Abstract:
A lossless coding method may be used to compress information, such as audio data, without introducing any artifacts. This lossless coding method may be used to compress audio signals for use in storage and/or transmission of audio data. The audio data may be compressed by first dividing digital samples taken from the audio data into frames. A predictor is then used on the frames to generate prediction coefficients that can then be quantized to form predictor bits. The frames may then be subdivided into subsets. Another predictor can be used on the subsets to produce error samples that can be entropy coded into codeword bits. The predictor bits and codeword bits can be included in the compressed audio output for use in decoding.

Description:
TECHNICAL FIELD  
         [0001]    This invention relates generally to the coding of audio signals and more particularly to a method of lossless compression of audio data for use in the transmission and/or storage of audio information.  
         BACKGROUND  
         [0002]    Over the past ten to twenty years, the audio industry has seen a major transition from analog formats, such as cassette tapes, FM radio, and records to new digital formats such as the compact disc (CD), mini-disks (MD), digital versatile disks (DVD), and others. The widespread use of personal computers and the Internet has furthered this trend with the introduction of new electronic music services that allow electronic distribution of music and/or other audio content through a computer and the Internet. Many of these digital audio products and services use various audio compression technologies (e.g., MP3, Dolby AC3, ATRACS, MPEG-AAC, and Windows Media Player) to reduce the bit rate of audio transmissions to the range of 64-256 kbps from the 1440 kbps used on many uncompressed recordings, such as CDs, while maintaining a sufficient quality of high fidelity music reproduction. The use of compression technologies as well as the increased storage capacity of semiconductor (i.e., SRAM, DRAM, and Flash) devices and computer disks has made possible several new products including the RIO portable music player, the AudioRequest music jukebox, the Lansonic™ Digital Audio Server, and other devices.  
           [0003]    In a typical digital audio application, an analog audio signal is sampled, for example, at 32, 44.1, or 48 kHz, and then is digitized with 16 or more bits using an analog-to-digital converter. If the audio source is a stereo source, then this process may be repeated for both the right and left channels. New surround sound audio may have six or more channels, each of which may be sampled and digitized. A typical CD contains two stereo channels, each of which is sampled at 44.1 kHz with 16 bits per sample, resulting in a data rate of approximately 1411.2 kbps. This allows storage of slightly more than 1 hour of music on a 650 MB CD. In a playback application, the digital music samples may be converted to an analog signal using a digital-to-analog converter, and then amplified and played through one or more speakers.  
           [0004]    Several audio compression techniques may be used to compress a stereo music signal to the range of 64-256 kbps without significantly changing the quality of the audio signal (i.e., while maintaining CD-like quality). The MPEG-1 standard, developed and maintained by a working group of the International Standards Organization (ISO/IEC), describes three audio compression methods, referred to as Layers 1, 2, and 3, for reducing the bit rate of a digital audio signal. The method described under Layer 3, which is commonly known as MP3, is generally considered to achieve acceptable quality at 128 kbps and very good quality at 256 kbps.  
           [0005]    These audio compression methods, as well as some other lossy techniques, use frequency domain coding techniques with a complex psychoacoustic model to discard portions of the audio signal that are considered inaudible. The techniques may be used to achieve near-CD quality at compression ratios of about, for example, 5-to-1 (256 kbps) or 11-to-1 (128 kbps). However, psychoacoustic modeling is an inexact process and some approaches may introduce artifacts into the audio signal that may be audible and annoying to some listeners. As a result, lossy compression may be less desirable in some applications requiring very high audio quality.  
           [0006]    In the absence of any compression, the storage capacity of current consumer hard drives is quite limited. A large capacity hard drive, such as one with a capacity of 60-80 GB, can only store approximately 95-125 hours of uncompressed CD-quality music. In contrast, a CD changer may hold as many as 400 discs, providing over 400 hours of audio. As a result, some method of significantly increasing the amount of audio that can be stored on a hard drive without increasing cost or adding artifacts is useful.  
           [0007]    One method of increasing the amount of data that can be stored is to compress the data before storing the data and then to expand the compressed data when needed. In lossy compression methods such as MP3, the expanded data differs slightly from the original data. For audio and video signals, this may be acceptable as long the differences are not too significant. However, for computer data, any difference may be unacceptable. As a result, lossless compression methods for which the expanded data are identical to the original uncompressed data have been developed. Various lossless or “entropy” coders attempt to remove redundancies from data (for example, after every “q” there is a “u”) and exploit the unequal probability of certain types of data (for example, vowels occur more often than other letters). Computer programs such as “tar” and “ZIP” have been developed to perform lossless compression on documents and other computer files. These algorithms are typically based on methods developed by Ziv and Lempel or use other standard method such as Huffman coding or Arithmetic coding techniques (see, for example, T. Bell et. al., “Text Compression”, Prentice-Hall, 1990).  
           [0008]    Unfortunately, many lossless coding techniques designed for text or other computer-type data do not perform well on digital audio data. In fact, programs such as “ZIP” actually may enlarge an audio file rather than compressing the file. The problem is that these techniques assume certain features that may be common in text files but are not typically found in audio data.  
           [0009]    Methods for lossless compression of audio typically attempt to compress an audio file by exploiting certain redundancies in the audio signal. Generally, these redundancies can be applied either in the time domain via prediction or in the frequency domain via bit allocation. In addition, entropy coding can be applied to take advantage of the varying probability of different data values by assigning shorter sequences of bits to represent higher probability values and longer sequences of bits to represent lower probability values. The result is a reduction in the average number of bits required to represent all of the data values. These advantages have resulted in the incorporation of lossless compression into the DVD-Audio format (see, “Meridian Lossless Packing Enabling High-Resolution Surround on DVD-Aduio”, MIX, December 1998).  
           [0010]    One technique for lossless compression is to divide the audio signal into segments or frames. Then, for each frame, to compute a low-order linear predictor that is quantized and stored for that frame. This predictor then may be applied to all the audio samples in the frame, and the prediction residuals (i.e., the error after prediction) may be coded using some form of entropy-type coder, such as, for example, a Huffman, Golomb, Rice, run-length, or arithmetic coder. In “Optimization of Digital Audio for Internet Transmission” (May 1998), Mat Hans describes the AudioPak lossless audio coder. This coder combines four low-order linear predictors (0, 1st, 2nd, and 3rd order), each having fixed prediction weights corresponding to known polynomials, with Golomb coding. Use of very low order predictors with fixed predictor weights results in a very simple algorithm with low complexity, but at the expense of lower prediction gain and larger file sizes.  
           [0011]    In U.S. Pat. No. 5,839,100, Wegener describes a lossless audio coder that may be used in the MUSICompress system. The Wegener method uses decimation (i.e., selection of every Nth sample) to implement non-linear time domain prediction of an audio signal which is combined with Huffman coding. Decimation introduces aliasing into the predicted signal whereby signal components at the same modulo N frequency are summed. This may distort the signal in a way that prevents accurate prediction of all frequency components, causing lower compression rates.  
           [0012]    A paper titled, “SHORTEN: Simple lossless and near-lossless waveform compression”, by Tony Robinson (December 1994) and U.S. Pat. No. 6,041,302 by Bruekers describe a lossless audio compression system using linear prediction and Rice coding. Rice coding is a form of Huffman coding optimized for Laplacian distributions. Rice codes form a family of codes parameterized by a single parameter “m” that can be adjusted to reasonably fit the statistics of the audio prediction residuals.  
           [0013]    Prediction may be used to remove redundancy from the signal prior to coding in a lossless or a lossy system for coding audio signals. In a lossy speech coding application, modest (e.g., 8-14th) order adaptive linear predictors may be applied to each frame of speech (for example, 15-30 ms per frame) and predictor coefficients or weights may be computed using the autocorrelation or covariance methods. The predictor weights for this so-called “forward” predictor then may be quantized for passage to the decoder to form part of the side information for a frame. Many methods for efficient quantization of linear predictor coefficients have been devised, including transformation to partial correlation coefficients, reflection coefficients, or line spectral pairs, and using scalar and/or vector quantization.  
           [0014]    Many low bit rate speech coders use forward prediction, where predictor coefficients are computed on data that has yet to be processed by the decoder, rather than backward prediction, where predictor coefficients are computed on data already processed by the decoder.  
           [0015]    In a backward prediction system, data determining the prediction coefficients are known to both the encoder and decoder, which means that, usually, predictor coefficients are not quantized and extra side information bits are not used. Backward prediction systems that do not use extra bits may be adapted quite rapidly. However, they may be sensitive to bit errors or missing data, and, due to error feedback they may provide lower overall quality when used in low bit rate lossy speech coding. As a result, backward prediction is generally used only in higher bit rate (&gt;=16 kbps) speech coding applications such as the ITU G.728 LD-CELP speech coding standard.  
         SUMMARY  
         [0016]    In a first general aspect, lossless audio coding uses a combined forward and backward predictor for better approximation of an audio signal. Forward prediction is applied as a first stage and backward prediction is applied as a second stage. The overall prediction error is reduced, which results in smaller file sizes with lower complexity than when just forward prediction is used.  
           [0017]    In another general aspect, an improved entropy coder more closely fits the statistics of the audio prediction residuals. A modified Golomb coder is parameterized by, for example, two parameters. An effective search procedure is used to find the best parameter values for each frame, resulting in more efficient entropy coding with smaller file sizes than previous techniques.  
           [0018]    In one general aspect, digital samples that have been obtained from an audio signal are compressed into output bits that can be used, for example, to transmit and/or store the audio data. The digital samples are compressed by first dividing the samples into one or more frames, where each frame includes multiple samples. Each frame is compressed by computing a first predictor for the digital samples within the frame, with the first predictor being characterized by first prediction coefficients. Then, the first prediction coefficients are quantized to produce first predictor bits. The frames also are divided into one or more subsets, where each subset contains at least one of the digital samples. Next, a subset predictor is computed for a subset using digital samples contained in previous subsets. Error samples are produced using the first predictor bits and the subset predictor. These error samples are entropy coded to produce codeword bits. The first predictor bits and the codeword bits then are used in output bits for decompressing digital information.  
           [0019]    Implementations may include one or more of the following features. For example, the first predictor may be a linear predictor, such as a first order linear predictor. Prediction coefficients may be quantized using scalar quantization for some or all of the prediction coefficients. The prediction coefficients also may be quantized using vector quantization. The first prediction coefficients may be computed by windowing digital samples to produce windowed samples. Autocorrelation coefficients may be computed from the windowed samples, and the first prediction coefficients may be computed by solving a system of linear equations using the autocorrelation coefficients.  
           [0020]    A subset predictor may be used to compute prediction coefficients using only digital samples contained in previous subsets of the frame being computed.  
           [0021]    The entropy coding of error samples to produce codeword bits may use at least one code parameter that determines the format of the codeword bit. The value of the code parameter may be encoded into one or more of the code parameter bits and included in the output bits. The code parameter bits may be determined by comparing two or more possible values of the code parameter and then encoding into the code parameter bits the value of the code parameter which is estimated to yield the smallest number of codeword bits. Also, the code parameter bits may be determined by entropy coding the error samples using two or more possible values of the code parameter and then encoding into the code parameter bits the value of the code parameter that yields the smallest number of codeword bits.  
           [0022]    Error samples may be produced by first processing the digital samples using the first predictor to produce intermediate samples. The intermediate samples may be processed using the subset predictor to produce the error samples.  
           [0023]    The output bits of the coder are such that they can be used with a suitable decoder to enable a substantially lossless reconstruction of the digital samples.  
           [0024]    In one example, the frame contains 1152 digital samples which are divided into 48 subsets each containing 24 digital samples.  
           [0025]    In another general aspect, compressing digital samples obtained from an audio source into output bits includes dividing the digital samples into frames, with each frame containing one or more of the digital samples. The digital samples then may be processed to produce error samples. These error samples may be entropy coded to produce codeword bits. The entropy coding uses at least a first code parameter and a second code parameter, with each code parameter varying from frame to frame. The codeword bits may be included in output bits.  
           [0026]    Compressing digital samples may include using entropy coding that produces codeword bits as a combination of at least two terms. The first term may include a predetermined number of codeword bits, and the second term may include a variable number of codeword bits. The value of the first term may include information on the least significant bits of an error sample and/or information on the sign of the error sample. The number of codeword bits in the second term may be greater for an error sample with large magnitude and smaller for an error sample with small magnitude. The number of codeword bits in the first term may depend, at least in part, on the first code parameter, and the number of codeword bits in the second term may depend, at least in part, on the second code parameter.  
           [0027]    The first code parameter for a frame may be encoded with the first code parameter bits, and the second code parameter for a frame may be encoded with the second code parameter bits. The first and second code parameter bits may be included in the output bits.  
           [0028]    Error samples may be produced by computing one or more predictors for a frame and using the predictors to produce errors samples from the digital samples. The digital samples also may include first channel samples from a first channel of the audio source and second channel samples from a second channel of the audio source. The digital samples may be processed to produce error samples. The processing may include predicting the second channel samples from the first channels samples.  
           [0029]    Error samples may be processed for a frame by computing a first predictor for the digital samples in a frame, with the first predictor having first prediction coefficients. The first prediction coefficients may be quantized to produce first predictor bits. The digital samples in a frame may be divided into one or more subsets. Each subset may contain one or more digital samples. A subset predictor may be computed for at least one of the subsets, using the digital samples contained in previous subsets. Error samples may be produced by processing the digital samples in a frame using both the first predictor and the subset predictor. The first predictor bits may be included in the output of the coder.  
           [0030]    In another general aspect, audio data is reconstructed from output bits generated by an audio coder. Output bits, generated by an audio coder, are received and codeword bits, a first code parameter, a second code parameter, and predictor bits are obtained from the output bits. Error samples are reconstructed from the codeword bits using the first code parameter and the second code parameter. An error signal is computed from the reconstructed error samples. Error samples may be reconstructed by entropy decoding the codeword bits. Also, prediction coefficients are reconstructed using the predictor bits that were previously generated by quantizing the prediction coefficients.  
           [0031]    The codeword bits may be a combination of at least two terms, including a first term that includes a predetermined number of codeword bits, and a second term including a variable number of codeword bits. The number of codeword bits in the second term may generally be greater for an error sample with large magnitude and generally smaller for an error sample with small magnitude. The value of the first term may include information on the least significant bits of an error sample.  
           [0032]    The number of codeword bits in the first term may depend at least in part on the first code parameter and the number of codeword bits in the second term may depend at least in part on the second code parameter.  
           [0033]    Audio data may be reconstructed using the prediction coefficients and the error samples by dividing the error samples for a frame into one or more subsets. Each subset may contain at least one of the error samples for the frame. A subset predictor is then computed for at least one of the subsets using information from previous subsets. The audio data may then be reconstructed using the prediction coefficients, the subset predictor, and the error samples.  
           [0034]    The audio data may include first audio data for a first audio channel and second audio data for a second audio channel. In this case, audio data may be reconstructed by reconstructing the first audio data, and then reconstructing the second audio data using the first audio data. 
       
    
    
       [0035]    Other features and advantages will be apparent from the description and drawings, and from the claims.  
       DESCRIPTION OF DRAWINGS  
       [0036]    [0036]FIG. 1 is a block diagram of a digital audio server.  
         [0037]    [0037]FIG. 2 is a flow chart of a procedure for compressing digital samples obtained from an audio signal.  
         [0038]    [0038]FIG. 3 is a flow chart of a procedure for decompressing a digital signal that has been compressed using a lossless audio coder.  
     
    
     DETAILED DESCRIPTION  
       [0039]    Referring to FIG. 1, a lossless audio coding system may be used in the transmission and/or storage of digital audio data. For example, lossless audio coding may be used to store CD-quality audio on a computer hard disk or other storage media. Lossless audio coding may be used to store audio data on a digital audio server device  100  containing a data storage device  101 , such as, for example, one or more large (e.g., 20-80 GB) hard drives. The data may be coded and/or decoded using audio coder  102 , which may be implemented either in hardware or software. For very high quality applications, lossy compression techniques may affect the playback quality of audio recordings. In such cases, lossless compression may be used to eliminate approximately half of the audio data, so as to allow twice the amount of audio data to be stored in data storage device  101  relative to the uncompressed audio found, for example, on a CD.  
         [0040]    Digital audio server  100  is connected to a device for playing back the audio recording, such as receiver  103  connected to one or more speakers  104 . Receiver  103  may be a standard stereo component receiver, such as a stereo receiver providing Dolby ProLogic or Dolby Digital decoding. Receiver  103  also may be implemented as a personal computer, a stereo amplifier, or any other audio playback device.  
         [0041]    Referring to FIG. 2, audio data may be compressed without loss by first dividing the audio data into small frames (step  201 ). For example, in one implementation, each frame includes N=1152 samples, which represents approximately 26.1 ms assuming a 44.1 kHz sampling rate. For multi-channel audio, all of the channels may be processed separately. However, for improved compression, interchannel prediction may be used for each additional channel beyond the first. For example, in the case of two-channel stereo audio, the first (i.e., the “right”) channel, r(n), may be first compressed using the methods described below. The second (i.e., the “left”) channel may be predicted from the first channel using interchannel processing to compute an interchannel prediction error signal el(n). This prediction error signal may then be further compressed using the techniques described below.  
         [0042]    In the case of multi-channel audio, prediction of the second channel from the first typically uses a first order adaptive linear predictor el(n)=l(n)−ρ*r(n), where the prediction coefficient, ρ, is computed as:  
             ρ   =         ∑       l        (   n   )            r        (   n   )             ∑       r   2          (   n   )           .             (   1   )                               
 
         [0043]    Typically, the prediction coefficient, ρ, then is quantized using a quantizer, such as, for example, a 6-bit non-uniform quantizer such as is described in Appendix A. The output of this quantizer may be multiplexed with the other side information for the left channel and the left error signal, el(n), then may be compressed further using the prediction and entropy coding described below. This interchannel technique can be readily applied to applications with more than two channels, where each successive channel can be predicted from previous channels that have already been compressed. Also, higher order adaptive predictors can be used to account for more complex relationships between the channels.  
         [0044]    Following any interchannel processing, a forward linear predictor may be computed for each channel for each frame of audio data (step  202 ) according to the following formula:  
                 fe        (   n   )       =       s        (   n   )       -       ∑     l   =   1     L            s        (     n   -   l     )                     a                   (   l   )             ,                  for                 0     ≤              n   &lt;   N     ,           (   2   )                               
 
         [0045]    where s(n) is one channel of the audio signal for the frame and the order L of the forward predictor is typically less than or equal to 20 with smaller values of L used when lower complexity is desired.  
         [0046]    The prediction coefficients a(l) for 1≦l≦L can be computed using several methods. For example, the prediction coefficients may be computed using the standard autocorrelation method with a 1,728 point Kaiser window centered on the frame with Beta=4.0. Solving for the coefficients a(l) may be accomplished using the Levinson recursion method, and the computed coefficients may be converted into partial correlation (PARCOR) coefficients k(l) which have the property |k(l)|≦1.  
         [0047]    The values of k(l) for 1≦l≦L are quantized (step  203 ) using a quantizer, such as, for example, the set of non-uniform scalar quantizers provided in Appendix B, with the number of bits for each quantizer given in Table 1. Note that other standard linear prediction quantization techniques using line spectral pairs (LSPs) or vector quantization may also be employed. The output of each of the L quantizers is normally included as part of the side information multiplexed into each frame of compressed data. Using L=20, the bit allocation in Table 1 produces 53 bits of side information per frame for each channel. Once the computed PARCOR coefficients are quantized, the quantized values may be converted back into prediction coefficients and used in accordance with Equation (2) to compute a forward prediction error, fe(n), for the frame. In this example, the quantized prediction coefficients are used to compute the prediction error, since only the quantized values are available to the decoder (via the side information) and for lossless decoding the decoder performs the exact inverse of this process using exactly the same prediction coefficients as the encoder.  
                                           TABLE 1                           Bit Allocation for k(l), l ≦ l ≦ 20                l   Bit Allocation for k(l)                            0   5           1   5           2   4           3   4           4   4           5   4           6   4           7   3           8   3           9   3           10   3           11   3           12   2           13   2           14   2           15   2           16   2           17   2           18   2           19   2                      
 
         [0048]    Once the forward prediction residuals are computed for the frame, a backward predictor may be used to operate on the forward prediction error fe(n). For the backward predictor, the frame is divided into small subframes (step  204 ) of, for example, 24 samples each. For the jth subframe, the backward prediction error be(n) is generally computed as:  
                 be        (   n   )       =       fe        (   n   )       -       ∑     i   =   1     I            b        (     j   -   1     )              (   i   )     ·     fe        (     n   -   i     )                 ,                
                       for                   j   ·   24       ≤   n   &lt;       (     j   +   1     )     ·   24.               (   3   )                               
 
         [0049]    The backward prediction coefficients b(j−1)(i) are updated (step  205 ) at the end of each subframe using data computed from that subframe and prior subframes within the frame. In one implementation, a lossless audio coder having I=1 and a first order back predictor be(n)=fe(n)−b(j−1)(1)*fe(n−1) are applied (step  206 ), and the backward prediction coefficents b(j)(1) are updated as follows:  
                 b        (   j   )            (   1   )       =         (     1   2     )          b        (     j   -   1     )            (   1   )       +           ∑     n   =   0     24            fe        (       24      j     +   n     )       ·     fe        (       24      j     +   n   -   1     )             2   ·       ∑     n   =   0     24            fe   2          (       j   *   24     +   n     )             .               (   4   )                               
 
         [0050]    The first subframe in the frame b(−1)(1) is initialized to a known constant, for example 0.375, and fe(−1) is initialized to zero. Initialization in this manner insures that the backward predictor only depends on data from the current frame rather than from previous frames. This significantly reduces sensitivity to bit errors and eliminates problems from missing data in previous frames. Furthermore, it allows the method to be used in streaming or broadcast applications where the receiver may start receiving some time after transmission begins and hence may not receive the beginning of the signal.  
         [0051]    The backward prediction error be(n) for 0≦n&lt;N is entropy coded (step  207 ) using a modified Golomb code. The original audio signal s(n) is typically integer valued and typically both the forward and backward prediction are done with integer arithmetic to reduce numerical sensitivity and to ensure that be(n) also has integer values. The modified Golomb code first maps the signed values of be(n) to a non-negative sequence p(n) as follows: 
           p ( n )= be ( n ), if  be ( n )=0, 
           p ( n )=2· be ( n )−1, if  be ( n )&gt;0, 
         [0052]    and 
           p ( n )=−2· be ( n ), if  be ( n )&lt;0.  (5) 
         [0053]    Note that due to the one-to-one mapping, there is a similar inverse mapping to recover the values of be(n) from p(n). The entropy coding of p(n) is performed by first separating p(n) into two terms, with the first term (A=p(n) mod M) representing the least significant M bits of p(n), the second term (B=└p(n)/M ┘) representing the remaining most significant bits, and the parameter M being a first parameter of the code.  
         [0054]    The first term, A, generally represent the least significant bits and the sign of be(n), while the second term, B, generally represents the most significant bits of be(n). The codeword corresponding to p(n) is produced by combining the two terms, using M bits to write A, followed by a variable number of bits to write B. The number of bits used to write A is predetermined and equal to the first code parameter M. Encoding of the variable sized term B is accomplished using Z zeros, followed by a 1, followed by X auxiliary bits, where the number of zeros, Z, and the number of auxiliary bits, X, are dependent on the value of B.  
         [0055]    In one implementation, the dependence on B of X and Z is given by the following equations: 
           X= 1, if  B&lt; 2 T,   
           X= 0,  (6) 
         [0056]    otherwise, and 
           Z=└B/ 2┘, if  B&lt; 2 T,   
           Z=B−T,   (7) 
         [0057]    otherwise,  
         [0058]    where T is a second parameter of the code. Each value of B is mapped to a unique combination of the number of zeros, Z, and of the X auxiliary bits, which preferably is set equal to the X least significant bits of B, whenever B&lt;2T.  
         [0059]    Table 2 shows exemplary encodings of B for different values of T, following the above procedure.  
                                                           TABLE 2                           Example Encodings of B for various T            B   T = 0   T = 1   T = 2   T = 3                    0   1   10   10   10       1   01   11   11   11       2   001   01   010   010       3   0001   001   011   011       4   00001   0001   001   0010       5   000001   00001   0001   0011       6   0000001   000001   00001   0001       7   00000001   0000001   000001   00001       8   000000001   00000001   0000001   000001       9   0000000001   000000001   00000001   0000001       10   00000000001   0000000001   000000001   00000001       11   000000000001   00000000001   0000000001   000000001       12   0000000000001   000000000001   00000000001   0000000001       13   00000000000001   0000000000001   000000000001   00000000001       14   000000000000001   00000000000001   0000000000001   000000000001       15   0000000000000001   000000000000001   00000000000001   0000000000001                  
 
         [0060]    Note that many other useful relationships between Z, X, and B can be formulated to allow further adaptability of the code. For example, Equation (6) can be generalized using a sequence of parameters (T 0 , T 1 , T 2 , . . . ) with a corresponding number of auxiliary bits (X 0 , X 1 , X 2 , . . . ) used for the respective conditions (Z&lt;T 0 , T 0 ≦Z&lt;T 1 , T 1 ≦Z&lt;T 2 , . . . ). In this case, Equation (7) and the values of the auxiliary bits are modified in a straightforward manner to maintain a unique mapping for each value of B.  
         [0061]    This implementation of lossless audio encoding provides adaptability in the selection of the code parameters M and T. While it is possible to fix M and/or T, compression may be improved by selecting one or more new values of M and/or T for each frame, where the selection is made in a manner to reduce the total number of bits required to represent some or all of the codewords for that frame. M and T may be selected by encoding p(n) with all the combinations of M and T in some limited range, and by selecting the combination which yields the smallest number of encoded bits. Typically, the selected values of M and T are encoded using 4 bits for M (0≦M&lt;16) and 2 bits for T (0≦T&lt;4), which yields a total of 64 combinations. However, in practice only a few of these combinations actually need to be tried. The selection of M may be limited to a small range (typically +/−1) around an initial estimate computed as: M 0 =log  2 [log(2) E(|be(n)|)], where the expected value E(|be(n)|) is approximated according to the standard formula:  
               E        (          be        (   n   )            )       =       1     N          ∑     n   =   0       N   -   1                 be        (   n   )                  .             (   8   )                               
 
         [0062]    Searching all combinations of T for the each of the values of M in a small range near M 0  produces virtually the same degree of compression as searching all combinations of M and T, with the added advantage that the partial search is much less complex. It is also possible to further analyze the data to limit the searches in T, and experiments have shown that even with fixed T=1, the performance of the modified Golomb code produces better compression than the standard Golomb code.  
         [0063]    For each audio channel, the encoder generates output data (step  208 ) that may include side information representing the quantized forward predictor (43 bits), the selected value of M (4 bits), and the selected value of T (2 bits), plus the modified Golomb encoded codewords for all N samples of be(n). In the case of multichannel audio (e.g., two channel stereo or five channel Dolby Digital surround sound), these data are output for each channel. However, the side information for the second channel as well as any additional channels beyond the second may include a quantized interchannel predictor (6 bits) as described previously.  
         [0064]    Referring to FIG. 3, a corresponding decoder may be used to reconstruct the original audio data from the encoded representation produced by the encoder (step  301 ). The decoder operates by reconstructing from the modified Golomb codewords the backward error signal, be(n), for each channel using the values of M and T carried in the side information for that frame (step  302 ). The backward error signal then may be passed through an inverse backward predictor (step  303 ), for example, fe(n)=be(n)+b(j−1)(1)*fe(n−1) to compute the forward error signal fe(n), where the first order backward predictor b(j)(1) is initialized and updated for each subframe using Equation (4) in the same manner as the encoder. The original audio signal s(n) is likewise reconstructed (step  304 ) from the forward error signal fe(n) according to the following equation:  
               s        (   n   )       =       fe        (   n   )       +       ∑     l   =   1     L            s        (     n   -   l     )       ·     a        (   l   )                     (   9   )                               
 
         [0065]    where the forward prediction coefficients, a(l), are reconstructed from the side information for that frame. In the case of multichannel audio, any interchannel prediction applied by the encoder is inverted in a similar manner by the decoder to reconstruct the final audio signal.  
         [0066]    Note that while this system provides lossless compression of audio data, it can also be used for very high quality lossy compression. In one method for lossy encoding of audio data, an extra optional shift factor, S, is applied to the backward error signal be(n). The shift factor in set according to the following rule: 
           S=M−Ms, M&gt;Ms,  and 
         S=0,  (10) 
         [0067]    otherwise,  
         [0068]    where the threshold, Ms, is determined by the amount of “loss” that is acceptable.  
         [0069]    The shift factor is applied by shifting out the S least significant bits of be(n) prior to Golomb encoding. In the decoder this procedure is reversed by shifting be(n) up by S bits and adding 2 (S−1)  prior to performing the inverse prediction. The result of these steps is that, whenever M&gt;Ms, some of the least significant bits are discarded prior to encoding and hence the decoded audio is not exactly the same as the original audio data. However, since the effect is primarily limited to the least significant and hence less audible part of the audio signal, high quality audio can still be achieved with compression rates of 3-5 times.  
         [0070]    Other implementations are within the scope of the following claims.  
                                           APPENDIX A                           6 Bit Non-Uniform Quantizer for First Order Interchannel Predictor                Index   Quantizer Value                            0   −.034098           1   4.3069           2   .6006           3   .2916           4   .4471           5   −.2574           6   .3884           7   .3300           8   .3964           9   .4335           10   .002889           11   .1888           12   .2311           13   .1562           14   1.000           15   .6174           16   .5519           17   .4639           18   .1460           19   .3493           20   .05874           21   .2778           22   .07971           23   .4811           24   .03375           25   .4224           26   −.3877           27   .2161           28   .1768           29   −.1597           30   −2.208           31   .2617           32   .4998           33   .09689           34   .1659           35   12.670           36   −.8778           37   .1237           38   .3599           39   .3049           40   .3397           41   −1.3362           42   .2021           43   .5838           44   .6657           45   .3703           46   .1354           47   −.5783           48   .4046           49   .3184           50   .3800           51   .5346           52   −.08667           53   .8520           54   1.4828           55   .5678           56   .5178           57   .1111           58   .2465           59   .6389           60   2.578           61   .7591           62   .7038           63   .4130                      
 
         [0071]    [0071]                                                                                                                                                                                                                                                                                                                                                                                                                                             APPENDIX B                           Non-Uniform Scalar Quantizers for Forward Predictor                Index   Quantizer Value                        B.0 5 bit quantizer for 1 = 0                0   .9659939           1   .9988664           2   .9994784           3   .9966566           4   .9844495           5   .9938794           6   .9957781           7   .9948506           8   .9974933           9   .8643624           10   .9861720           11   .9891772           12   .9982287           13   .9928406           14   .9703388           15   .9600936           16   .9522324           17   .7419546           18   .9877445           19   .9787532           20   .8137161           21   .9904836           22   .9413784           23   .9826772           24   .6393074           25   .9009055           26   .9917094           27   .9736391           28   .9807975           29   .9253348           30   .9764101           31   0.0            B.1 5 bit quantizer for l = 1                0   −.7524270           1   −.9877042           2   −.9736536           3   −.7293493           4   −.9621547           5   −.9486010           6   −.6779138           7   −.05932157           8   −.4678430           9   −.6221167           10   .1635733           11   −.8139132           12   .5402579           13   −.8317617           14   −.5134417           15   −.1681219           16   −.9656837,           17   −.9157286,           18   −.5536591,           19   −.6512799,           20   −.5893744,           21   −.8826373,           22   −.8994818,           23   −.7947098,           24   −.8488274,           25   .04328764,           26   −.3463203,           27   −.9319999,           28   −.7044382,           29   −.7741293,           30   −.4145659,           31   −.2639911            B.2 4 bit quantizer for l = 2                0   .08794872           1   −.7750393           2   .8766201           3   −.4662539           4   .1922842           5   .2760510           6   .5111743           7   .4010011           8   −.04721336           9   .7018681           10   .4557702           11   .6305268           12   .5684454           13   .3428863           14   −.2381265           15   .7875859            B.3 4 bit quantizer for l = 3                0   .5710726           1   .3914019           2   .2692767           3   −.5202016           4   −.6868389           5   .05093540           6   .1541075           7   −.5872226           8   −.4621386           9   −.3001415           10   −.4070184           11   −.3537728           12   −.1188258           13   −.2453600           14   −.03932683           15   −.1856052            B.4 4 bit quantizer for l = 4                0   .2103013           1   .3083340           2   −.2522253           3   −.3438762           4   .1660577           5   .1231071           6   −.06150698           7   .5417671           8   .4428142           9   .03734619           10   .3694975           11   −.1822241           12   −.008753308           13   −.1201142           14   .08071340           15   .2568181            B.5 4 bit quantizer for l = 5                0   .2145806           1   .3402392           2   −.4227384           3   −.2322869           4   −.4904339           5   −.003712975           6   .05283693           7   −.3174772           8   −.04884965           9   −.1957825           10   −.08868919           11   −.3676099           12   .1259245           13   −.2721864           14   −.1252577           15   −.1603424            B.6 4 bit quantizer for l = 6                0   −.2597265           1   .4115449           2   .04184072           3   .1215950           4   −.1584679           5   −.08816823           6   .09694316           7   .3345242           8   .2325162           9   .7098457           10   .2757551           11   .1983530           12   .1698541           13   −.03445147           14   .1447476           15   .008154644            B.7 3 bit quantizer for l = 7                0   −.2344300           1   .1676646           2   −.3189372           3   −.06671936           4   .06891654           5   −.1751942           6   −.1213538           7   −.004475277            B.8 3 bit quantizer for l = 8                0   −.0002137973           1   .2196834           2   −.1621969           3   .3084771           4   .05321136           5   .1032912           6   .1563970           7   −.06488300            B.9 3 bit quantizer for l = 9                0   .1548602           1   −.2440517           2   −.1341489           3   −.08104721           4   .05495924           5   −.02045774           6   −.1851722           7   −.3300617            B.10 3 bit quantizer for l = 10                0   .2625484           1   −.1808913           2   .07588041           3   .1246535           4   .1824803           5   .02915521           6   −.08648710           7   −.02223778            B.11 3 bit quantizer for l = 11                0   .1249600           1   −.2839665           2   −.01346401           3   −.06213566           4   −.2080165           5   −.1078273           6   −.1540408           7   .04275909            B.12 2 bit quantizer for l = 12                0   .2042079           1   −.06843125           2   .1106078           3   .03018990            B.13 2 bit quantizer for l = 13                0   .06919591           1   −.2225718           2   −.1256930           3   −.03975704            B.14 2 bit quantizer for l = 14                0   .1046253           1   .02314145           2   .1954758           3   −.07630695            B.15 2 bit quantizer for l = 15                0   −.1410635           1   −.05384010           2   −.2418302           3   .0497693            B.16 2 bit quantizer for l = 16                0   .1046253           1   .02314145           2   .1954758           3   −.07630695            B.17 2 bit quantizer for l = 17                0   −.1410635           1   −.05384010           2   −.2418302           3   .0497693            B.18 2 bit quantizer for l = 18                0   .1046253           1   .02314145           2   .1954758           3   −.07630695            B.19 2 bit quantizer for l = 19                0   −.1410635           1   −.05384010           2   −.2418302           3   .0497693