic plane wave amplitudes by a truncated Spherical Harmonics (SH) expansion. Each expansion coefficient is a function of angular frequency, which can be equivalently represented by a time domain function. Hence, without loss of generality, the complete HOA sound field representation actually can be assumed to consist of O time domain functions, where O denotes the number of expansion coefficients. These time domain functions will be equivalently referred to as HOA coefficient sequences or as HOA channels in the following. 
         [0004]    The spatial resolution of the HOA representation improves with a growing maximum order N of the expansion. Unfortunately, the number of expansion coefficients O grows quadratically with the order N, in particular O=(N+1) 2 . For example, typical HOA representations using order N=4 require O=25 HOA (expansion) coefficients. According to the previously made considerations, the total bit rate for the transmission of HOA representation, given a desired single-channel sampling rate f s  and the number of bits N b  per sample, is determined by O·f s ·N b . Consequently, transmitting an HOA representation of order N=4 with a sampling rate of f s =48 kHz employing N b =16 bits per sample results in a bit rate of 19.2 MBits/s, which is very high for many practical applications like e.g. streaming. Thus, compression of HOA representations is highly desirable. 
         [0005]    The compression of HOA sound field representations is proposed in WO 2013/171083 A1, EP 13305558.2 and PCT/EP2013/075559. These processings have in common that they perform a sound field analysis and decompose the given HOA representation into a directional component and a residual ambient component. On one hand the final compressed representation is assumed to consist of a number of quantised signals, resulting from the perceptual coding of the directional signals and relevant coefficient sequences of the ambient HOA component. On the other hand it is assumed to comprise additional side information related to the quantised signals, which side information is necessary for the reconstruction of the HOA representation from its compressed version. 
         [0006]    An important part of that side information is a description of a prediction of portions of the original HOA representation from the directional signals. Since for this prediction the original HOA representation is assumed to be equivalently represented by a number of spatially dispersed general plane waves impinging from spatially uniformly distributed directions, the prediction is referred to as spatial prediction in the following. 
         [0007]    The coding of such side information related to spatial prediction is described in ISO/IEC JTC1/SC29/WG11, N14061, “Working Draft Text of MPEG-H 3D Audio HOA RMO”, November 2013, Geneva, Switzerland. However, this state-of-the-art coding of the side information is rather inefficient. 
       SUMMARY OF INVENTION 
       [0008]    A problem to be solved by the invention is to provide a more efficient way of coding side information related to that spatial prediction. 
         [0009]    This problem is solved by the methods disclosed in claims  1  and  6 . An apparatus that utilises these methods is disclosed in claims  2  and  7 . 
         [0010]    A bit is prepended to the coded side information representation data ζ COD , which bit signals whether or not any prediction is to be performed. This feature reduces over time the average bit rate for the transmission of the ζ COD  data. Further, in specific situations, instead of using a bit array indicating for each direction if the prediction is performed or not, it is more efficient to transmit or transfer the number of active predictions and the respective indices. A single bit can be used for indicating in which way the indices of directions are coded for which a prediction is supposed to be performed. On average, this operation over time further reduces the bit rate for the transmission of the ζ COD  data. 
         [0011]    In principle, the inventive method is suited for improving the coding of side information required for coding a Higher Order Ambisonics representation of a sound field, denoted HOA, with input time frames of HOA coefficient sequences, wherein dominant directional signals as well as a residual ambient HOA component are determined and a prediction is used for said dominant directional signals, thereby providing, for a coded frame of HOA coefficients, side information data describing said prediction, and wherein said side information data can include:
   a bit array indicating whether or not for a direction a prediction is performed;   a bit array in which each bit indicates, for the directions where a prediction is to be performed, the kind of the prediction;   a data array whose elements denote, for the predictions to be performed, indices of the directional signals to be used;   a data array whose elements represent quantised scaling factors,   
 
         [0016]    said method including the step:
   providing a bit value indicating whether or not said prediction is to be performed;   if no prediction is to be performed, omitting said bit arrays and said data arrays in said side information data;   if said prediction is to be performed, providing a bit value indicating whether or not, instead of said bit array indicating whether or not for a direction a prediction is performed, a number of active predictions and a data array containing the indices of directions where a prediction is to be performed are included in said side information data.   
 
         [0020]    In principle the inventive apparatus is suited for improving the coding of side information required for coding a Higher Order Ambisonics representation of a sound field, denoted HOA, with input time frames of HOA coefficient sequences, wherein dominant directional signals as well as a residual ambient HOA component are determined and a prediction is used for said dominant directional signals, thereby providing, for a coded frame of HOA coefficients, side information data describing said prediction, and wherein said side information data can include:
   a bit array indicating whether or not for a direction a prediction is performed;   a bit array in which each bit indicates, for the directions where a prediction is to be performed, the kind of the prediction;   a data array whose elements denote, for the predictions to be performed, indices of the directional signals to be used;   a data array whose elements represent quantised scaling factors, said apparatus including means which:   provide a bit value indicating whether or not said prediction is to be performed;   if no prediction is to be performed, omit said bit arrays and said data arrays in said side information data;   if said prediction is to be performed, provide a bit value indicating whether or not, instead of said bit array indicating whether or not for a direction a prediction is performed, a number of active predictions and a data array containing the indices of directions where a prediction is to be performed are included in said side information data.   
 
         [0028]    Advantageous additional embodiments of the invention are disclosed in the respective dependent claims. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0029]    Exemplary embodiments of the invention are described with reference to the accompanying drawings, which show in: 
           [0030]      FIG. 1  Exemplary coding of side information related to spatial prediction in the HOA compression processing described in EP 13305558.2; 
           [0031]      FIG. 2  Exemplary decoding of side information related to spatial prediction in the HOA decompression processing described in patent application EP 13305558.2; 
           [0032]      FIG. 3  HOA decomposition as described in patent application PCT/EP2013/075559; 
           [0033]      FIG. 4  Illustration of directions (depicted as crosses) of general plane waves representing the residual signal and the directions (depicted as circles) of dominant sound sources. The directions are presented in a three-dimensional coordinate system as sampling positions on the unit sphere; 
           [0034]      FIG. 5  State of art coding of spatial prediction side information; 
           [0035]      FIG. 6  Inventive coding of spatial prediction side information; 
           [0036]      FIG. 7  Inventive decoding of coded spatial prediction side information; 
           [0037]      FIG. 8  Continuation of  FIG. 7 . 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0038]    In the following, the HOA compression and decompression processing described in patent application EP 13305558.2 is recapitulated in order to provide the context in which the inventive coding of side information related to spatial prediction is used. 
       HOA Compression 
       [0039]    In  FIG. 1  it is illustrated how the coding of side information related to spatial prediction can be embedded into the HOA compression processing described patent application EP 13305558.2. For the HOA representation compression, a frame-wise processing with non-overlapping input frames C(k) of HOA coefficient sequences of length L is assumed, where k denotes the frame index. The first step or stage  11 / 12  in  FIG. 1  is optional and consists of concatenating the non-overlapping k-th and (k−1)-th frames of HOA coefficient sequences C(k) into a long frame {tilde over (C)}(k) as 
         [0000]        {tilde over (C)} ( k ):=[ C ( k− 1)  C ( k )],   (1)
 
         [0000]    which long frame is 50% overlapped with an adjacent long frame and which long frame is successively used for the estimation of dominant sound source directions. Similar to the notation for {tilde over (C)}(k), the tilde symbol is used in the following description for indicating that the respective quantity refers to long overlapping frames. If step/stage  11 / 12  is not present, the tilde symbol has no specific meaning. A parameter in bold means a set of values, e.g. a matrix or a vector. 
         [0040]    The long frame {tilde over (C)}(k) is successively used in step or stage  13  for the estimation of dominant sound source directions as described in EP 13305558.2. This estimation provides a data set            DIR,ACT (k) ⊂ {1, . . . , D} of indices of the related directional signals that have been detected, as well as a data set            Ω,ACT (k) of the corresponding direction estimates of the directional signals. D denotes the maximum number of directional signals that has to be set before starting the HOA compression and that can be handled in the known processing which follows. 
         [0041]    In step or stage  14 , the current (long) frame {tilde over (C)}(k) of HOA coefficient sequences is decomposed (as proposed in EP 13305156.5) into a number of directional signals X DIR (k−2) belonging to the directions contained in the set            Ω,ACT (k), and a residual ambient HOA component C AMB (k−2). The delay of two frames is introduced as a result of overlap-add processing in order to obtain smooth signals. It is assumed that X DIR (k−2) is containing a total of D channels, of which however only those corresponding to the active directional signals are non-zero. The indices specifying these channels are assumed to be output in the data set            DIR,ACT (k−2) Additionally, the decomposition in step/stage  14  provides some parameters ζ(k−2) which can be used at decompression side for predicting portions of the original HOA representation from the directional signals (see EP 13305156.5 for more details). In order to explain the meaning of the spatial prediction parameters ζ(k−2), the HOA decomposition is described in more detail in the below section HOA decomposition. 
         [0042]    In step or stage  15 , the number of coefficients of the ambient HOA component C AMB (k−2) is reduced to contain only O RED +D−N DIR,ACT (k−2) non-zero HOA coefficient sequences, where N DIR,ACT (k−2)=|           DIR,ACT (k−2)| indicates the cardinality of the data set            DIR,ACT (k−2), i.e. the number of active directional signals in frame k−2. Since the ambient HOA component is assumed to be always represented by a minimum number O RED  of HOA coefficient sequences, this problem can be actually reduced to the selection of the remaining D−N DIR,ACT (k−2) HOA coefficient sequences out of the possible O-O RED  ones. In order to obtain a smooth reduced ambient HOA representation, this choice is accomplished such that, compared to the choice taken at the previous frame k−3, as few changes as possible will occur. 
         [0043]    The final ambient HOA representation with the reduced number of O RED +N DIR,ACT (k−2) non-zero coefficient sequences is denoted by C AMB,RED (k−2). The indices of the chosen ambient HOA coefficient sequences are output in the data set            AMB,ACT (k−2) In step/stage  16 , the active directional signals contained in X DIR (k−2) and the HOA coefficient sequences contained in C AMB,RED (k−2) are assigned to the frame Y(k−2) of I channels for individual perceptual encoding as described in EP 13305558.2. Perceptual coding step/stage  17  encodes the I channels of frame Y(k−2) and outputs an encoded frame {hacek over (Y)}(k−2). 
         [0044]    According to the invention, following the decomposition of the original HOA representation in step/stage  14 , the spatial prediction parameters or side information data ζ(k−2) resulting from the decomposition of the HOA representation are losslessly coded in step or stage  19  in order to provide a coded data representation ζ COD (k−2), using the index set            DIR,ACT (k) delayed by two frames in delay  18 . 
       HOA Decompression 
       [0045]    In  FIG. 2  it is exemplary shown how to embed in step or stage  25  the decoding of the received encoded side information ζ COD (k−2) related to spatial prediction into the HOA decompression processing described in  FIG. 3  of patent application EP 13305558.2. The decoding of the encoded side information data ζ COD (k−2) is carried out before entering its decoded version λ(k−2) into the composition of the HOA representation in step or stage  23 , using the received index set            DIR,ACT (k) delayed by two frames in delay  24 . 
         [0046]    In step or stage  21  a perceptual decoding of the I signals contained in {hacek over (Y)}(k−2) is performed in order to obtain the I decoded signals in Ŷ(k−2). 
         [0047]    In signal re-distributing step or stage  22 , the perceptually decoded signals in Ŷ(k−2) are re-distributed in order to recreate the frame {circumflex over (X)} DIR (k−2) of directional signals and the frame Ĉ AMB,RED (k−2) of the ambient HOA component. The information about how to re-distribute the signals is obtained by reproducing the assigning operation performed for the HOA compression, using the index data sets            DIR,ACT (k) and            AMB,ACT (k−2). In composition step or stage  23 , a current frame Ĉ(k−3) of the desired total HOA representation is re-composed (according to the processing described in connection with FIGS. 2 b  and FIG. 4 of PCT/EP2013/075559 using the frame {circumflex over (X)} DIR (k−2) of the directional signals, the set            DIR,ACT (k) of the active directional signal indices together with the set            Ω,ACT (k) of the corresponding directions, the parameters ζ(k−2) for predicting portions of the HOA representation from the directional signals, and the frame Ĉ AMB,RED (k−2) of HOA coefficient sequences of the reduced ambient HOA component. 
         [0048]    Ĉ AMB,RED (k−2) corresponds to component {circumflex over (D)} A (k−2) in PCT/EP2013/075559, and            Ω,ACT (k) and            DIR,ACT (k) correspond to A {circumflex over (Ω)} (k) in PCT/EP2013/075559, wherein active directional signal indices can be obtained by taking those indices of rows of A {circumflex over (Ω)} (k) which contain valid elements. I.e., directional signals with respect to uniformly distributed directions are predicted from the directional signals {circumflex over (X)} DIR (k−2) using the received parameters ζ(k−2) for such prediction, and thereafter the current decompressed frame Ĉ(k−3) is re-composed from the frame of directional signals {circumflex over (X)} DIR (k−2), from            DIR,ACT (k) and            Ω,ACT (k), and from the predicted portions and the reduced ambient HOA component Ĉ AMB,RED (k−2). 
       HOA Decomposition 
       [0049]    In connection with  FIG. 3  the HOA decomposition processing is described in detail in order to explain the meaning of the spatial prediction therein. This processing is derived from the processing described in connection with FIG. 3 of patent application PCT/EP2013/075559. 
         [0050]    First, the smoothed dominant directional signals X DIR (k−1) and their HOA representation C DIR (k−1) are computed in step or stage  31 , using the long frame {tilde over (C)}(k) of the input HOA representation, the set            Ω,ACT (k) of directions and the set            DIR,ACT (k) of corresponding indices of directional signals. It is assumed that X DIR (k−1) contains a total of D channels, of which however only those corresponding to the active directional signals are non-zero. The indices specifying these channels are assumed to be output in the set            DIR,ACT (k−1). In step or stage  33  the residual between the original HOA representation {tilde over (C)}(k−1) and the HOA representation C DIR (k−1) of the dominant directional signals is represented by a number of O directional signals {tilde over (X)} RES (k−1), which can be considered as being general plane waves from uniformly distributed directions, which are referred to a uniform grid. 
         [0051]    In step or stage  34  these directional signals are predicted from the dominant directional signals X DIR (k−1) in order to provide the predicted signals {tilde over ({circumflex over (X)})} RES (k−1) together with the respective prediction parameters ζ(−1). For the prediction only the dominant directional signals x DIR,ACT (k−1) with indices d, which are contained in the set            DIR,ACT (k−1), are considered. The prediction is described in more detail in the below section Spatial prediction. 
         [0052]    In step or stage  35  the smoothed HOA representation Ĉ RES (k−2) of the predicted directional signals {tilde over ({circumflex over (X)})} RES (k−1) is computed. In step or stage  37  the residual C AMB (k−2) between the original HOA representation {tilde over (C)}(k−2) and the HOA representation C DIR (k−2) of the dominant directional signals together with the HOA representation Ĉ RES (k−2) of the predicted directional signals from uniformly distributed directions is computed and is output. 
         [0053]    The required signal delays in the  FIG. 3  processing are performed by corresponding delays  381  to  387 . 
       Spatial Prediction 
       [0054]    The goal of the spatial prediction is to predict the O residual signals 
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         [0000]    of smoothed directional signals (see the description in above section HOA decomposition and in patent application PCT/EP2013/075559). 
         [0055]    Each residual signal {tilde over (x)} RES,GRID,q (k−1), q=1, . . . , O, represents a spatially dispersed general plane wave impinging from the direction Ω q , whereby it is assumed that all the directions Ω q , q=1, . . . , O l are nearly uniformly distributed over the unit sphere. The total of all directions is referred to as a ‘grid’. 
         [0056]    Each directional signal {tilde over (x)} DIR,d (k−1), d=1, . . . , D represents a general plane wave impinging from a trajectory interpolated between the directions Ω ACT,d (k−3), Ω ACT,d (k−2). Ω ACT,d (k−1) and Ω ACT,d (k), assuming that the d-th directional signal is active for the respective frames. 
         [0057]    To illustrate the meaning of the spatial prediction by means of an example, the decomposition of an HOA representation of order N=3 is considered, where the maximum number of directions to extract is equal to D=4. For simplicity it is further assumed that only the directional signals with indices ‘1’ and ‘4’ are active, while those with indices ‘2’ and ‘3’ are non-active. Additionally, for simplicity it is assumed that the directions of the dominant sound sources are constant for the considered frames, i.e. 
         [0000]      Ω ACT,d ( k− 3)=Ω ACT,d ( k− 2)=Ω ACT,d ( k− 1)= ΩACT,d ( k )=Ω ACT,d  for  d= 1,4   (5)
 
         [0058]    As a consequence of order N=3, there are O=16 directions Ω q  of spatially dispersed general plane waves {tilde over (x)} RES,GRID,q (k−1), q=1, . . . , O.  FIG. 4  shows these directions together with the directions Ω ACT,1  and Ω ACT,4  of the active dominant sound sources. 
         [0059]    State-of-the-Art Parameters for Describing the Spatial Prediction 
         [0060]    One way of describing the spatial prediction is presented in the above-mentioned ISO/IEC document. In this document, the signals {tilde over (x)} RES,GRID,q (k−1), q=1, . . . , O are assumed to be predicted by a weighted sum of a predefined maximum number D PRED  of directional signals, or by a low pass filtered version of the weighted sum. The side information related to spatial prediction is described by the parameter set ζ(k−1)={p TYPE (k−1), P IND (k−1), P Q,F (k−1)}, which consists of the following three components:
   The vector p TYPE (k−1) whose elements p TYPE,q (k−1), q=1, . . . , O indicate whether or not for the q-th direction Ω q  a prediction is performed, and if so, then they also indicate which kind of prediction. The meaning of the elements is as follows:   
 
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         The matrix P IND (k−1), whose elements p IND,d,q (k−1), d=1, . . . D PRED , q=1, . . . , O denote the indices from which directional signals the prediction for the direction Ω q  has to be performed. If no prediction is to be performed for a direction Ω q , the corresponding column of the matrix P IND (k−1) consists of zeros. Further, if less than D PRED  directional signals are used for the prediction for a direction Ω q , the non-required elements in the q-th column of P IND (k−1) are also zero. 
         The matrix P Q,F (k−1), which contains the corresponding quantised prediction factors p Q,F,d,q (k−1), d=1, . . . , D PRED , q=1, . . . , O. 
       
     
         [0064]    The following two parameters have to be known at decoding side for enabling the appropriate interpretation of these parameters:
   The maximum number D PRED  of directional signals, from which a general plane wave signal {tilde over (x)} RES,GRID,q (k−1) is allowed to be predicted.   The number B SC  of bits used for quantising the prediction factors p Q,F,d,q (k−1), d=1, . . . , D PRED , q=1, . . . , O. The de quantisation rule is given in equation (10).   
 
         [0067]    These two parameters have to either be set to fixed values known to the encoder and decoder, or to be additionally transmitted, but distinctly less frequently than the frame rate. The latter option may be used for adapting the two parameters to the HOA representation to be compressed. 
         [0068]    An example for a parameter set may look like the following, assuming O=16, D PRED =2 and B SC =8: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         p 
                         TYPE 
                       
                        
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             2 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         p 
                         IND 
                       
                        
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             4 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       
                         Q 
                         , 
                         F 
                       
                     
                      
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             40 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             15 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               - 
                               13 
                             
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0069]    Such parameters would mean that the general plane wave signal {tilde over (x)} RES,GRID,1 (k−1) from direction Ω 1  is predicted from the directional signal {tilde over (x)} DIR,1 (k−1) from direction Ω ACT,1  by a pure multiplication (i.e. full band) with a factor that results from de-quantising the value  40 . Further, the general plane wave signal {tilde over (x)} RES,GRID,7 (k−1) from direction Ω 7  is predicted from the directional signals {tilde over (x)} DIR,1 (k−1) and {tilde over (x)} DIR,4 (k−1) by a lowpass filtering and multiplication with factors that result from de-quantising the values 15 and −13. 
         [0070]    Given this side information, the prediction is assumed to be performed as follows: 
         [0071]    First, the quantised prediction factors p Q,F,d,q (k−1), d=1, . . . , D PRED , q=1, . . . , O are dequantised to provide the actual prediction factors 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       p 
                       
                         F 
                         , 
                         d 
                         , 
                         q 
                       
                     
                      
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       p 
                                       
                                         Q 
                                         , 
                                         F 
                                         , 
                                         d 
                                         , 
                                         q 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     1 
                                     2 
                                   
                                 
                                 ) 
                               
                                
                               
                                 2 
                                 
                                   
                                     - 
                                     
                                       B 
                                       SC 
                                     
                                   
                                   + 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     p 
                                     
                                       IND 
                                       , 
                                       d 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               ≠ 
                               0 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     p 
                                     
                                       IND 
                                       , 
                                       d 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               = 
                               0 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0072]    As already mentioned, B SC  denotes a predefined number of bits to be used for the quantisation of the prediction factors. Additionally, p F,d,q (k−1) is assumed to be set to zero, if p IND,d,q (k−1) is equal to zero. 
         [0073]    For the previously mentioned example, assuming B SC =8, the de-quantised prediction factor vector would result in 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       F 
                     
                      
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   ≈ 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               0.3164 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0.1211 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 - 
                                 0.0977 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0074]    Further, for performing a low pass prediction a predefined low pass FIR filter 
         [0000]        h   LP   :=[h   LP (0)  h   LP (1) . . .  h   LP ( L   h −1)]  (12)
 
         [0000]    of length L h =31 is used. The filter delay is given by D h =15 samples. 
         [0075]    Assuming as signals the predicted signals 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         X 
                         
                           ~ 
                           ^ 
                         
                       
                       RES 
                     
                      
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 x 
                                 
                                   ~ 
                                   ^ 
                                 
                               
                               
                                 RES 
                                 , 
                                 1 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 
                                   ~ 
                                   ^ 
                                 
                               
                               
                                 RES 
                                 , 
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 
                                   ~ 
                                   ^ 
                                 
                               
                               
                                 RES 
                                 , 
                                 O 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and the directional signals 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         X 
                         ~ 
                       
                       DIR 
                     
                      
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 x 
                                 ~ 
                               
                               
                                 DIR 
                                 , 
                                 1 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 ~ 
                               
                               
                                 DIR 
                                 , 
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 ~ 
                               
                               
                                 DIR 
                                 , 
                                 D 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0000]    to be composed of their samples by 
         [0000]      {tilde over ({circumflex over ( x )})} RES,q (k−1)=[{tilde over ({circumflex over ( x )})} RES,q ( k− 1,1) {tilde over ({circumflex over ( x )})} RES,q (k−1,2) . . . {tilde over ({circumflex over ( x )})} RES,q ( k− 1,2 L )] for  q= 1, . . . , O,   (15)
 
         [0000]    and 
         [0000]        {tilde over (x)}   DIR,d ( k− 1)=[ {tilde over (x)}   DIR,d (k−1,1)  {tilde over (x)}   DIR,d ( k− 1,2) . . .  {tilde over (x)}   DIR,d l (   k− 1,3 L )] for  d= 1, . . . , D,   (16)
 
         [0000]    the sample values of the predicted signals are given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           ~ 
                         
                         ^ 
                       
                       
                         RES 
                         , 
                         q 
                       
                     
                      
                     
                       ( 
                       
                         
                           k 
                           - 
                           1 
                         
                         , 
                         l 
                       
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             0 
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     p 
                                     
                                       TYPE 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               = 
                               0 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     
                                       ∑ 
                                       
                                         d 
                                         = 
                                         1 
                                       
                                       
                                         D 
                                         PRED 
                                       
                                     
                                      
                                     
                                       
                                         
                                           p 
                                           
                                             F 
                                             , 
                                             d 
                                             , 
                                             q 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             k 
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                       · 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         x 
                                         ~ 
                                       
                                       
                                         DIR 
                                         , 
                                         
                                           
                                             p 
                                             
                                               IND 
                                               , 
                                               d 
                                               , 
                                               q 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               k 
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           k 
                                           - 
                                           1 
                                         
                                         , 
                                         
                                           L 
                                           + 
                                           l 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     p 
                                     
                                       TYPE 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               = 
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   d 
                                   = 
                                   1 
                                 
                                 
                                   D 
                                   PRED 
                                 
                               
                                
                               
                                 
                                   
                                     p 
                                     
                                       F 
                                       , 
                                       d 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 · 
                                 
                                   
                                     
                                       y 
                                       ~ 
                                     
                                     
                                       LP 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       , 
                                       l 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     p 
                                     
                                       TYPE 
                                       , 
                                       q 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               = 
                               2 
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                           
                       
                        
                       with 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         y 
                         ~ 
                       
                       
                         LP 
                         , 
                         q 
                       
                     
                      
                     
                       ( 
                       
                         
                           k 
                           - 
                           1 
                         
                         , 
                         l 
                       
                       ) 
                     
                   
                   := 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         0 
                       
                       
                         min 
                          
                         
                           ( 
                           
                             
                               
                                 L 
                                 h 
                               
                               - 
                               1 
                             
                             , 
                             
                               l 
                               + 
                               
                                 2 
                                  
                                 
                                   D 
                                   h 
                                 
                               
                               - 
                               1 
                             
                           
                           ) 
                         
                       
                     
                      
                     
                       
                         
                           h 
                           LP 
                         
                          
                         
                           ( 
                           j 
                           ) 
                         
                       
                       · 
                       
                         
                           
                             
                               x 
                               ~ 
                             
                             
                               DIR 
                               , 
                               
                                 
                                   p 
                                   
                                     IND 
                                     , 
                                     d 
                                     , 
                                     q 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 - 
                                 1 
                               
                               , 
                               
                                 L 
                                 + 
                                 l 
                                 + 
                                 
                                   D 
                                   h 
                                 
                                 - 
                                 j 
                               
                             
                             ) 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0076]    As already mentioned and as now can be seen from equation (17), the signals {tilde over (x)} RES,GRID,q (k−1), q=1, . . . , O are assumed to be predicted by a weighted sum of a predefined maximum number D PRED  of directional signals, or by a low pass filtered versions of the weighted sum. 
       State-of-the-Art Coding of the Side Information Related to Spatial Prediction 
       [0077]    In the above-mentioned ISO/IEC document the coding of the spatial prediction side information is addressed. It is summarised in Algorithm 1 depicted in  FIG. 5  and will be explained in the following. For a clearer presentation the frame index k−1 is neglected in all expressions. First, a bit array ActivePred consisting of 0 bits is created, in which the bit ActivePred[q] indicates whether or not for the direction Ω q  a prediction is performed. The number of ‘ones’ in this array is denoted by NumActivePred. 
         [0078]    Next, the bit array PredType of length NumActivePred is created where each bit indicates, for the directions where a prediction is to be performed, the kind of the prediction, i.e. full band or low pass. At the same time, the unsigned integer array PredDirSigIds of length NumActivePred D PRED  is created, whose elements denote for each active prediction the D PRED  indices of the directional signals to be used. If less than D PRED  directional signals are to be used for the prediction, the indices are assumed to be set to zero. Each element of the array PredDirSigIds is assumed to be represented by ┌log 2 (D+1)┐ bits. The number of non-zero elements in the array PredDirSigIds is denoted by NumNonZeroIds. 
         [0079]    Finally, the integer array QuantPredGains of length NumNonZeroIds is created, whose elements are assumed to represent the quantised scaling factors P Q,F,d,q (k−1) to be used in equation (17). The dequantisation to obtain the corresponding dequantised scaling factors P F,d,q (k−1) is given in equation (10). 
         [0080]    Each element of the array QuantPredGains is assumed to be represented by B SC  bits. 
         [0081]    In the end, the coded representation of the side information ζ COD  consists of the four aforementioned arrays according to 
         [0000]      ζ COD =[ActivePred PredType PredDirSigIds QuantPredGains].   (19)
 
         [0082]    For explaining this coding by an example, the coded representation of equations (7) to (9) is used: 
         [0000]      ActivePred=[1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]  (20)
 
         [0000]      PredType=[0 1]  (21)
 
         [0000]      PredDirSigIds=[1 0 1 4]  (22)
 
         [0000]      QuantPredGains=[40 15 −13].   (23)
 
         [0083]    The number of required bits is equal to 16+2+3·4+8·3=54. 
       Inventive Coding of the Side Information Related to Spatial Prediction 
       [0084]    In order to increase the efficiency of the coding of the side information related to spatial prediction, the state-of-the-art processing is advantageously modified.
   A) When coding HOA representations of typical sound scenes, the inventors have observed that there are often frames where in the HOA compression processing the decision is taken to not perform any spatial prediction at all. However, in such frames the bit array ActivePred consists of zeros only, the number of which is equal to 0. Since such frame content occurs quite often, the inventive processing prepends to the coded representation ζ COD  a single bit PSPredictionActive, which indicates if any prediction is to be performed or not. If the value of the bit PSPredictionActive is zero (or ‘1’ as an alternative), the array ActivePred and further data related to the prediction are not to be included into the coded side information ζ COD . In practise, this operation reduces over time the average bit rate for the transmission of ζ COD .   B) A further observation made while coding HOA representations of typical sound scenes is that the number NumActivePred of active prediction is often very low. In such situation, instead of using the bit array ActivePred for indicating for each direction Ω q  whether or not the prediction is performed, it can be more efficient to transmit or transfer instead the number of active predictions and the respective indices. In particular, this modified kind of coding the activity is more efficient in case that   
 
         [0000]      NumActivePred≦M M ,   (24)
 
         [0000]    where M M  is the greatest integer number that satisfies 
         [0000]      ┌log 2 ( M   M )┐+ M   M ·┌log 2 ( O )┐&lt; O.    (25)
 
         [0087]    The value of M M  can be computed only with the knowledge of the HOA order N: O=(N+1) 2  as mentioned above. 
         [0088]    In equation (25), ┌log 2 (M M )┐ denotes the number of bits required for coding the actual number NumActivePred of active predictions, and M M ·┌log 2 (O)┐ is the number of bits required for coding the respective direction indices. The right hand side of equation (25) corresponds to the number of bits of the array ActivePred, which would be required for coding the same information in the known way. According to the aforementioned explanations, a single bit KindOfCodedPredIds can be used for indicating in which way the indices of those directions, where a prediction is supposed to be performed, are coded. If the bit KindOfCodedPredIds has the value ‘1’ (or ‘0’ in the alternative), the number NumActivePred and the array PredIds containing the indices of directions, where a prediction is supposed to be performed, are added to the coded side information ζ COD . Otherwise, if the bit KindOfCodedPredIds has the value ‘0’ (or ‘1’ in the alternative), the array ActivePred is used to code the same information. On average, this operation reduces over time the bit rate for the transmission of ζ COD .
   C) To further increase the side information coding efficiency, the fact is exploited that often the actually available number of active directional signals to be used for prediction is less than D. This means that for the coding of each element of the index array PredDirSigIds less than ┌log 2 (D+1)┐ bits are required. In particular, the actually available number of active directional signals to be used for prediction is given by the number {tilde over (D)} ACT  of elements of the data set            DIR,ACT , which contains the indices {tilde over (l)} ACT,1 , . . . , {tilde over (l)} ACT,{tilde over (D)}     ACT    of the active directional signals. Hence, ┌log 2 (|{tilde over (D)} ACT +1|)┐ bits can be used for coding each element of the index array PredDirSigIds, which kind of coding is more efficient. In the decoder the data set            DIR,ACT  is assumed to be known, and thus the decoder also knows how many bits have to be read for decoding an index of a directional signal. Note that the frame indices of ζ COD  to be computed and the used index data set            DIR,ACT  have to be identical.   
 
         [0090]    The above modifications A) to C) for the known side information coding processing result in the example coding processing depicted in  FIG. 6 . 
         [0091]    Consequently, the coded side information consists of the following components: 
         [0000]    
       
         
           
             
               
                 
                   
                     ζ 
                     COD 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             [ 
                             PSPredictionActive 
                             ] 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               PSPredictionActive 
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           
                             [ 
                             
                               
                                 
                                   PSPredictionActive 
                                 
                               
                               
                                 
                                   KindOfCodedPredIds 
                                 
                               
                               
                                 
                                   ActivePred 
                                 
                               
                               
                                 
                                   PredType 
                                 
                               
                               
                                 
                                   PredDirSigIds 
                                 
                               
                               
                                 
                                   QuantPredGains 
                                 
                               
                             
                             ] 
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     if 
                                      
                                     
                                         
                                     
                                      
                                     PSPredictionActive 
                                   
                                   = 
                                 
                               
                             
                             
                               
                                 
                                   
                                     1 
                                      
                                     KindOfCodedPredIds 
                                   
                                   = 
                                   0 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             [ 
                             
                               
                                 
                                   PSPredictionActive 
                                 
                               
                               
                                 
                                   KindOfCodedPredIds 
                                 
                               
                               
                                 
                                   NumActivePred 
                                 
                               
                               
                                 
                                   PredIds 
                                 
                               
                               
                                 
                                   PredType 
                                 
                               
                               
                                 
                                   PredDirSigIds 
                                 
                               
                               
                                 
                                   QuantPredGains 
                                 
                               
                             
                             ] 
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     if 
                                      
                                     
                                         
                                     
                                      
                                     PSPredictionActive 
                                   
                                   = 
                                 
                               
                             
                             
                               
                                 
                                   
                                     1 
                                      
                                     KindOfCodedPredIds 
                                   
                                   = 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
         [0092]    Remark: in the above-mentioned ISO/IEC document e.g. in section 6.1.3, QuantPredGains is called PredGains, which however contains quantised values. 
         [0093]    The coded representation for the example in equations (7) to (9) would be: 
         [0000]      PSPredictionActive=1   (27)
 
         [0000]      KindOfCodedPredIds=1   (28)
 
         [0000]      NumActivePred=2   (29)
 
         [0000]      PredIds=[1 7]  (30)
 
         [0000]      PredType=[0 1]  (31)
 
         [0000]      PredDirSigIds=[1 0 1 4]  (32)
 
         [0000]      QuantPredGains=[40 15 −13],   (33)
 
         [0000]    and the required number of bits is 1+1+2+2·4+2+2·4+8·3=46. Advantageously, compared to the state of the art coded representation in equations (20) to (23), this representation coded according to the invention requires 8 bits less. 
         [0094]    It is also possible to not provide bit array PredType at encoder side. 
       Decoding of the Modified Side Information Coding Related to Spatial Prediction 
       [0095]    The decoding of the modified side information related to spatial prediction is summarised in the example decoding processing depicted in  FIG. 7  and  FIG. 8  (the processing depicted in  FIG. 8  is the continuation of the processing depicted in  FIG. 7 ) and is explained in the following. 
         [0096]    Initially, all elements of vector p TYPE  and matrices P IND  and P Q,F  are initialised by zero. Then the bit PSPredictionActive is read, which indicates if a spatial prediction is to be performed at all. In the case of a spatial prediction (i.e. PSPredictionActive=1), the bit KindOfCodedPredIds is read, which indicates the kind of coding of the indices of directions for which a prediction is to be performed. 
         [0097]    In the case that KindOfCodedPredIds=0, the bit array ActivePred of length O is read, of which the q-th element indicates if for the direction Ω q  a prediction is performed or not. In a next step, from the array ActivePred the number NumActivePred of predictions is computed and the bit array PredType of length NumActivePred is read, of which the elements indicate the kind of prediction to be performed for each of the relevant directions. With the information contained in ActivePred and PredType, the elements of the vector p TYPE  are computed. 
         [0098]    It is also possible to not provide bit array PredType at encoder side and to compute the elements of vector p TYPE  from bit array ActivePred. 
         [0099]    In case KindOfCodedPredIds=1, the number NumActivePred of active predictions is read, which is assumed to be coded with ┌log 2 (M M )┐ bits, where M M  is the greatest integer number satisfying equation (25). Then, the data array PredIds consisting of NumActivePred elements is read, where each element is assumed to be coded by ┌log 2 (O)┐ bits. The elements of this array are the indices of directions, where a prediction has to be performed. Successively, the bit array PredType of length NumActivePred is read, of which the elements indicate the kind of prediction to be performed for each one of the relevant directions. With the knowledge of NumActivePred, PredIds and PredType, the elements of the vector p TYPE  are computed. 
         [0100]    It is also possible to not provide bit array PredType at encoder side and to compute the elements of vector p TYPE  from number NumActivePred and from data array PredIds. 
         [0101]    For both cases (i.e. KindOfCodedPredIds=0 and KindOfCodedPredIds=1), in the next step the array PredDirSigIds is read, which consists of NumActivePred·D PRED  elements. Each element is assumed to be coded by ┌log 2 ({tilde over (D)} ACT )┐ bits. Using the information contained in p TYPE ,            5   DIR,ACT  and PredDirSigIds, the elements of matrix P IND  are set and the number NumNonZeroIds of non-zero elements in P IND  is computed. 
         [0102]    Finally, the array QuantPredGains is read, which consists of NumNonZeroIds elements, each coded by B SC  bits. Using the information contained in P IND  and QuantPredGains, the elements of the matrix P Q,F  are set. 
         [0103]    The inventive processing can be carried out by a single processor or electronic circuit, or by several processors or electronic circuits operating in parallel and/or operating on different parts of the inventive processing.