Abstract:
A method of digital audio broadcasting comprises the steps of providing a plurality of bits of digital information to be transmitted, forward error correcting the bits of digital information using a combination of pragmatic trellis code modulation and complementary punctured code, and transmitting the bits of digital information. The step of forward error correcting the bits of digital information can comprise the steps of representing the bits as independently coded in-phase and quadrature signals, applying a first error correcting code to the in-phase signals, and applying a second error correcting code to the quadrature signals. The bits of digital information can be arranged in a plurality of partitions of code, wherein first and second ones of the partitions do not overlap, a third one of the partitions overlaps a first portion of the first and second partitions, and a fourth one of the partitions overlaps a second portion of the first and second partitions. Apparatus for transmitting and receiving digital audio broadcasting signals in accordance with the above method are also provided.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application is a divisional application of U.S. patent application Ser. No. 09/438, 822, filed Nov. 11, 1999. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    This invention relates to methods and apparatus for forward error correction coding, and more particularly to such methods and apparatus for use in digital audio broadcasting systems.  
           [0003]    Digital Audio Broadcasting (DAB) is a medium for providing digital-quality audio, superior to existing analog broadcasting formats. AM In-Band, On-Channel (IBOC) to DAB can be transmitted in a hybrid format where a digitally modulated signal coexists with the AM signal, or it can be transmitted in an all-digital format where the removal of the analog signal enables improved digital coverage with reduced interference. The hybrid format allows existing receivers to continue to receive the AM signal while allowing new IBOC receivers to decode the DAB signal. In the future, when IBOC receivers are abundant, a broadcaster may elect to transmit the all-digital format. The DAB signal of the all-digital format is even more robust than the hybrid DAB signal because of allowed increased power of the former with a digital time diversity backup channel. IBOC requires no new spectral allocations because each DAB signal is simultaneously transmitted within the spectral mask of an existing AM channel allocation. IBOC promotes economy of spectrum while enabling broadcasters to supply digital quality audio to their present base of listeners.  
           [0004]    U.S. Pat. No. 5,588,022 teaches a method for simultaneously broadcasting analog and digital signals in a standard AM broadcasting channel. An amplitude modulated radio frequency signal having a first frequency spectrum is broadcast. The amplitude modulated radio frequency signal includes a first carrier modulated by an analog program signal. Simultaneously, a plurality of digitally modulated carrier signals are broadcast within a bandwidth that encompasses the first frequency spectrum. Each of the digitally modulated carrier signals is modulated by a portion of a digital program signal. A first group of the digitally modulated carrier signals lies within the first frequency spectrum and is modulated in quadrature with the first carrier signal Second and third groups of the digitally modulated carrier signals lie outside of the first frequency spectrum and are modulated both in-phase and in-quadrature with the first carrier signal. U.S. patent application Ser. No. 09/049,217, assigned to the same assignee as the present invention, discloses another embodiment of an AM Digital Audio Broadcasting system.  
           [0005]    Coding for an IBOC DAB system has been described in: B. Kroeger, D. Cammarata, “Robust Modem and Coding Techniques for FM Hybrid IBOC DAB,” IEEE Trans. on Broadcasting, Vol. 43, No. 4, pp. 412-420, December 1997. Trellis coded modulation has been proposed for use in AM IBOC DAB systems. Pragmatic trellis coded modulation (PCTM) has been described in: A. Viterbi, et al., “A Pragmatic Approach to Trellis-Coded Modulation,” IEEE Communications Magazine, pp. 11-19, July 1989. The use of complementary punctured codes has also been proposed for IBOC DAB systems. Complementary punctured codes have been described in: S. Kallel, “Complementary Punctured Convolution (CPC) Codes and Their Applications,” IEEE Trans. Comm., Vol 43, No. 6, pp. 2005-2009, June 1995. The present invention seeks to provide an improved forward error correction method for use in AM IBOC DAB transmitters. Receivers that process signals that were transmitted in accordance with the method are also described.  
         SUMMARY OF THE INVENTION  
         [0006]    The invention provides a method of digital audio broadcasting comprising the steps of providing a plurality of bits of digital information to be transmitted, forward error correcting the bits of digital information using a combination of pragmatic trellis code modulation and complementary punctured code, and transmitting the bits of digital information. The step of forward error correcting the bits of digital information can comprise the steps of representing the bits as independently coded in-phase and quadrature signals, applying a first error correcting code to the in-phase signals, and applying a second error correcting code to the quadrature signals.  
           [0007]    The invention also encompasses a method of digital audio broadcasting comprising the steps of providing a plurality of bits of digital information, encoding the plurality of bits of digital information to produce a plurality of partitions of digital information code, wherein first and second ones of the partitions do not overlap, a third one of the partitions overlaps a first portion of the first and second partitions, and a fourth one of the partitions overlaps a second portion of the first and second partitions.  
           [0008]    The plurality of partitions can include a main partition, a backup partition, an upper partition, and a lower partition, with the upper partition and the lower partition being non-overlapping. The upper partition and lower partition can be symmetric.  
           [0009]    The code can comprise a plurality of symbols and the step of transmitting the plurality of partitions of code can comprise the step of quadrature amplitude modulating a plurality of carrier signals using the symbols to produce in-phase (I) and quadrature (Q) components.  
           [0010]    The in-phase and quadrature components can be modulated with independent amplitude shift keying (ASK) signals to produce in-phase and quadrature ASK symbols. One bit of each of the ASK symbols can be uncoded. Each of the ASK symbols can be coded with a first error correction scheme and additional bits of each of the ASK symbols can be coded with a second error correction scheme.  
           [0011]    The invention also includes apparatus for digital audio broadcasting in accordance with the above methods  
           [0012]    The invention further encompasses a method of receiving a digital audio broadcasting signal comprising the steps of receiving a plurality of bits of digital information, wherein the bits of digital information have been forward error corrected using a combination of pragmatic trellis code modulation and complementary punctured code, and decoding the bits of digital information to produce an output signal.  
           [0013]    The forward error corrected bits of digital information can be independently coded for in-phase and quadrature signals, with a first error correcting code applied to the in-phase signals and a second error correcting code applied to the quadrature signals.  
           [0014]    The invention also encompasses a method of receiving a digital audio broadcasting signal comprising the steps of receiving a plurality of bits of digital information, wherein the plurality of bits of digital information are separated into a plurality of partitions of digital information code, wherein first and second ones of the partitions do not overlap, a third one of the partitions overlaps a first portion of the first and second partitions, and a fourth one of the partitions overlaps a second portion of the first and second partitions, and decoding the bits of digital information to produce an output signal.  
           [0015]    The plurality of partitions can include a main partition, a backup partition, an upper partition, and a lower partition, with the upper partition and the lower partition being non-overlapping.  
           [0016]    The bits of digital information can comprise a plurality of symbols, and the digital audio broadcasting signal can comprise a plurality of carrier signals quadrature amplitude modulated using the symbols to produce in-phase (I) and quadrature (Q) components.  
           [0017]    The in-phase and quadrature components can be modulated with independent amplitude shift keying (ASK) signals to produce in-phase and quadrature ASK symbols. One bit of each of the ASK symbols can be uncoded. Alternatively, one bit of each of the ASK symbols can be coded with a first error correction scheme and additional bits of each of the ASK symbols can be coded with a second error correction scheme.  
           [0018]    The invention further encompasses a method for receiving a digital audio broadcast signal comprising the steps of receiving a plurality of bits of digital information divided into a plurality of partitions of code, wherein first and second ones of the partitions do not overlap, a third one of the partitions overlaps a first portion of the first and second partitions, and a fourth one of the partitions overlaps a second portion of the first and second partitions and the code includes quadrature amplitude modulated symbols having in-phase (I) and quadrature (Q) components modulated with independent amplitude shift keying (ASK) signals to produce in-phase and quadrature ASK symbols, wherein one bit of each of the ASK symbols is coded with a first error correction scheme and additional bits of each of the ASK symbols are coded with a second error correction scheme, decoding the additional bits of the ASK symbols using soft decision decoding, and decoding the one bit of the ASK symbols using a decoder responsive to the results of the step of decoding the additional bits of the ASK symbols using soft decision decoding.  
           [0019]    The step of decoding the additional bits of the ASK symbols using soft decision decoding can comprise the step of applying a soft binary metric to the additional bits of the ASK symbols. The soft binary metric can be a soft limiter. The soft binary metric can be a linear clipper.  
           [0020]    The invention also includes apparatus for receiving digital audio broadcasting signals in accordance with the above methods. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]    [0021]FIG. 1 is a schematic representation of the sub-carrier assignments in an AM hybrid IBOC DAB signal;  
         [0022]    [0022]FIG. 2 is schematic representation of the sub-carrier assignments in an AM all-digital IBOC DAB signal;  
         [0023]    [0023]FIG. 3 is a functional block diagram of a transmitter for use in an IBOC DAB system;  
         [0024]    [0024]FIG. 4 is a functional block diagram of a receiver for use in an IBOC DAB system;  
         [0025]    [0025]FIG. 5 is a functional block diagram of a core interleaver that may be used in an AM IBOC DAB transmitter that transmits signals in accordance with this invention;  
         [0026]    [0026]FIG. 6 is a functional block diagram of an enhancement interleaver that may be used in an AM IBOC DAB transmitter that transmits signals in accordance with this invention;  
         [0027]    [0027]FIG. 7 is a diagram that illustrates a robust soft metric for an 8-ASK IBOC DAB signal; and  
         [0028]    [0028]FIG. 8 is a functional block diagram of a deinterleaver and FEC decoder that may be used in an AM IBOC DAB receiver that processes signals in accordance with this invention. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0029]    This invention provides a Forward Error Correction (FEC) technique for an AM IBOC (In-Band On-Channel) DAB (Digital Audio Broadcast) system. This FEC technique is herein referred to as Complementary Pragmatic Trellis-Coded Modulation (CPTCM). The CPTCM coding is designed to accommodate the likely interference scenarios encountered in the AM channel.  
         [0030]    Referring to the drawings, FIG. 1 is a schematic representation of the carrier placement of an AM hybrid IBOC DAB signal  10  of the type that can be used to practice the invention. The hybrid format includes the conventional amplitude modulated signal  12  formed by analog modulating a carrier at frequency f o  positioned at the center of the channel, along with a nearly 20 kHz wide DAB signal  14  transmitted beneath the AM signal. The conventional AM signal is bandlimited to ±5 kHz. The spectrum of the IBOC DAB signal is contained within a channel  16  having a bandwidth of 20 kHz. The channel is divided into a central frequency band  18 , and upper  20  and lower  22  sidebands. The central frequency band is about 10 kHz wide and encompasses frequencies lying within about plus and minus 5 kHz of the central frequency of the channel. The upper sideband extends from about +5 kHz from the central frequency to about +10 kHz from the central frequency. The lower sideband extends from about −5 kHz from the central frequency to about −10 kHz from the central frequency.  
         [0031]    The AM hybrid IBOC DAB signal includes the analog AM signal produced by modulating carrier  24  at frequency f o  plus a plurality of evenly spaced OFDM sub-carriers locations, designated as sub-carrier positions from −54 to +54, and spanning the central frequency band and the upper and lower sidebands. Coded digital information representative of the audio or data signals to be transmitted (program material), is transmitted on the sub-carriers. The AM IBOC DAB signal is digitally modulated using COFDM (Coded Orthogonal Frequency Division Multiplexing). In the preferred embodiment, sub-carriers located in the central frequency band  18  on either side of the analog modulated carrier frequency, f o , are transmitted in twenty eight complementary pairs such that the modulated resultant DAB signal is in quadrature to the analog modulated AM signal. The two sub-carriers  26  and  28  located a positions −1 and +1 use binary phase shift keying to transmit timing information. The remaining sub-carriers in the central frequency band are used to transmit digital information referred to as enhancement information. Sub-carriers in the upper and lower sidebands, at positions from 30 to 54 and −54 to −30 respectively, are QAM modulated sub-carriers. These sub-carriers are used to transmit information referred to as core information. Using this format, the analog modulated carrier and all digitally modulated sub-carriers are transmitted within the channel mask specified for standard AM broadcasting in the United States. Signal processing techniques are employed to reduce the mutual interference between the AM and DAB signals.  
         [0032]    [0032]FIG. 2 is a schematic representation of the spectral placement of an all-digital IBOC DAB broadcasting format  30  that may utilize the present invention. The power of the central frequency band  32  sub-carriers is increased, relative to the hybrid format of FIG. 1. Again, the two sub-carriers  34  and  36  located a locations −1 and +1 use binary phase shift keying to transmit timing information. A core upper sideband  38  is comprised of carriers at locations 2 through 26, and a core lower sideband  40  is comprised of sub-carriers at locations −2 through −26. Two groups  42  and  44  of additional enhancement sub-carriers occupy locations 27 through 54 and −54 through −27 respectively. The all-digital format of FIG. 2 is very similar to the hybrid format except that the AM signal is replaced with a delayed and digitally encoded tuning and backup version of the program material. The central frequency band occupies approximately the same spectral location in both hybrid and all-digital formats. In the all-digital format, there are two options for transmitting the main version of the program material in combination with the tuning and back-up version. The all-digital system has been designed to be constrained within ±10 kHz of the channel central frequency, f o , where the main audio information is transmitted within ±5 kHz of f o , and the less important audio information is transmitted in the wings of the channel mask out to ±10 kHz at a lower power level. This format allows for graceful degradation of the signal while increasing coverage area. The all-digital system carries a digital time diversity tuning and backup channel within the ±5 kHz protected region (assuming the digital audio compression was capable of delivering both the main and audio backup signal within the protected ±5 kHz). The modulation characteristics of the AM all-digital system are based upon the AM IBOC hybrid system, described in U.S. Pat. No. 5,588,022 and modifications thereof, see for example, D. Hartup, D. Alley, D. Goldston, “AM Hybrid IBOC DAB System,” presented at the NAB Radio Show, New Orleans, September 1997 and IEEE 47 th  Annual Broadcast Symposium, Washington, D.C., September 1997.  
         [0033]    A significant functional difference between the hybrid and all-digital formats is the particular signal used for the time diversity tuning and backup. The hybrid system uses the analog AM signal, while the all-digital system replaces the analog AM signal with the low-rate digital tuning and backup coded signal. In the all-digital system, both backup diversity signals can occupy the same bandwidth and spectral location. Furthermore, the complication of interference to and from second adjacent signals is eliminated by bandlimiting the DAB signals to ±10 kHz. Since locations of subcarriers potentially impacted by the first adjacent interferers is easily identified, these subcarriers would hold optional digitally encoded information (less important program material) to increase audio quality.  
         [0034]    The minimum required embedded digitally encoded information, along with the required diversity backup signal resides in the protected bandwidth region within ±5 kHz from the center carrier. Any additional digitally encoded information (to enhance the audio quality of the program material over the minimum) is placed in the “wings” between 5 kHz and 10 kHz away from the center carrier on each side to avoid any second adjacent interference. This partitioning of digitally encoded segments leads to four approximately equal-size segments (i.e. both main digitally encoded and backup AM or digitally encoded segments in the protected central frequency band ±5 kHz region, and one segment in each of the two wings).  
         [0035]    [0035]FIG. 3 is a block diagram of a DAB transmitter  46  that can broadcast digital audio broadcasting signals in accordance with the present invention. A signal source  48  provides the signal to be transmitted. The source signal may take many forms, for example, an analog program signal and/or a digital information signal. A digital signal processor (DSP) based modulator  50  processes the source signal in accordance with various signal processing techniques, such as source coding, interleaving and forward error correction, to produce in-phase and quadrature components of the complex base band signal on lines  52  and  54 . These components are shifted up in frequency, filtered and interpolated to a higher sampling rate in up-converter block  56 . This produces digital samples at a rate f s , on intermediate frequency signal f if  on line  58 . Digital-to-analog converter  60  converts the signal to an analog signal on line  62 . An intermediate frequency filter  64  rejects alias frequencies to produce the intermediate frequency signal fit on line  66 . A local oscillator  68  produces a signal f lo , on line  70 , which is mixed with the intermediate frequency signal on line  66  by mixer  72  to produce sum and difference signals on line  74 . The sum signal and other unwanted intermodulation components and noise are rejected by image reject filter  76  to produce the modulated carrier signal f c  on line  78 . A high power amplifier  80  then sends this signal to an antenna  82 .  
         [0036]    [0036]FIG. 4 is a block diagram of a radio receiver  84  constructed in accordance with this invention. The DAB signal is received on antenna  86 . A bandpass preselect filter  88  passes the frequency band of interest, including the desired signal at frequency f c , but rejects the image signal at f c −2f if  (for a low side lobe injection local oscillator). Low noise amplifier  90  amplifies the signal. The amplified signal is mixed in mixer  92  with a local oscillator signal f lo  supplied on line  94  by a tunable local oscillator  96 . This creates sum (f c +f lo ) and difference (f c −f lo ) signals on line  98 . Intermediate frequency filter  100  passes the intermediate frequency signal fit and attenuates frequencies outside of the bandwidth of the modulated signal of interest. An analog-to-digital converter  102  operates using a clock signal f s  to produce digital samples on line  104  at a rate f s . Digital down converter  106  frequency shifts, filters and decimates the signal to produce lower sample rate in-phase and quadrature signals on lines  108  and  110 . A digital signal processor based demodulator  1   2  then provides additional signal processing to produce an output signal on line  114  for output device  116 .  
         [0037]    The present invention is based upon a combination of the pragmatic trellis code modulation (PTCM) technique, and the application of Complementary Punctures Codes to an IBOC DAB system, expanding the complementary-like properties to multiple dimensions. In the preferred embodiment of the invention, each of the sub-carriers is modulated using 64-QAM symbols. The digital information, which may represent for example audio program material and/or data, is interleaved in partitions, and then Forward Error Correction (FEC) coded. The FEC method of this invention is particularly applicable to AM IBOC (In-Band On-Channel) DAB (Digital Audio Broadcast) systems. This FEC technique is hereafter referred to as Complementary Pragmatic Trellis-Coded Modulation (CPTCM). The CPTCM coding is designed to accommodate the likely interference scenarios encountered in the AM channel.  
         [0038]    The basic requirements for the CPTCM code include the ability to puncture the original code in various partitions including main, backup, lower sideband and upper sideband. Each of the four partitions must survive as a good code. The performance of the lower and upper sidebands should be optimized as a pair of symmetric complementary non-overlapping partitions. The main and backup partitions each overlap portions of the lower and upper sideband partitions. In the preferred embodiment, the backup and main partitions can be skewed such that the backup partition has better performance than the main partition. Of course, all partitions should be noncatastrophic codes. In the event of a loss of a signal in the other partitions, each of the four partitions must survive as a good code.  
         [0039]    The PTCM technique is applied to a QAM symbol by treating the I and Q components as independently coded amplitude shift keyed (ASK) signals. In the preferred embodiment of this invention, each 64-QAM symbol is created by modulating the I or Q component with independent 8-ASK signals. The 8-ASK symbols are generated from 3-bit groups using a unique PTCM mapping. The bits comprising the ASK symbol component are further separated into two categories where one of the bits is typically uncoded (or coded with a forward error correction scheme designated as FECb), and the remaining of the bits are coded using another forward error correction scheme designated as FECa. The typically uncoded bit is designated as ASK0. The pair of coded bits are designated as ASK1 and ASK2. The mapping of the code bit triplets to the 8 levels of the 8-ASK symbols is presented in Table 1.  
                                                     TABLE 1                           Mapping of CPTCM-Coded Bits to 8 Levels       of the 8-ASK Symbols.                Level   Level   Level   Level   Level   Level   Level   Level       MAPPING   −3.5   −2.5   −1.5   −0.5   0.5   1.5   2.5   3.5               ASK0   0   0   0   0   1   1   1   1       (FECb)       ASK1   0   0   1   1   0   0   1   1       (FECa)       ASK2   0   1   1   0   0   1   1   0       (FECa)                  
 
         [0040]    In the decoding process, first FECa decoding is performed on the ASK1 and ASK2 bits. Then the ASK0 bits can be corrected by mapping the ASK1 and ASK2 bit pair to the one of the two possible levels which minimizes the error correction distance. This process of correcting the original symbols involves re-encoding and interleaving of the decoded FECa bits. FECb may be decoded after applying the correction to bit ASK0 from FECa. This multilevel decoding has the effect of yielding a minimum distance of 4 for bit ASK0 (in this 8-ASK example) prior to FECb decoding (if any).  
         [0041]    In the preferred embodiment of a transmitter constructed in accordance with the invention, the interleaver is designed for CPTCM with a scalable (2-layer) audio codec. The interleaver is comprised of two parts: a core interleaver spanning 50 subcarriers (25 upper plus 25 lower sideband) and an enhancement interleaver spanning 28 subcarriers (28 complementary subcarriers for the hybrid system, and 28 in each the lower and upper “wings for the all-digital system). Specifically, subcarriers  2  through  54  on either side of the main carrier are utilized in the 20 kHz system. The core interleaver partitions for the hybrid system are transmitted on the sub-carriers located at positions 30 through 54 and −30 through −54. The enhancement interleaver partitions are transmitted on 28 complementary sub-carriers located at positions 2 through 28 and −2 through −28. In the all digital system, core interleaver partitions for the hybrid system are transmitted on the sub-carriers located at positions 2 through 26 and −2 through −26. The enhancement interleaver partitions are transmitted on sub-carriers located at positions 27 through 54 and −27 through −54.  
         [0042]    In the preferred embodiment, the CPTCM codes are created through puncturing of industry standard rate 1/3 convolutional, K-7 codes, which can be decoded using a standard Viterbi decoder. Preferably, the codes use generator polynomials described in conventional octal notation as 133, 171 and 165. A generator of 100 can also used for some of the partitions where a systematic code is desired.  
         [0043]    The forward error correction of the preferred embodiment of the invention provides good results in both the hybrid system and all-digital system. For the hybrid system as illustrated in FIG. 1, the puncture pattern would provide code bits to an upper sideband and lower sideband. In the preferred embodiment, each sideband is required to provide a good quality code in the case of the other sideband being corrupted. In the preferred embodiment, each sideband is coded using a rate 3/4 code for FECa producing a combined code rate of 3/8 for FECa. Each sideband is coded using a rate 1 code for FECb producing a combined code rate of 1/2 for FECb. Therefore the overall rate of FECa plus FECb is 5/12, or rate 5/6 on the lower or upper sideband.  
         [0044]    For the preferred embodiment of the all-digital system as illustrated in FIG. 2, the core FECa puncture pattern is distributed between a main audio channel and a backup audio channel. In the preferred embodiment, the backup channel would be used for fast tuning of the main channel, and when code combined with the backup channel, would provide stereo audio. The main channel is preferably coded at rate 1 while the backup channel will be coded at rate 3/5.  
         [0045]    The best rate 3/4 code determined from puncturing the generators [133, 171, 165] was based on the following puncture pattern:  
           1       0       0           0       1       1           1       0       0                             
 
         [0046]    this pattern resulted in a code with a free distance=5, a=4, and c=28. The best r=3/8 pattern studied resulted in free distance=12, a=1, c=3. However, this pattern was based on combining the best rate 3/4 with a less than optimal rate 3/4 puncture pattern:  
               1       0       0           0       1       1           1       0       0         +         0       0       1           1       0       0           0       1       1           =         1       0       1           1       1       1           1       1       1                               
 
         [0047]    This puncture pattern is not used in the preferred embodiment since it is preferable to maximize the performance of the component rate 3/4 codes at the expense of some performance of the combined rate 3/8 code. Combining the best r=3/4 pattern with a cyclically shifted version yielded the following r=3/8 pattern:  
           1       0       1           1       2       1           1       0       1                             
 
         [0048]    or equivalently,  
           1       0       1           1       1       1           1       0       1           0       1       0                             
 
         [0049]    with the second generator polynomial repeated [133, 171, 165, 171]. The properties of this punctured code are free distance=11, a=1, c=3. The puncture pattern was expanded for a period of 6 as shown below:  
           1       0       1       1       0       1           1       1       1       1       1       1           1       0       1       1       0       1           0       1       0       0       1       0                             
 
         [0050]    The elements of the pattern were assigned to the upper sideband and lower sideband. Assignment to upper and lower sidebands resulted in r=3/4 codes for each side with free distance=5, a=4, c=28.  
           L       0       U       L       0       U           U       U       L       U       U       L           L       0       U       L       0       U           0       L       0       0       L       0                             
 
         [0051]    Core FECa Puncture Pattern  
         Upper Sideband r=3/4;  
         Lower Sideband r=3/4  
         [0052]    To fit the all-digital AM system, code bits from each sideband must be assigned to the main and backup channels. Since in the preferred embodiment, the main channel is coded at r=1 and the backup channel is coded at r=3/5, the upper and lower sidebands combined must contain 6 code bits from main and 10 code bits from backup. Since the main channel is more restrictive, the best way to puncture the hybrid pattern to provide a non-catastrophic r=1 code was determined. When considering combinations of upper and lower that could be used to define the main code bits, out of 225 possible patterns, only 16 were determined to be non-catastrophic.  
         [0053]    For each non-catastrophic main puncture pattern, there is a corresponding backup puncture pattern which would yield the r=3/8 pattern given above when combined. The best non-catastrophic backup pattern from this set has a free distance=6, a=1, c=3.  
           0       0       0       L       0       U           0       U       0       U       L       L           L       0       U       L       0       U                             
 
         [0054]    FECa Backup Channel Puncture Pattern  
         r=3/5  
         [0055]    In theory, a free distance=7 can be obtained from a r=3/5 code. The corresponding non-catastrophic main pattern has free distance=1, a=6, c=70. This is also the best performing main pattern out of the set of 16. For a r=1 systematic code, the properties would be free distance=1, a=1, c=1.  
           L       0       U       0       0       0           U       L       L       0       U       0           0       0       0       0       0       0                             
 
         [0056]    Core FECa Main Channel Puncture Pattern  
         r=1  
         [0057]    The combined main, backup, upper, and lower puncture pattern for the core FECa code is defined as follows:  
             MLa             0           0         MUa             0             BLa   0         0         BUa   0               MUa             1             BUa   1           MLa             1             BUa   2           MUa             2             BLa   1               BLa   2         0         BUa   3           BLa   3         0         BUa   4             0         MLa             2           0       0         BLa   4         0                             
 
         [0058]    Core FECa Composite Puncture Pattern Using G=[133, 171, 165, 171].  
                                                                   TABLE 2                           Core FECa Summary of Parameters.                Partition   Rated   d f     a   c                            Main   1   1   6   70           Backup   3/5   6   1   3           Lower   3/4   5   4   28           Upper   3/4   5   4   28           Composite   3/8   11   1   3                      
 
         [0059]    Given the generator polynomials [133, 171, 165], a puncture pattern was found to satisfy conditions for both the FECa core hybrid AM and core all-digital AM  15  requirements. This pattern provides a r=3/8 code with free distance=11, a=1, c=3. It can be separated into upper and lower sidebands resulting in r=3/4 codes with free distance=5, a=4, c=28. The upper and lower sideband code bits may then be assigned to a main channel and backup channel for all digital AM. The main channel code is a non-catastrophic r=1 code with free distance=1, a=6, and c=70. The backup channel code is a non-catastrophic r=3/5 code with free distance=6, a=1, and c=3.  
         [0060]    The core FECb code was designed using techniques similar to the creation of the FECa code. The overall rate of the core FECb code is 1/2. It is desirable to provide a non-catastrophic rate 1 code in each of the main, backup, lower, and upper partitions. The best performance should be provided on the backup partition, which can be accomplished through a systematic rate 1 code. One possible puncture pattern is  
             ML   0         0       0         MU   0               ML   1         0         MU   1         0             BU   0           BL   0           BL   1           BU   1                               
 
         [0061]    Core FECb Composite Puncture Pattern Using Generators [171, 165, 100].  
                                                                   TABLE 3                           Core FECb Summary of Parameters.                Partition   Rate   d f     a   c                            Main   1   1   4   38           Backup   1   1   1   1           Lower   1   1   4   12           Upper   1   1   4   12           Composite   1/2   4   1   1                      
 
         [0062]    However, in the preferred embodiment a systematic puncture pattern for the core FECb code with better rate 1 was chosen. The preferred pattern requiring no coding is:  
             MUb   0           BUb   1               BLb   0           MLb   1                               
 
         [0063]    Core FECb Composite Puncture Pattern using systematic generators [100, 100].  
                                         TABLE 4                           Core FECb Summary of Parameters.                Partition   Rate   d f     a   c                       Main   1   1   1   1           Backup   1   1   1   1           Lower   1   1   1   1           Upper   1   1   1   1           Composite   1/2   2   1   1                      
 
         [0064]    The preferred all-digital enhancement FECa code was determined using techniques similar to the creation of the core FECa code. In the preferred embodiment the overall rate of the upper plus lower enhancement FECa code is rate 1/4. A performance goal is to provide the best rate 1/2 code for the lower and upper partitions. The performance of the best rate 1/4 code (d=20, a=4, c=9, G=[173, 167, 135, 111]) has been found to be slightly better than the rate 1/4 performance of a pair (d=20, a=11, c=36) of replicated standard rate 1/2 codes (d=10, a=11, c=36, G=[133, 171]). However, a computer search revealed that the latter code cannot be divided into a complementary pair of rate 1/2 codes each with a free distance of 10. Alternatively, a pair of optimum rate 1/2 codes can be created by reversing the coefficients of the generator polynomials for one of them. This rate 1/4 code achieves good performance (d=20, a=5, c=11, G=[133, 171, 155, 117]). However, the small improvement in performance over simple replication of the rate 1/2 code does not justify the extra coding complexity. Therefore, it is preferable to replicate the optimum rate 1/2 codes rather than compromise the rate 1/2 performance to achieve a slight improvement after code combining, when possible.  
         [0065]    The all-digital enhancement FECb code shall be a systematic rate 1 code for the same reasons as the core FECb code. Although improved performance when code-combining upper and lower sidebands could be achieved if complementary rate 1 codes were used, the optimization of performance on each individual sideband is determined to be more important.  
         [0066]    Since the hybrid enhancement partitions are not to be code-combined, the hybrid enhancement FECa code in the preferred embodiment is the industry standard rate 1/2, K=7, G=[133, 171] code yielding a free distance of 10, a=3, c=12. The hybrid enhancement FECb code in the preferred embodiment is a rate 1 systematic code with G=[100], yielding a free distance of 1, a=1, c=1. This choice is the same as the all-digital enhancement FECa and FECb codes.  
         [0067]    Interleaver blocks consist of 32 COFDM symbols (baud). There are nominally 8 blocks in a modem frame (interleaver span) for the main and the enhancement partitions. The backup partition is interleaved over only 1 block to permit rapid tuning. The core interleaver consists of an upper sideband and a lower sideband (25 subcarriers each). Each core block sideband holds a total of 800 64-QAM symbols (750 data+50 Training) The enhancement interleaver holds 896 64-QAM symbols (840 data+56 Training).  
         [0068]    The scalable audio codec is comprised of 2 layers (core anid enhancement). The core layer is mapped onto 64-QAM subcarriers (50 subcarriers on each side) while the enhancement layer is mapped onto 28 64-QAM complementary subcarrier pairs. The core and enhancement layers are coded separately.  
         [0069]    Interleaving within each core partition block spanning 25 subcarriers and 32 OFDM symbols performed using the following expression for the row and column indices:  
               row        (   k   )       =     mod   [         11   ·     mod   (       9   ·   k     ,   25     )       +     16   ·     floor   (     k   25     )       +     11   ·     floor   (     k   50     )         ,   32                     col        (   k   )       =     mod   [       9   ·   k     ,   25     ]                     k   =       0                 …                   BLOCKS   ·   30   ·   25       -   1       ,       where                 BLOCKS     ≡   8                                              
 
         [0070]    The index k points to one of the 750 64-QAM symbols within the core partition block. Each of the 64-QAM symbols carries 6 code bits that are mapped to the core partition block. The remaining 50 64-QAM symbols that are not indexed with the row and column indices of the core partition block array are used as training symbols.  
                                                                                                                                               TABLE 5                           64-QAM Symbol Indices Within A Core Block.                    0   1   2   3   4   5   6   7   8   9   10   11   12               A =   0   0   “T”   728   692   631   595   534   498   437   376   340   279   243           1   150   114   53   17   “T”   745   684   648   587   526   490   429   393           2   300   264   203   167   106   70   9   “T”   737   676   640   579   543           3   450   414   353   317   256   220   159   123   62   1   “T”   729   693           4   600   564   503   467   406   370   309   273   212   151   115   54   18           5   “T”   714   653   617   556   520   459   423   362   301   265   204   168           6   125   89   28   “T”   706   670   609   573   512   451   415   354   318           7   275   239   178   142   81   45   “T”   723   662   601   565   504   468           8   425   389   328   292   231   195   134   98   37   “T”   715   654   618           9   575   539   478   442   381   345   284   248   187   126   90   29   “T”           10   725   689   628   592   531   495   434   398   337   276   240   179   143           11   50   14   “T”   742   681   645   584   548   487   426   390   329   293           12   200   164   103   67   6   “T”   734   698   637   576   540   479   443           13   350   314   253   217   156   120   59   23   “T”   726   690   629   593           14   500   464   403   367   306   270   209   173   112   51   15   “T”   743           15   650   614   553   517   456   420   359   323   262   201   165   104   68           16   25   “T”   703   667   606   570   509   473   412   351   315   254   218           17   175   139   78   42   “T”   720   659   623   562   501   465   404   368           18   325   289   228   192   131   95   34   “T”   712   651   615   554   518           19   475   439   378   342   281   245   184   148   87   26   “T”   704   668           20   625   589   528   492   431   395   334   298   237   176   140   79   43           21   “T”   739   678   642   581   545   484   448   387   326   290   229   193           22   100   64   3   “T”   731   695   634   598   537   476   440   379   343           23   250   214   153   117   55   20   “T”   748   687   626   590   529   493           24   400   364   303   267   206   170   109   73   12   “T”   740   679   643           25   550   514   453   417   356   320   259   223   162   101   65   4   “T”           26   700   664   603   567   506   470   409   373   312   251   215   154   118           27   75   39   “T”   717   656   620   559   523   462   401   365   304   268           28   225   189   128   92   31   “T”   709   673   612   551   515   454   418           29   375   339   278   242   181   145   84   48   “T”   701   665   604   568           30   525   489   428   392   331   295   234   198   137   76   40   “T”   718           31   675   639   578   542   481   445   384   348   287   226   190   129   93                                13   14   15   16   17   18   19   20   21   22   23   24                           A =   0   182   146   85   49   “T”   702   666   605   569   508   472   411               1   332   296   235   199   138   77   41   “T”   719   658   622   561               2   482   446   385   349   288   227   191   130   94   33   “T”   711               3   632   596   535   499   438   377   341   280   244   183   147   86               4   “T”   746   685   649   588   527   491   430   394   333   297   236               5   107   71   10   “T”   738   677   641   580   544   483   447   386               6   257   221   160   124   63   2   “T”   730   694   633   597   536               7   407   371   310   274   213   152   116   55   19   “T”   747   686               8   557   521   460   424   363   302   266   205   169   108   72   11               9   707   671   610   574   513   452   416   355   319   259   222   161               10   82   46   “T”   724   663   602   566   505   469   408   372   311               11   232   196   135   99   38   “T”   716   655   619   558   522   451               12   382   346   285   249   188   127   91   30   “T”   708   672   611               13   532   496   435   399   338   277   241   180   144   83   47   “T”               14   682   646   585   549   488   427   391   330   294   233   197   136               15   7   “T”   735   699   638   577   541   480   444   383   347   286               16   157   121   60   24   “T”   727   691   630   594   533   497   436               17   307   271   210   174   113   52   16   “T”   744   683   647   586               18   457   421   360   324   263   202   166   105   69   8   “T”   736               19   607   571   510   474   413   352   316   255   219   158   122   61               20   “T”   721   660   624   563   502   466   405   369   308   272   211               21   132   96   35   “T”   713   652   616   555   519   458   422   361               22   282   246   185   149   88   27   “T”   705   669   608   572   511               23   432   396   335   299   238   177   141   80   44   “T”   722   661               24   582   546   485   449   388   327   291   230   194   133   97   36               25   732   696   635   599   538   477   441   380   344   283   247   186               26   57   21   “T”   749   688   627   591   530   494   433   397   336               27   207   171   110   74   13   “T”   741   680   644   583   547   486               28   357   321   260   224   163   102   66   5   “T”   733   697   636               29   507   471   410   374   313   252   216   155   119   58   22   “T”               30   657   621   560   524   463   402   366   305   269   208   172   111               31   32   “T”   710   674   613   552   516   455   419   358   322   261   .                      
 
         [0071]    The 30000 core information bits comprising each modem frame are coded and assembled in groups of bits from the puncture patterns, as defined previously and illustrated in FIG. 5. In FIG. 5, block  128  shows that the 30,000 bits are assembled into a modem frame. These bits are divided into 3000 10-bit groups as shown in block  130 . Block  132  shows that six bits of each 10-bit group are encoded and punctured according to FECa, while block  134  shows that the other four bits of each 10-bit group are encoded and punctured in accordance with FECb. The FECa encoded and punctured bits are assigned to backup upper partition  136 , the backup lower partition  138 , the main upper partition  144  and the main lower partition  146 . The FECb encoded and punctured bits are assigned to backup upper partition  140 , the backup lower partition  142 , the main upper partition  148  and the main lower partition  150 . These groupings are mapped into the core interleaver using the expressions presented in Table 6. Delay ovals  152 ,  154 ,  156  and  158  show that the backup partitions are delayed with respect to the main partitions. The backup symbols are then delivered on lines  160  and the main symbols are delivered on lines  162 .  
         [0072]    Core interleaver indices: k, b and p are defined as follows:  
         [0073]    k=Block index, 0 to 749 symbols in each core block, 0 to 839 symbols in each enhancement block;  
         [0074]    b=Block number, 0 to 7 within each modem frame; and  
         [0075]    p=PTCM bit mapping within each 64-QAM symbol, with (IASK0=0, IASK1=1, IASK2=2, QASK2=3, QASK1=4, QASK0=5).  
                                                           TABLE 6                           Core Interleaver Mapping.            Partition   N, n=   k   b   p       X k,b,p     0 . . . N−1   index in block b   block #   I&amp;Q,ASK mapping                    BUb k,b,p     6000   mod(n,750)   floor(n/750)   0       BLb k,b,p     6000   mod(n+7, 750)   floor(n/750)   0       BUa k,b,p     15000   mod(mod(n,1875),750)   floor(n/1875)   1+floor[mod (n,1875)/750)]       BLa k,b,p     15000   mod(mod(n,1875)+7, 750)   floor(n/1875)   1+floor[(mod(n,1875)/750)]       MUb k,b,p     6000   mod(n,750)   mod[3n+floor(n/3000),8]   5       MLb k,b,p     6000   mod(n,750)   mod[3n+floor(n/3000)+3,8]   5       MUa k,b,p     9000   mod(mod(n,1125)+375, 750)   mod[3n,8]   4−floor[mod(n,1125)/750]       MLa k,b,p     9000   mod(mod(n,1125)+382, 750)   mod[3n+3,8]   4−floor[mod(n,1125)/750]                  
 
         [0076]    [0076]FIG. 6 is a functional block diagram of the enhancement partition block interleaver. Block  164  shows that the 26880 enhancement bits are assembled into a modem frame. These bits are then divided into 13440 2-bit groups as shown in block  166 . One bit of each 2-bit group is encoded and punctured according to FECa as shown in block  168 . This encoding and puncturing results in 2-bit outputs that are assigned to enhancement partition  170 . The other bit of the 2-bit groups in block  166  is assigned to enhancement partition  172 . The interleaving of FIG. 7 within each enhancement partition block spanning 28 subcarriers and 32 OFDM symbols is performed using the following expression for the row and column indices:  
               row        (   k   )       =     mod   [         11   ·     mod   (       9   ·   k     ,   28     )       +       16   ·   floor                     (     k   28     )       +       11   ·   floor                     (     k   56     )         ,   32                     col        (   k   )       =     mod   [       9   ·   k     ,   28     ]                     k   =       0                 …                   BLOCKS   ·   30   ·   28       -   1       ,       where                 BLOCKS     ≡   8                                              
 
         [0077]    The index k points to one of the 840 64-QAM symbols within the enhancement partition block. Each of the 64-QAM symbols carries 6 code bits that are mapped to the enhancement partition block. The remaining 56 64-QAM symbols that are not indexed with the row and column indices of the enhancement partition block array are used as training symbols.  
                                                                                 TABLE 7                           64-QAM Symbol Indices Within An Enhancement Block.                    0   1   2   3   4   5   6   7   8   9   10   11   12   13               A =   0   0   “T”   834   775   715   657   598   539   480   421   390   331   272   213           1   168   137   78   19   “T”   825   766   707   648   589   558   499   440   381           2   336   305   246   187   128   69   10   “T”   816   757   726   667   608   549           3   504   473   414   355   296   237   178   119   60   1   “T”   835   776   717           4   672   641   582   523   464   405   346   287   228   169   138   79   20   “T”           5   “T”   809   750   691   632   573   514   455   396   337   306   247   188   129           6   140   109   50   “T”   800   741   682   623   564   505   474   415   356   297           7   308   277   218   159   100   41   “T”   791   732   673   642   583   524   465           8   476   445   386   327   268   209   150   91   32   “T”   810   751   692   633           9   644   613   554   495   436   377   318   258   200   141   110   51   “T”   801           10   812   781   722   663   604   545   486   427   368   309   278   219   160   101           11   56   25   “T”   831   772   713   654   595   536   477   446   387   328   269           12   224   193   134   75   16   “T”   822   763   704   645   614   555   496   437           13   392   361   302   243   184   125   66   7   “T”   813   782   723   664   605           14   560   529   470   411   352   293   234   175   116   57   26   “T”   832   773           15   728   697   638   579   520   461   402   343   284   225   194   135   76   17           16   28   “T”   806   747   688   629   570   511   452   393   362   303   244   185           17   196   165   106   47   “T”   797   738   679   620   561   530   471   412   353           18   364   333   274   215   156   97   38   “T”   788   729   698   639   580   521           19   532   501   442   383   324   265   206   147   88   29   “T”   807   748   689           20   700   669   610   551   492   433   374   315   256   197   168   107   48   “T”           21   “T”   837   778   719   660   601   542   483   424   365   334   275   216   157           22   112   81   22   “T”   828   769   710   651   592   533   502   443   384   325           23   280   249   190   131   72   13   “T”   819   760   701   670   611   552   493           24   448   417   358   299   240   181   122   63   4   “T”   838   779   720   661           25   616   585   526   467   408   349   290   231   172   113   82   23   “T”   829           26   784   753   694   635   576   517   458   399   340   281   250   191   132   73           27   84   53   “T”   803   744   685   626   587   508   449   418   359   300   241           28   252   221   162   103   44   “T”   794   735   676   617   586   527   468   409           29   420   389   330   271   212   153   94   35   “T”   785   754   695   636   577           30   588   557   496   439   380   321   262   203   144   85   54   “T”   804   745           31   756   725   666   607   548   489   430   371   312   253   222   163   104   45                       14   15   16   17   18   19   20   21   22   23   24   25   26   27       A =   0   154   95   36   “T”   786   755   696   637   578   519   460   401   342   283           1   322   203   204   145   86   55   “T”   805   746   687   628   569   510   451           2   490   431   372   313   254   223   164   105   46   “T”   796   737   678   619           3   658   599   540   481   422   391   332   273   214   155   96   37   “T”   787           4   826   767   708   649   590   559   500   441   382   323   264   205   146   87           5   70   11   “T”   817   758   727   668   609   550   491   432   373   314   255           6   238   179   120   61   2   “T”   836   777   718   659   600   541   482   423           7   406   347   288   229   170   139   80   21   “T”   827   768   709   650   591           8   574   515   456   397   338   307   248   189   130   71   12   “T”   818   759           9   742   683   624   565   506   475   416   357   298   239   180   121   62   3           10   42   “T”   792   733   674   643   584   525   466   407   348   289   230   171           11   210   151   92   33   “T”   811   752   693   634   575   516   457   398   339           12   378   319   260   201   142   111   52   “T”   802   743   684   625   566   507           13   546   487   428   369   310   279   220   161   102   43   “T”   793   734   675           14   714   655   596   537   478   447   388   329   270   211   152   93   34   “T”           15   “T”   823   764   705   646   615   556   497   438   379   320   261   202   143           16   126   67   8   “T”   814   783   724   665   606   547   488   429   370   311           17   294   235   176   117   58   27   “T”   833   774   715   656   597   538   479           18   462   403   344   285   226   195   136   77   18   “T”   824   765   706   647           19   630   571   512   453   394   363   304   245   186   127   68   9   “T”   815           20   798   739   680   621   562   531   472   413   354   295   236   177   118   59           21   98   39   “T”   789   730   699   640   581   522   463   404   345   286   227           22   266   207   148   89   30   “T”   808   749   690   631   572   513   454   395           23   434   375   316   257   198   167   108   49   “T”   799   740   681   622   563           24   602   543   484   425   366   335   276   217   158   99   40   “T”   790   731           25   770   711   652   593   534   503   444   385   326   267   208   149   90   31           26   14   “T”   820   761   702   871   612   553   494   435   376   317   258   199           27   182   123   64   5   “T”   839   780   721   662   603   544   485   426   307           28   350   291   232   173   114   83   24   “T”   830   771   712   653   594   535           29   518   459   400   341   282   251   192   133   74   15   “T”   821   762   703           30   686   627   568   509   450   419   360   301   242   183   124   65   6   “T”           31   “T”   795   736   677   618   587   528   469   410   351   292   233   174   115                  
 
         [0078]    The 26880 enhancement information bits comprising each modem frame are coded and assembled in groups of bits from the puncture patterns, as defined previously and illustrated in FIG. 6. These groupings are mapped into the enhancement interleaver using the expressions presented in Table 8.  
         [0079]    The enhancement interleaver indices k, b and p are defined as follows:  
         [0080]    k=Block index, 0 to 839 symbols in each core block,  
         [0081]    b=Block number, 0 to 7 within each modem frame, and  
         [0082]    p=PTCM bit mapping within each 64-QAM symbol, with (IASK0=0, IASK1=1, IASK2=2, QASK2=3, QASK1=4, QASK0=5).  
                                                           TABLE 8                           Enhancement Interleaver Mapping.            Partition   N   k   b   p       X k,b,p     n=0 . . . N−1   index in block b   block #   I&amp;Q,ASK mapping                    EUb k,b,p     13440   k=mod(n,840)   mod(3n+floor(n/840),8]   5*floor(n/6720)       ELb k,b,p     13440   k=mod(n,840)   mod(3n+floor(n/840)+3,8]   5*floor(n/6720)       EUa k,b,p     26880   k=mod(n,840)   mod(3n+floor(n/840),8]   1+mod[n+floor(n/6720),4]       ELa k,b,p     26880   k=mod(n,840)   mod(3n+floor(n/840)+3,8]   1+mod[n+floor(n/6720),4]                  
 
         [0083]    A functional block diagram of the deinterleaver and FEC decoder portions of a receiver is shown in FIG. 7. The constellation data at the inputs  174  and  176  consists of the I and Q values for each of the 64-QAM symbols which have been demodulated and normalized to the constellation grid. Blocks  178  and  180  show that Channel State Information (CSI) is associated with each I and Q value to permit subsequent soft-decision detection of the bits in blocks  182  and  184 . The soft decision outputs are deinterleaved as illustrated by blocks  186  and  188  and decoded as illustrated by blocks  190  and  192 . The purpose of the four delay elements  194 ,  196 ,  198  and  200  in the figure is to time-align the backup audio information with the main and enhancement audio information. This delay compensates for the diversity delay experienced by the backup audio information inserted at the transmitter.  
         [0084]    The core and enhancement bits are also input on lines  202  and  204  and are subjected to FECa encoding as shown in blocks  206  and  208 . The encoded bits are reinterleaved as shown by blocks  210 ,  212  and  214 . Soft decisions are then produced as shown in blocks  216 ,  218  and  220 . The soft decisions are deinterleaved as shown in blocks  222  and  224  and decoded as illustrated by blocks  226  and  228 . Blocks  178 ,  182 ,  186 ,  190 ,  206 ,  210 ,  216 ,  222  and  226  in FIG. 8 indicate functions that must be processed on interleaver block boundaries (as opposed to modem frame boundaries) in order to minimize delay in processing the backup audio information.  
         [0085]    Assuming K information bits per symbol, the binary metric for the k-th bit is given by:  
           λ     i   ,   k       =       ln          P                   r   (       b   k     =     1             y   i     )               P                   r   (       b   k     =     0             y   i     )                 =     ln            ∑     all                   s   j     1      k                  f   n          (       y   i     -     s   j     1   ,   k         )             ∑     all                   s   j     0      k                  f   n          (       y   i     -     s   j     0   ,   k         )                 ,     k   =   1     ,   …              ,   K                         
 
         [0086]    For soft metric generation, since binary codes are used for PTCM, it is necessary to obtain soft binary metrics from noisy M-ary symbols. Suppose that the received noise symbol is:  
           y   i   =s   i   +n   i ,  
         i=1,.N  
         [0087]    Assuming K information bits per symbol, the binary metric for the k-th bit is given by:  
           λ     i   ,   k       =       ln          P                   r   (       b   k     =     1             y   i     )               P                   r   (       b   k     =     0             y   i     )                 =     ln            ∑     all                   s   j     1   ,   k                  f   n          (       y   i     -     s   j     1   ,   k         )             ∑     all                   s   j     0   ,   k                  f   n          (       y   i     -     s   j     0   ,   k         )                 ,     k   =   1     ,   …              ,   K                         
 
         [0088]    where s j   1,k  stands for the j-th symbol in the constellation that has bit value 1 in the k-th bit position (and similarly for s j   0,k , the j-th symbol in the constellation that has bit value 0 in the k-th bit) and  
           f   n          (   x   )       =       1       2                 π                   σ   2                exp        [     -       x   2       2                   σ   2           ]                               
 
         [0089]    is the probability density function of noise, assuming AWG noise. The above formula for the soft bit metric applies for any constellation. The main disadvantage of this approach is that it requires computations of exponentials. An approximate metric can be obtained by approximating the sum of exponentials by the maximum exponential, so that  
                 λ     i   ,   k       ≅            ln            max     all                   s   j     1   ,   k                exp        [       -     1     2                   σ   i   2                  (       y   i     -     s   j     1   ,   k         )     2       ]             max     all                   s   j     0   ,   k                exp        [       -     1     2                   σ   i   2                  (       y   i     -     s   j     0   ,   k         )     2       ]               ,     k   =   1     ,   …              ,   K               ≅              1                  σ   i   2              [         y   i          (       s     1   ,     k   min         -     s     0   ,     k   min           )       -     0.5        (       s     1   ,     k     min   2           -     s     0   ,     k     min   2             )         ]                                   
 
         [0090]    where irrelevant terms and constants are dropped and s 1,k   min  denotes the symbol closest to y i  that has 1 in the k-th bit position (and similarly for s 0,k   min ). Thus, by means of this approximation (so called log-max approximation) we avoid calculating exponentials. However, as a consequence of using this approximation a fraction of dB can be lost in performance.  
         [0091]    [0091]FIG. 8 is a graphic representation of the soft metrics  230 ,  232  and  234  with linear clipper. Using this clipper achieves improvements of soft metrics for the impulsive noise scenario. Let us assume that the noisy symbol sample is passed through a nonlinearity of the form (soft limiter or linear clipper). It is desired to construct a soft metric that performs approximately the same in AWGN as previously considered metrics, yet that will have smaller degradation in impulsive noise. That is, it has to have enough “softness” to maximize the performance in AWGN and to limit metric samples when impulsive noise is present, i.e. to prevent the excessive metric growth when large noise samples are present. Toward that goal consider the 8-ASK constellation and nonlinearities shown in FIG. 8.  
         [0092]    Based on the value of a received noisy signal we construct soft metrics by passing the received sample through two different nonlinearities shown in FIG. 8. The constructed soft bit values are further divided by the corresponding values of average noise power.  
         [0093]    The nonlinearity for bit 1 (MSB) is positioned depending upon decisions for bits 2 and 3. In this figure we show an example when a di-bit 10 is decided for bits 2 and 3. Thus, we can see that this metric performs almost the same as other soft metrics in the absence of impulsive noise, but outperforms other soft metrics if impulsive noise is present. It can also outperform hard decision decoding. In summary, the soft metric can be represented by:  
         soft_out   i     =       F        (     y   i     )         σ   i   2                             
 
         [0094]    where y represents the received noisy symbol and F(.) is the desired nonlinearity.  
         [0095]    While the present invention has been described in terms of its preferred embodiment, it will be understood by those skilled in the art that various modifications can be made to the disclosed embodiment without departing from the scope of the invention as set forth in the claims.