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 
   This application is a divisional application of U.S. patent application Ser. No. 09/438,822, filed Nov. 11, 1999. 

   BACKGROUND OF THE INVENTION 
   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. 
   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. 
   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. 
   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 
   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. 
   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. 
   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. 
   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. 
   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. 
   The invention also includes apparatus for digital audio broadcasting in accordance with the above methods. 
   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. 
   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. 
   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. 
   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 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. 
   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. 
   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. 
   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. 
   The invention also includes apparatus for receiving digital audio broadcasting signals in accordance with the above methods. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic representation of the sub-carrier assignments in an AM hybrid IBOC DAB signal; 
       FIG. 2  is schematic representation of the sub-carrier assignments in an AM all-digital IBOC DAB signal; 
       FIG. 3  is a functional block diagram of a transmitter for use in an IBOC DAB system; 
       FIG. 4  is a functional block diagram of a receiver for use in an IBOC DAB system; 
       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; 
       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; 
       FIG. 7  is a diagram that illustrates a robust soft metric for an 8-ASK IBOC DAB signal; and 
       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 
   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. 
   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. 
   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. 
     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. 
   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. 
   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). 
     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 f if  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 . 
     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 f if  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  112  then provides additional signal processing to produce an output signal on line  114  for output device  116 . 
   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. 
   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. 
   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 ASK 0 . The pair of coded bits are designated as ASK 1  and ASK 2 . 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) 
             
             
                 
             
           
        
       
     
   
   In the decoding process, first FECa decoding is performed on the ASK 1  and ASK 2  bits. Then the ASK 0  bits can be corrected by mapping the ASK 1  and ASK 2  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 ASK 0  from FECa. This multilevel decoding has the effect of yielding a minimum distance of 4 for bit ASK 0  (in this 8-ASK example) prior to FECb decoding (if any). 
   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. 
   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. 
   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. 
   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. 
   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             
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               
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             
or equivalently,
 
               1       0       1           1       1       1           1       0       1           0       1       0             
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             
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 
             
           
         
       
     
   
   Core FECa Puncture Pattern 
   Upper Sideband r=3/4; Lower Sideband r=3/4 
   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. 
   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 
             
           
         
       
     
   
   FECa Backup Channel Puncture Pattern 
   r=3/5 
   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 
             
           
         
       
     
   
   Core FECa Main Channel Puncture Pattern 
     r=1 
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 
             
           
         
       
     
   
   Core FECa Composite Puncture Pattern Using G=[133, 171, 165, 171] 
   
     
       
             
           
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Core FECa Summary of Parameters. 
             
           
        
         
             
                 
               Partition 
               Rate 
               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 
             
             
                 
                 
             
           
        
       
     
   
   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 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. 
   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 
               
             
           
         
       
     
   
   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                        
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 
               
             
           
         
       
     
   
   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 
             
             
                 
                 
             
           
        
       
     
   
   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. 
   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. 
   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. 
   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). 
   The scalable audio codec is comprised of 2 layers (core and 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. 
   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           
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, 
             
             
                 
                 
             
           
        
       
     
   
   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 . 
   Core interleaver indices: k, b and p are defined as follows:
     k=Block index, 0 to 749 symbols in each core block, 0 to 839 symbols in each enhancement block;   b=Block number, 0 to 7 within each modem frame; and   p=PTCM bit mapping within each 64-QAM symbol, with (IASK 0 =0, IASK 1 =1, IASK 2 =2, QASK 2 =3, QASK 1 =4, QASK 0 =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] 
             
             
                 
             
           
        
       
     
   
     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 
           
         
       
     
   
   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 
               14 
             
             
                 
             
             
               A = 
               0 
               0 
               “T” 
               834 
               775 
               715 
               657 
               598 
               539 
               480 
               421 
               390 
               331 
               272 
               213 
               154 
             
             
                 
               1 
               168 
               137 
               78 
               19 
               “T” 
               825 
               766 
               707 
               648 
               589 
               558 
               499 
               440 
               381 
               322 
             
             
                 
               2 
               336 
               305 
               246 
               187 
               128 
               69 
               10 
               “T” 
               816 
               757 
               726 
               667 
               608 
               549 
               490 
             
             
                 
               3 
               504 
               473 
               414 
               355 
               296 
               237 
               178 
               119 
               60 
               1 
               “T” 
               835 
               776 
               717 
               658 
             
             
                 
               4 
               672 
               641 
               582 
               523 
               464 
               405 
               346 
               287 
               228 
               169 
               138 
               79 
               20 
               “T” 
               826 
             
             
                 
               5 
               “T” 
               809 
               750 
               691 
               632 
               573 
               514 
               455 
               396 
               337 
               306 
               247 
               188 
               129 
               70 
             
             
                 
               6 
               140 
               109 
               50 
               “T” 
               800 
               741 
               682 
               623 
               564 
               505 
               474 
               415 
               356 
               297 
               238 
             
             
                 
               7 
               308 
               277 
               218 
               159 
               100 
               41 
               “T” 
               791 
               732 
               673 
               642 
               583 
               524 
               465 
               406 
             
             
                 
               8 
               476 
               445 
               386 
               327 
               268 
               209 
               150 
               91 
               32 
               “T” 
               810 
               751 
               692 
               633 
               574 
             
             
                 
               9 
               644 
               613 
               554 
               495 
               436 
               377 
               318 
               258 
               200 
               141 
               110 
               51 
               “T” 
               801 
               742 
             
             
                 
               10 
               812 
               781 
               722 
               663 
               604 
               545 
               486 
               427 
               368 
               309 
               278 
               219 
               160 
               101 
               42 
             
             
                 
               11 
               56 
               25 
               “T” 
               831 
               772 
               713 
               654 
               595 
               536 
               477 
               446 
               387 
               328 
               269 
               210 
             
             
                 
               12 
               224 
               193 
               134 
               75 
               16 
               “T” 
               822 
               763 
               704 
               645 
               614 
               555 
               496 
               437 
               378 
             
             
                 
               13 
               392 
               361 
               302 
               243 
               184 
               125 
               66 
               7 
               “T” 
               813 
               782 
               723 
               664 
               605 
               546 
             
             
                 
               14 
               560 
               529 
               470 
               411 
               352 
               293 
               234 
               175 
               116 
               57 
               26 
               “T” 
               832 
               773 
               714 
             
             
                 
               15 
               728 
               697 
               638 
               579 
               520 
               461 
               402 
               343 
               284 
               225 
               194 
               135 
               76 
               17 
               “T” 
             
             
                 
               16 
               28 
               “T” 
               806 
               747 
               688 
               629 
               570 
               511 
               452 
               393 
               362 
               303 
               244 
               185 
               126 
             
             
                 
               17 
               196 
               165 
               106 
               47 
               “T” 
               797 
               738 
               679 
               620 
               561 
               530 
               471 
               412 
               353 
               294 
             
             
                 
               18 
               364 
               333 
               274 
               215 
               156 
               97 
               38 
               “T” 
               788 
               729 
               698 
               639 
               580 
               521 
               462 
             
             
                 
               19 
               532 
               501 
               442 
               383 
               324 
               265 
               206 
               147 
               88 
               29 
               “T” 
               807 
               748 
               689 
               630 
             
             
                 
               20 
               700 
               669 
               610 
               551 
               492 
               433 
               374 
               315 
               256 
               197 
               168 
               107 
               48 
               “T” 
               798 
             
             
                 
               21 
               “T” 
               837 
               778 
               719 
               660 
               601 
               542 
               483 
               424 
               365 
               334 
               275 
               216 
               157 
               98 
             
             
                 
               22 
               112 
               81 
               22 
               “T” 
               828 
               769 
               710 
               651 
               592 
               533 
               502 
               443 
               384 
               325 
               266 
             
             
                 
               23 
               280 
               249 
               190 
               131 
               72 
               13 
               “T” 
               819 
               760 
               701 
               670 
               611 
               552 
               493 
               434 
             
             
                 
               24 
               448 
               417 
               358 
               299 
               240 
               181 
               122 
               63 
               4 
               “T” 
               838 
               779 
               720 
               661 
               602 
             
             
                 
               25 
               616 
               585 
               526 
               467 
               408 
               349 
               290 
               231 
               172 
               113 
               82 
               23 
               “T” 
               829 
               770 
             
             
                 
               26 
               784 
               753 
               694 
               635 
               576 
               517 
               458 
               399 
               340 
               281 
               250 
               191 
               132 
               73 
               14 
             
             
                 
               27 
               84 
               53 
               “T” 
               803 
               744 
               685 
               626 
               587 
               508 
               449 
               418 
               359 
               300 
               241 
               182 
             
             
                 
               28 
               252 
               221 
               162 
               103 
               44 
               “T” 
               794 
               735 
               676 
               617 
               586 
               527 
               468 
               409 
               350 
             
             
                 
               29 
               420 
               389 
               330 
               271 
               212 
               153 
               94 
               35 
               “T” 
               785 
               754 
               695 
               636 
               577 
               518 
             
             
                 
               30 
               588 
               557 
               496 
               439 
               380 
               321 
               262 
               203 
               144 
               85 
               54 
               “T” 
               804 
               745 
               686 
             
             
                 
               31 
               756 
               725 
               666 
               607 
               548 
               489 
               430 
               371 
               312 
               253 
               222 
               163 
               104 
               45 
               “T” 
             
             
                 
             
           
        
         
             
                 
                 
                 
               15 
               16 
               17 
               18 
               19 
               20 
               21 
               22 
               23 
               24 
               25 
               26 
               27 
             
             
                 
                 
             
             
                 
               A = 
               0 
               95 
               36 
               “T” 
               786 
               755 
               696 
               637 
               578 
               519 
               460 
               401 
               342 
               283 
             
             
                 
                 
               1 
               203 
               204 
               145 
               86 
               55 
               “T” 
               805 
               746 
               687 
               628 
               569 
               510 
               451 
             
             
                 
                 
               2 
               431 
               372 
               313 
               254 
               223 
               164 
               105 
               46 
               “T” 
               796 
               737 
               678 
               619 
             
             
                 
                 
               3 
               599 
               540 
               481 
               422 
               391 
               332 
               273 
               214 
               155 
               96 
               37 
               “T” 
               787 
             
             
                 
                 
               4 
               767 
               708 
               649 
               590 
               559 
               500 
               441 
               382 
               323 
               264 
               205 
               146 
                87 
             
             
                 
                 
               5 
               11 
               “T” 
               817 
               758 
               727 
               668 
               609 
               550 
               491 
               432 
               373 
               314 
               255 
             
             
                 
                 
               6 
               179 
               120 
               61 
               2 
               “T” 
               836 
               777 
               718 
               659 
               600 
               541 
               482 
               423 
             
             
                 
                 
               7 
               347 
               288 
               229 
               170 
               139 
               80 
               21 
               “T” 
               827 
               768 
               709 
               650 
               591 
             
             
                 
                 
               8 
               515 
               456 
               397 
               338 
               307 
               248 
               189 
               130 
               71 
               12 
               “T” 
               818 
               759 
             
             
                 
                 
               9 
               683 
               624 
               565 
               506 
               475 
               416 
               357 
               298 
               239 
               180 
               121 
               62 
                3 
             
             
                 
                 
               10 
               “T” 
               792 
               733 
               674 
               643 
               584 
               525 
               466 
               407 
               348 
               289 
               230 
               171 
             
             
                 
                 
               11 
               151 
               92 
               33 
               “T” 
               811 
               752 
               693 
               634 
               575 
               516 
               457 
               398 
               339 
             
             
                 
                 
               12 
               319 
               260 
               201 
               142 
               111 
               52 
               “T” 
               802 
               743 
               684 
               625 
               566 
               507 
             
             
                 
                 
               13 
               487 
               428 
               369 
               310 
               279 
               220 
               161 
               102 
               43 
               “T” 
               793 
               734 
               675 
             
             
                 
                 
               14 
               655 
               596 
               537 
               478 
               447 
               388 
               329 
               270 
               211 
               152 
               93 
               34 
               “T” 
             
             
                 
                 
               15 
               823 
               764 
               705 
               646 
               615 
               556 
               497 
               438 
               379 
               320 
               261 
               202 
               143 
             
             
                 
                 
               16 
               67 
               8 
               “T” 
               814 
               783 
               724 
               665 
               606 
               547 
               488 
               429 
               370 
               311 
             
             
                 
                 
               17 
               235 
               176 
               117 
               58 
               27 
               “T” 
               833 
               774 
               715 
               656 
               597 
               538 
               479 
             
             
                 
                 
               18 
               403 
               344 
               285 
               226 
               195 
               136 
               77 
               18 
               “T” 
               824 
               765 
               706 
               647 
             
             
                 
                 
               19 
               571 
               512 
               453 
               394 
               363 
               304 
               245 
               186 
               127 
               68 
               9 
               “T” 
               815 
             
             
                 
                 
               20 
               739 
               680 
               621 
               562 
               531 
               472 
               413 
               354 
               295 
               236 
               177 
               118 
                59 
             
             
                 
                 
               21 
               39 
               “T” 
               789 
               730 
               699 
               640 
               581 
               522 
               463 
               404 
               345 
               286 
               227 
             
             
                 
                 
               22 
               207 
               148 
               89 
               30 
               “T” 
               808 
               749 
               690 
               631 
               572 
               513 
               454 
               395 
             
             
                 
                 
               23 
               375 
               316 
               257 
               198 
               167 
               108 
               49 
               “T” 
               799 
               740 
               681 
               622 
               563 
             
             
                 
                 
               24 
               543 
               484 
               425 
               366 
               335 
               276 
               217 
               158 
               99 
               40 
               “T” 
               790 
               731 
             
             
                 
                 
               25 
               711 
               652 
               593 
               534 
               503 
               444 
               385 
               326 
               267 
               208 
               149 
               90 
                31 
             
             
                 
                 
               26 
               “T” 
               820 
               761 
               702 
               871 
               612 
               553 
               494 
               435 
               376 
               317 
               258 
               199 
             
             
                 
                 
               27 
               123 
               64 
               5 
               “T” 
               839 
               780 
               721 
               662 
               603 
               544 
               485 
               426 
               307 
             
             
                 
                 
               28 
               291 
               232 
               173 
               114 
               83 
               24 
               “T” 
               830 
               771 
               712 
               653 
               594 
               535 
             
             
                 
                 
               29 
               459 
               400 
               341 
               282 
               251 
               192 
               133 
               74 
               15 
               “T” 
               821 
               762 
               703 
             
             
                 
                 
               30 
               627 
               568 
               509 
               450 
               419 
               360 
               301 
               242 
               183 
               124 
               65 
               6 
               “T” 
             
             
                 
                 
               31 
               795 
               736 
               677 
               618 
               587 
               528 
               469 
               410 
               351 
               292 
               233 
               174 
                115, 
             
             
                 
                 
             
           
        
       
     
   
   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. 
   The enhancement interleaver indices k, b and p are defined as follows:
     k=Block index, 0 to 839 symbols in each core block,   b=Block number, 0 to 7 within each modem frame, and   p=PTCM bit mapping within each 64-QAM symbol, with (IASK 0 =0, IASK 1 =1, IASK 2 =2, QASK 2 =3, QASK 1 =4, QASK 0 =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] 
             
             
                 
             
           
        
       
     
   
   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. 
   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. 
   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 
         
       
     
   
   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  
 
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         
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           ]               
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             )         ]                   
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.
 
     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 . 
   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. 
   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             
where y represents the received noisy symbol and F(.) is the desired nonlinearity.
 
   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.