# Patent

## Title
Method and system for routing in low density parity check (LDPC) decoders

## Abstract

An approach is provided for decoding a low density parity check (LDPC) coded signal. Edge values associated with a structured parity check matrix used to generate the LDPC coded signal are retrieved from memory. The edge values specify the relationship of bit nodes and check nodes, and are stored within memory according to a predetermined scheme that permits concurrent retrieval of a set of the edge values. A decoded signal corresponding to the LDPC coded signal is output based on the retrieved edge values.

## Background
RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 10/613,824 filed Jul. 3, 2003 now U.S. Pat. No. 7,203,887, entitled “Method and System for Routing in Low Density Parity Check (LDPC) Decoders” which is related to, and claims the benefit of the earlier filing date under 35 U.S.C. §119(e) of, U.S. Provisional Patent Application (Ser. No. 60/393,457) filed Jul. 3, 2002, entitled “Code Design and Implementation Improvements for Low Density Parity Check Codes,” U.S. Provisional Patent Application (Ser. No. 60/398,760) filed Jul. 26, 2002, entitled “Code Design and Implementation Improvements for Low Density Parity Check Codes,” U.S. Provisional Patent Application (Ser. No. 60/403,812) filed Aug. 15, 2002, entitled “Power and Bandwidth Efficient Modulation and Coding Scheme for Direct Broadcast Satellite and Broadcast Satellite Communications,” U.S. Provisional Patent Application (Ser. No. 60/421,505), filed Oct. 25, 2002, entitled “Method and System for Generating Low Density Parity Check Codes,” U.S. Provisional Patent Application (Ser. No. 60/421,999), filed Oct. 29, 2002, entitled “Satellite Communication System Utilizing Low Density Parity Check Codes,” U.S. Provisional Patent Application (Ser. No. 60/423,710), filed Nov. 4, 2002, entitled “Code Design and Implementation Improvements for Low Density Parity Check Codes,” U.S. Provisional Patent Application (Ser. No. 60/440,199) filed Jan. 15, 2003, entitled “Novel Solution to Routing Problem in Low Density Parity Check Decoders,” U.S. Provisional Patent Application (Ser. No. 60/447,641) filed Feb. 14, 2003, entitled “Low Density Parity Check Code Encoder Design,” U.S. Provisional Patent Application (Ser. No. 60/451,548) filed Mar. 3, 2003, entitled “System and Method for Advanced Modulation and Coding,” U.S. Provisional Patent Application (Ser. No. 60/456,220) filed Mar. 20, 2003, entitled “Description LDPC and BCH Encoders,” U.S. Provisional Patent Application (Ser. No. 60/440,199) filed Jan. 15, 2003, entitled “A Novel Solution to Routing Problem in Low Density Parity Check Decoders,” U.S. Provisional Patent Application (Ser. No. 60/447,641) filed Feb. 14, 2003, entitled “Low Density Parity Check Code Encoder Design,” U.S. Provisional Patent Application (Ser. No. 60/456,220) filed Mar. 20, 2003, entitled “Description LDPC and BCH Encoders,” and U.S. Provisional Patent Application (Ser. No. 60/469,356) filed May 9, 2003, entitled “Description LDPC and BCH Encoders”; the entireties of which are incorporated herein by reference.


FIELD OF THE INVENTION
The present invention relates to communication systems, and more particularly to coded systems.
BACKGROUND OF THE INVENTION
Communication systems employ coding to ensure reliable communication across noisy communication channels. These communication channels exhibit a fixed capacity that can be expressed in terms of bits per symbol at certain signal to noise ratio (SNR), defining a theoretical upper limit (known as the Shannon limit). As a result, coding design has aimed to achieve rates approaching this Shannon limit. One such class of codes that approach the Shannon limit is Low Density Parity Check (LDPC) codes.
Traditionally, LDPC codes have not been widely deployed because of a number of drawbacks. One drawback is that the LDPC encoding technique is highly complex. Encoding an LDPC code using its generator matrix would require storing a very large, non-sparse matrix. Additionally, LDPC codes require large blocks to be effective; consequently, even though parity check matrices of LDPC codes are sparse, storing these matrices is problematic.
From an implementation perspective, a number of challenges are confronted. For example, storage is an important reason why LDPC codes have not become widespread in practice. Also, a key challenge in LDPC code implementation has been how to achieve the connection network between several processing engines (nodes) in the decoder. Further, the computational load in the decoding process, specifically the check node operations, poses a problem.
Therefore, there is a need for a LDPC communication system that employs simple encoding and decoding processes. There is also a need for using LDPC codes efficiently to support high data rates, without introducing greater complexity. There is also a need to improve performance of LDPC encoders and decoders. There is also a need to minimize storage requirements for implementing LDPC coding. There is a further need for a scheme that simplifies the communication between processing nodes in the LDPC decoder.
SUMMARY OF THE INVENTION
These and other needs are addressed by the present invention, wherein an approach for decoding a structured Low Density Parity Check (LDPC) codes is provided. Structure of the LDPC codes is provided by restricting portion part of the parity check matrix to be lower triangular and/or satisfying other requirements such that the communication between bit nodes and check nodes of the decoder is simplified. Edge values associated with the structured parity check matrix used to generate the LDPC coded signal are retrieved from memory. The edge values specify the relationship of bit nodes and check nodes, and according to one embodiment of the present invention, are stored within the memory according to a predetermined scheme (e.g., contiguous physical memory locations) that permits concurrent retrieval of a set of the edge values. According to another embodiment of the present invention, the edge values having bit nodes of n degrees are stored in a first portion of the memory, and edge values having bit nodes of greater than n degrees are stored in a second portion of the memory. The storage arrangement of the edge values advantageously allows fast retrieval of the edge values during the decoding process.
Also, the approach can advantageously exploit the unequal error protecting capability of LDPC codes on transmitted bits to provide extra error protection to more vulnerable bits of high order modulation constellations (such as 8-PSK (Phase Shift Keying)). The decoding process involves iteratively regenerating signal constellation bit metrics into an LDPC decoder after each decoder iteration or several decoder iterations. The above arrangement provides a computational efficient approach to decoding LDPC codes.
According to one aspect of an embodiment of the present invention, a method for decoding a low density parity check (LDPC) coded signal is disclosed. The method includes retrieving edge values associated with a structured parity check matrix used to generate the LDPC coded signal, wherein the edge values specify relationship of bit nodes and check nodes, and are stored according to a predetermined scheme that permits concurrent retrieval of a set of the edge values. The method also includes outputting a decoded signal corresponding to the LDPC coded signal based on the retrieved edge values.
According to another aspect of an embodiment of the present invention, a decoder for decoding a low density parity check (LDPC) coded signal is disclosed. The decoder includes means for retrieving edge values associated with a structured parity check matrix used to generate the LDPC coded signal. The decoder also includes memory for storing the edge values according to a predetermined scheme that permits concurrent retrieval of a set of the edge values, wherein the edge values specify relationship of bit nodes and check nodes. Further, the decoder includes means for outputting a decoded signal corresponding to the LDPC coded signal based on the retrieved edge values.
According to another aspect of an embodiment of the present invention, a memory accessible by a low density parity check (LDPC) decoder for decoding a LDPC coded signal is disclosed. The memory includes a first portion storing a first group of edge values associated with a structured parity check matrix used to generate the LDPC coded signal, the first group of edges being connected to bit nodes of n degrees. Additionally, the memory includes a second portion storing a second group of edge values associated with the structured parity check matrix used to generate the LDPC coded signal, the second group of edges being connected to bit nodes of greater than n degrees, wherein a set of edge values from the first group or the second group is retrieved to output a decoded signal.
Still other aspects, features, and advantages of the present invention are readily apparent from the following detailed description, simply by illustrating a number of particular embodiments and implementations, including the best mode contemplated for carrying out the present invention. The present invention is also capable of other and different embodiments, and its several details can be modified in various obvious respects, all without departing from the spirit and scope of the present invention. Accordingly, the drawing and description are to be regarded as illustrative in nature, and not as restrictive.



BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:
FIG. 1 is a diagram of a communications system configured to utilize Low Density Parity Check (LDPC) codes, according to an embodiment of the present invention;
FIG. 2 is a diagram of an exemplary transmitter in the system of FIG. 1;
FIG. 3 is a diagram of an exemplary receiver in the system of FIG. 1;
FIG. 4 is a diagram of a sparse parity check matrix, in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of a bipartite graph of an LDPC code of the matrix of FIG. 4;
FIG. 6 is a diagram of a sub-matrix of a sparse parity check matrix, wherein the sub-matrix contains parity check values restricted to the lower triangular region, according to an embodiment of the present invention;
FIG. 7 is a graph showing performance between codes utilizing unrestricted parity check matrix (H matrix) versus restricted H matrix having a sub-matrix as in FIG. 6;
FIGS. 8A and 8B are, respectively, a diagram of a non-Gray 8-PSK modulation scheme, and a Gray 8-PSK modulation, each of which can be used in the system of FIG. 1;
FIG. 9 is a graph showing performance between codes utilizing Gray labeling versus non-Gray labeling;
FIG. 10 is a flow chart of the operation of the LDPC decoder using non-Gray mapping, according to an embodiment of the present invention;
FIG. 11 is a flow chart of the operation of the LDPC decoder of FIG. 3 using Gray mapping, according to an embodiment of the present invention;
FIGS. 12A-12C are diagrams of the interactions between the check nodes and the bit nodes in a decoding process, according to an embodiment of the present invention;
FIGS. 13A and 13B are flowcharts of processes for computing outgoing messages between the check nodes and the bit nodes using, respectively, a forward-backward approach and a parallel approach, according to various embodiments of the present invention;
FIGS. 14A-14C are graphs showing simulation results of LDPC codes generated in accordance with various embodiments of the present invention;
FIGS. 15A and 15B are diagrams of the top edge and bottom edge, respectively, of memory organized to support structured access as to realize randomness in LDPC coding, according to an embodiment of the present invention; and
FIG. 16 is a diagram of a computer system that can perform the processes of encoding and decoding of LDPC codes, in accordance with embodiments of the present invention.



DESCRIPTION OF THE PREFERRED EMBODIMENT
A system, method, and software for efficiently decoding structured Low Density Parity Check (LDPC) codes are described. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It is apparent, however, to one skilled in the art that the present invention may be practiced without these specific details or with an equivalent arrangement. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention.
FIG. 1 is a diagram of a communications system configured to utilize Low Density Parity Check (LDPC) codes, according to an embodiment of the present invention. A digital communications system 100 includes a transmitter 101 that generates signal waveforms across a communication channel 103 to a receiver 105. In this discrete communications system 100, the transmitter 101 has a message source that produces a discrete set of possible messages; each of the possible messages has a corresponding signal waveform. These signal waveforms are attenuated, or otherwise altered, by communications channel 103. To combat the noise channel 103, LDPC codes are utilized.
The LDPC codes that are generated by the transmitter 101 enables high speed implementation without incurring any performance loss. These structured LDPC codes output from the transmitter 101 avoid assignment of a small number of check nodes to the bit nodes already vulnerable to channel errors by virtue of the modulation scheme (e.g., 8-PSK).
Such LDPC codes have a parallelizable decoding algorithm (unlike turbo codes), which advantageously involves simple operations such as addition, comparison and table look-up. Moreover, carefully designed LDPC codes do not exhibit any sign of error floor.
According to one embodiment of the present invention, the transmitter 101 generates, using a relatively simple encoding technique, LDPC codes based on parity check matrices (which facilitate efficient memory access during decoding) to communicate with the receiver 105. The transmitter 101 employs LDPC codes that can outperform concatenated turbo+RS (Reed-Solomon) codes, provided the block length is sufficiently large.
FIG. 2 is a diagram of an exemplary transmitter in the system of FIG. 1. A transmitter 200 is equipped with an LDPC encoder 203 that accepts input from an information source 201 and outputs coded stream of higher redundancy suitable for error correction processing at the receiver 105. The information source 201 generates k signals from a discrete alphabet, X. LDPC codes are specified with parity check matrices. On the other hand, encoding LDPC codes require, in general, specifying the generator matrices. Even though it is possible to obtain generator matrices from parity check matrices using Gaussian elimination, the resulting matrix is no longer sparse and storing a large generator matrix can be complex.
Encoder 203 generates signals from alphabet Y to a modulator 205 using a simple encoding technique that makes use of only the parity check matrix by imposing structure onto the parity check matrix. Specifically, a restriction is placed on the parity check matrix by constraining certain portion of the matrix to be triangular. The construction of such a parity check matrix is described more fully below in FIG. 6. Such a restriction results in negligible performance loss, and therefore, constitutes an attractive trade-off.
Modulator 205 maps the encoded messages from encoder 203 to signal waveforms that are transmitted to a transmit antenna 207, which emits these waveforms over the communication channel 103. Accordingly, the encoded messages are modulated and distributed to a transmit antenna 207. The transmissions from the transmit antenna 207 propagate to a receiver, as discussed below.
FIG. 3 is a diagram of an exemplary receiver in the system of FIG. 1. At the receiving side, a receiver 300 includes a demodulator 301 that performs demodulation of received signals from transmitter 200. These signals are received at a receive antenna 303 for demodulation. After demodulation, the received signals are forwarded to a decoder 305, which attempts to reconstruct the original source messages by generating messages, X′, in conjunction with a bit metric generator 307. With non-Gray mapping, the bit metric generator 307 exchanges probability information with the decoder 305 back and forth (iteratively) during the decoding process, which is detailed in FIG. 10. Alternatively, if Gray mapping is used (according to one embodiment of the present invention), one pass of the bit metric generator is sufficient, in which further attempts of bit metric generation after each LDPC decoder iteration are likely to yield limited performance improvement; this approach is more fully described with respect to FIG. 11. To appreciate the advantages offered by the present invention, it is instructive to examine how LDPC codes are generated, as discussed in FIG. 4.
FIG. 4 is a diagram of a sparse parity check matrix, in accordance with an embodiment of the present invention. LDPC codes are long, linear block codes with sparse parity check matrix H(n−k)xn. Typically the block length, n, ranges from thousands to tens of thousands of bits. For example, a parity check matrix for an LDPC code of length n=8 and rate 1⁄2 is shown in FIG. 4. The same code can be equivalently represented by the bipartite graph, per FIG. 5.
FIG. 5 is a diagram of a bipartite graph of an LDPC code of the matrix of FIG. 4. Parity check equations imply that for each check node, the sum (over GF (Galois Field)(2)) of all adjacent bit nodes is equal to zero. As seen in the figure, bit nodes occupy the left side of the graph and are associated with one or more check nodes, according to a predetermined relationship. For example, corresponding to check node m1, the following expression exists n1+n4+n5+n8=0 with respect to the bit nodes.
Returning the receiver 303, the LDPC decoder 305 is considered a message passing decoder, whereby the decoder 305 aims to find the values of bit nodes. To accomplish this task, bit nodes and check nodes iteratively communicate with each other. The nature of this communication is described below.
From check nodes to bit nodes, each check node provides to an adjacent bit node an estimate (“opinion”) regarding the value of that bit node based on the information coming from other adjacent bit nodes. For instance, in the above example if the sum of n4, n5 and n8 “looks like” 0 to m1, then m1 would indicate to n1 that the value of n1 is believed to be 0 (since n1+n4+n5+n8=0); otherwise m1 indicate to n1 that the value of n1 is believed to be 1. Additionally, for soft decision decoding, a reliability measure is added.
From bit nodes to check nodes, each bit node relays to an adjacent check node an estimate about its own value based on the feedback coming from its other adjacent check nodes. In the above example n1 has only two adjacent check nodes m1 and m3. If the feedback coming from m3 to n1 indicates that the value of n1 is probably 0, then n1 would notify m1 that an estimate of n1's own value is 0. For the case in which the bit node has more than two adjacent check nodes, the bit node performs a majority vote (soft decision) on the feedback coming from its other adjacent check nodes before reporting that decision to the check node it communicates. The above process is repeated until all bit nodes are considered to be correct (i.e., all parity check equations are satisfied) or until a predetermined maximum number of iterations is reached, whereby a decoding failure is declared.
FIG. 6 is a diagram of a sub-matrix of a sparse parity check matrix, wherein the sub-matrix contains parity check values restricted to the lower triangular region, according to an embodiment of the present invention. As described previously, the encoder 203 (of FIG. 2) can employ a simple encoding technique by restricting the values of the lower triangular area of the parity check matrix. According to an embodiment of the present invention, the restriction imposed on the parity check matrix is of the form:

H(n−k)xn=[A(n−k)xkB(n−k)x(n−k)],

where B is lower triangular.

Any information block i=(i0, i1, . . . , ik−1) is encoded to a codeword C=(i0, i1, . . . , ik−1, p0, p1, . . . , pn-k−1) using HcT=0, and recursively solving for parity bits; for example,

a00i0+a01i1+ . . . +a0,k−1ik−1+p0=0Solve p0,

a10i0+a11i1+ . . . +a1,k−1ik−1+b10p0+p1=0Solve p1 

and similarly for p2,p3, . . . ,pn−k−1. 

FIG. 7 is a graph showing performance between codes utilizing unrestricted parity check matrix (H matrix) versus restricted H matrix of FIG. 6. The graph shows the performance comparison between two LDPC codes: one with a general parity check matrix and the other with a parity check matrix restricted to be lower triangular to simplify encoding. The modulation scheme, for this simulation, is 8-PSK. The performance loss is within 0.1 dB. Therefore, the performance loss is negligible based on the restriction of the lower triangular H matrices, while the gain in simplicity of the encoding technique is significant. Accordingly, any parity check matrix that is equivalent to a lower triangular or upper triangular under row and/or column permutation can be utilized for the same purpose.
FIGS. 8A and 8B are, respectively, a diagram of a non-Gray 8-PSK modulation scheme, and a Gray 8-PSK modulation, each of which can be used in the system of FIG. 1. The non-Gray 8-PSK scheme of FIG. 8A can be utilized in the receiver of FIG. 3 to provide a system that requires very low Frame Erasure Rate (FER). This requirement can also be satisfied by using a Gray 8-PSK scheme, as shown in FIG. 8B, in conjunction with an outer code, such as Bose, Chaudhuri, and Hocquenghem (BCH), Hamming, or Reed-Solomon (RS) code.
Under this scheme, there is no need to iterate between the LDPC decoder 305 (FIG. 3) and the bit metric generator 307, which may employ 8-PSK modulation. In the absence of an outer code, the LDPC decoder 305 using Gray labeling exhibit an earlier error floor, as shown in FIG. 9 below.
FIG. 9 is a graph showing performance between codes utilizing Gray labeling versus non-Gray labeling of FIGS. 8A and 8B. The error floor stems from the fact that assuming correct feedback from LDPC decoder 305, regeneration of 8-PSK bit metrics is more accurate with non-Gray labeling since the two 8-PSK symbols with known two bits are further apart with non-Gray labeling. This can be equivalently seen as operating at higher Signal-to-Noise Ratio (SNR). Therefore, even though error asymptotes of the same LDPC code using Gray or non-Gray labeling have the same slope (i.e., parallel to each other), the one with non-Gray labeling passes through lower FER at any SNR.
On the other hand, for systems that do not require very low FER, Gray labeling without any iteration between LDPC decoder 305 and 8-PSK bit metric generator 307 may be more suitable because re-generating 8-PSK bit metrics before every LDPC decoder iteration causes additional complexity. Moreover, when Gray labeling is used, re-generating 8-PSK bit metrics before every LDPC decoder iteration yields only very slight performance improvement. As mentioned previously, Gray labeling without iteration may be used for systems that require very low FER, provided an outer code is implemented.
The choice between Gray labeling and non-Gray labeling depends also on the characteristics of the LDPC code. Typically, the higher bit or check node degrees, the better it is for Gray labeling, because for higher node degrees, the initial feedback from LDPC decoder 305 to 8-PSK (or similar higher order modulation) bit metric generator 307 deteriorates more with non-Gray labeling.
When 8-PSK (or similar higher order) modulation is utilized with a binary decoder, it is recognized that the three (or more) bits of a symbol are not received “equally noisy”. For example with Gray 8-PSK labeling, the third bit of a symbol is considered more noisy to the decoder than the other two bits. Therefore, the LDPC code design does not assign a small number of edges to those bit nodes represented by “more noisy” third bits of 8-PSK symbol so that those bits are not penalized twice.
FIG. 10 is a flow chart of the operation of the LDPC decoder using non-Gray mapping, according to an embodiment of the present invention. Under this approach, the LDPC decoder and bit metric generator iterate one after the other. In this example, 8-PSK modulation is utilized; however, the same principles apply to other higher modulation schemes as well. Under this scenario, it is assumed that the demodulator 301 outputs a distance vector, d, denoting the distances between received noisy symbol points and 8-PSK symbol points to the bit metric generator 307, whereby the vector components are as follows:




  
    
      d
      i
    
    =
    
      
        
          -
          
            
              E
              s
            
            
              N
              0
            
          
        
        ⁢
        
          {
          
            
              
                (
                
                  
                    r
                    x
                  
                  -
                  
                    s
                    
                      i
                      ,
                      x
                    
                  
                
                )
              
              2
            
            +
            
              
                (
                
                  
                    r
                    y
                  
                  -
                  
                    s
                    
                      i
                      ,
                      y
                    
                  
                
                )
              
              2
            
          
          }
        
        ⁢
        
          
        
        ⁢
        i
      
      =
      0
    
  
  ,
  1
  ,
  
    ...
    ⁢
    
      
    
    ⁢
    7.
  




The 8-PSK bit metric generator 307 communicates with the LDPC decoder 305 to exchange a priori probability information and a posteriori probability information, which respectively are represented as u, and a. That is, the vectors u and a respectively represent a priori and a posteriori probabilities of log likelihood ratios of coded bits.
The 8-PSK bit metric generator 307 generates the a priori likelihood ratios for each group of three bits as follows. First, extrinsic information on coded bits is obtained:

ej=aj−ujj=0,1,2.

Next, 8-PSK symbol probabilities, pi i=0,1, . . . ,7, are determined.

*yj=−ƒ(0, ej) j=0,1,2 where ƒ(a,b)=max(a,b)+LUTf(a,b) with LUTf(a,b)=1n(1+e−|a−b|)

*xj=yj+ej j=0,1,2

*p0=x0+x1+x2 p4=y0+x1+x2 

p1=x0+x1+y2 p5=y0+x1+y2 

p2=x0+y1+x2 p6=y0+y1+x2 

p3=x0+y1+y2 p7=y0+y1+y2 

Next, the bit metric generator 307 determines a priori log likelihood ratios of the coded bits as input to LDPC decoder 305, as follows:

u0=ƒ(d0+p0,d1+p1d2+p2,d3+p3)−ƒ(d4+p4,d5+p5,d6+p6,d7+p7)−e0 

u1=ƒ(d0+p0,d1+p1,d4+p4,d5+p5)−ƒ(d2+p2,d3+p3,d6+p6,d7+p7)−e1 

u2=ƒ(d0+p0,d2+p2,d4+p4,d6+p6)−ƒ(d1+p1,d3+p3,d5+p5,d7+p7)−e2 

It is noted that the function ƒ(.) with more than two variables can be evaluated recursively; e.g. ƒ(a,b,c)=ƒ(ƒ(a,b),c).
The operation of the LDPC decoder 305 utilizing non-Gray mapping is now described. In step 1001, the LDPC decoder 305 initializes log likelihood ratios of coded bits, v, before the first iteration according to the following (and as shown in FIG. 12A):




  
    
      v
      
        n
        →
        
          k
          i
        
      
    
    =
    
      u
      n
    
  
  ,




n=0,1, . . . , N−1,i=1,2, . . . , deg(bit node n)

Here,




  v
  
    n
    →
    
      k
      i
    
  




denotes the message that goes from bit node n to its adjacent check node ki, un denotes the demodulator output for the bit n and N is the codeword size.

In step 1003, a check node, k, is updated, whereby the input v yields the output w. As seen in FIG. 12B, the incoming messages to the check node k from its dc adjacent bit nodes are denoted by




  
    v
    
      
        n
        1
      
      →
      k
    
  
  ,
  
    v
    
      
        n
        2
      
      →
      k
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    
      v
      
        
          n
          
            d
            ⁢
            
              
            
            ⁢
            c
          
        
        →
        k
      
    
    .
  




The goal is to compute the outgoing messages from the check node k back to dc adjacent bit nodes. These messages are denoted by




  
    
      w
      
        k
        →
        
          n
          1
        
      
    
    ,
    
      w
      
        k
        →
        
          n
          2
        
      
    
    ,
    ...
    ⁢
    
      
    
    ,
    
      w
      
        k
        →
        
          n
          
            d
            ⁢
            
              
            
            ⁢
            c
          
        
      
    
    ,
    where
  




  
    
      w
      
        k
        →
        
          n
          i
        
      
    
    =
    
      
        g
        ⁡
        
          (
          
            
              v
              
                
                  n
                  1
                
                →
                k
              
            
            ,
            
              v
              
                
                  n
                  2
                
                →
                k
              
            
            ,
            ...
            ⁢
            
              
            
            ,
            
              v
              
                
                  n
                  
                    i
                    -
                    1
                  
                
                →
                k
              
            
            ,
            
              v
              
                
                  n
                  
                    i
                    +
                    1
                  
                
                →
                k
              
            
            ,
            ...
            ⁢
            
              
            
            ,
            
              v
              
                
                  n
                  
                    d
                    ⁢
                    
                      
                    
                    ⁢
                    c
                  
                
                →
                k
              
            
          
          )
        
      
      .
    
  



The function g( ) is defined as follows:

g(a,b)=sign(a)×sign(b)×{min(|a|,|b|)}+LUTg(a,b),

where LUTg(a,b)=1n(1+e−|a+b|)−1n(1+e−|a−b|). Similar to function ƒ, function g with more than two variables can be evaluated recursively.

Next, the decoder 305, per step 1205, outputs a posteriori probability information (FIG. 12C), such that:




  
    a
    n
  
  =
  
    
      u
      n
    
    +
    
      
        ∑
        j
      
      ⁢
      
        
          w
          
            
              k
              j
            
            →
            n
          
        
        .
      
    
  




Per step 1007, it is determined whether all the parity check equations are satisfied. If these parity check equations are not satisfied, then the decoder 305, as in step 1009, re-derives 8-PSK bit metrics and channel input un. Next, the bit node is updated, as in step 1011. As shown in FIG. 14C, the incoming messages to the bit node n from its dv adjacent check nodes are denoted by




  
    w
    
      
        k
        1
      
      →
      n
    
  
  ,
  
    w
    
      
        k
        2
      
      →
      n
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    w
    
      
        k
        
          d
          ⁢
          
            
          
          ⁢
          v
        
      
      →
      n
    
  




The outgoing messages from the bit node n are computed back to dv adjacent check nodes; such messages are denoted by





  
    v
    
      n
      →
      
        k
        1
      
    
  
  ,
  
    v
    
      n
      →
      
        k
        2
      
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    v
    
      n
      →
      
        k
        
          d
          ⁢
          
            
          
          ⁢
          v
        
      
    
  
  ,




and computed as follows:





  
    v
    
      n
      →
      
        k
        i
      
    
  
  =
  
    
      u
      n
    
    +
    
      
        ∑
        
          j
          ≠
          i
        
      
      ⁢
      
        w
        
          
            k
            j
          
          →
          n
        
      
    
  




In step 1013, the decoder 305 outputs the hard decision (in the case that all parity check equations are satisfied):





  
    
      c
      ^
    
    n
  
  =
  
    {
    
      
        
          
            
              
                0
                ,
              
            
            
              
                
                  a
                  n
                
                ≥
                0
              
            
          
          
            
              
                1
                ,
              
            
            
              
                
                  a
                  n
                
                <
                0
              
            
          
        
        ⁢
        
          
        
        ⁢
        Stop
        ⁢
        
          
        
        ⁢
        if
        ⁢
        
          
        
        ⁢
        H
        ⁢
        
          
        
        ⁢
        
          
            c
            ^
          
          T
        
      
      =
      0
    
  




The above approach is appropriate when non-Gray labeling is utilized. However, when Gray labeling is implemented, the process of FIG. 11 is executed.
FIG. 11 is a flow chart of the operation of the LDPC decoder of FIG. 3 using Gray mapping, according to an embodiment of the present invention. When Gray labeling is used, bit metrics are advantageously generated only once before the LDPC decoder, as re-generating bit metrics after every LDPC decoder iteration may yield nominal performance improvement. As with steps 1001 and 1003 of FIG. 10, initialization of the log likelihood ratios of coded bits, v, are performed, and the check node is updated, per steps 1101 and 1103. Next, the bit node n is updated, as in step 1105. Thereafter, the decoder outputs the a pasteriori probability information (step 1107). In step 1109, a determination is made whether all of the parity check equations are satisfied; if so, the decoder outputs the hard decision (step 1111). Otherwise, steps 1103-1107 are repeated.
FIG. 13A is a flowchart of process for computing outgoing messages between the check nodes and the bit nodes using a forward-backward approach, according to an embodiment of the present invention. For a check node with dc adjacent edges, the computation of dc(dc−1) and numerous g(.,.) functions are performed. However, the forward-backward approach reduces the complexity of the computation to 3(dc−2), in which dc−1 variables are stored.
Referring to FIG. 12B, the incoming messages to the check node k from dc adjacent bit nodes are denoted by




  
    v
    
      
        n
        1
      
      →
      k
    
  
  ,
  
    v
    
      
        n
        2
      
      →
      k
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    
      v
      
        
          n
          
            d
            ⁢
            
              
            
            ⁢
            c
          
        
        →
        k
      
    
    .
  




It is desired that the outgoing messages are computed from the check node k back to dc adjacent bit nodes; these outgoing messages are denoted by





  
    w
    
      k
      →
      
        n
        1
      
    
  
  ,
  
    w
    
      k
      →
      
        n
        2
      
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    
      w
      
        k
        →
        
          n
          
            d
            ⁢
            
              
            
            ⁢
            c
          
        
      
    
    .
  




Under the forward-backward approach to computing these outgoing messages, forward variables, ƒ1, ƒ2, . . . , ƒdc, are defined as follows:

ƒ1=v1→k 

ƒ2=g(ƒ1,v2→k)

ƒ3=g(ƒ2,v3→k)

: : :

ƒdc=g(ƒdc−1,vdc→k)

In step 1301, these forward variables are computed, and stored, per step 1303.

Similarly, backward variables, b1, b2, . . . , bdc, are defined by the following:

bdc=vdc→k 

bdc−1=g(bdc,vdc−1→k)

: : :

bi=g(b2,vdc→k)

In step 1305, these backward variables are then computed. Thereafter, the outgoing messages are computed, as in step 1307, based on the stored forward variables and the computed backward variables. The outgoing messages are computed as follows:

wk→1=b2 

wk→i=g(ƒi−1,vi+1)=2,3, . . . ,dc−1

wk→dc=ƒdc−1 

Under this approach, only the forward variables, ƒ2, ƒ3, . . . , ƒdc, are required to be stored. As the backward variables bi are computed, the outgoing messages, wk→i, are simultaneously computed, thereby negating the need for storage of the backward variables.
The computation load can be further enhance by a parallel approach, as next discussed.
FIG. 13B is a flowchart of process for computing outgoing messages between the check nodes and the bit nodes using a parallel approach, according to an embodiment of the present invention. For a check node k with inputs




  
    v
    
      
        n
        1
      
      →
      k
    
  
  ,
  
    v
    
      
        n
        2
      
      →
      k
    
  
  ,
  ...
  ⁢
  
    
  
  ,
  
    v
    
      
        n
        
          d
          ⁢
          
            
          
          ⁢
          c
        
      
      →
      k
    
  




from dc adjacent bit nodes, the following parameter is computed, as in step 1311:





  
    
      γ
      k
    
    ⁢
    g
  
  =
  
    
      (
      
        
          v
          
            
              n
              1
            
            →
            k
          
        
        ,
        
          v
          
            
              n
              2
            
            →
            k
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          v
          
            
              n
              
                d
                ⁢
                
                  
                
                ⁢
                c
              
            
            →
            k
          
        
      
      )
    
    .
  




It is noted that the g(.,.) function can also be expressed as follows:




  
    g
    ⁡
    
      (
      
        a
        ,
        b
      
      )
    
  
  =
  
    ln
    ⁢
    
      
        
          1
          +
          
            e
            
              a
              +
              b
            
          
        
        
          
            e
            a
          
          +
          
            e
            b
          
        
      
      .
    
  




Exploiting the recursive nature of the g(.,.) function, the following expression results:




  
    
      
        
          γ
          k
        
        =
        
          ln
          ⁢
          
            
              1
              +
              
                e
                
                  
                    g
                    ⁡
                    
                      (
                      
                        
                          v
                          
                            
                              n
                              1
                            
                            →
                            k
                          
                        
                        ,
                        
                          
                        
                        ⁢
                        ...
                        ⁢
                        
                          
                        
                        ,
                        
                          v
                          
                            
                              n
                              
                                i
                                -
                                1
                              
                            
                            →
                            k
                          
                        
                        ,
                        
                          v
                          
                            
                              n
                              
                                i
                                +
                                1
                              
                            
                            →
                            k
                          
                        
                        ,
                        
                          
                        
                        ⁢
                        ...
                        ⁢
                        
                          
                        
                        ,
                        
                          v
                          
                            
                              n
                              i
                            
                            →
                            k
                          
                        
                      
                      )
                    
                  
                  +
                  
                    v
                    
                      
                        n
                        i
                      
                      →
                      k
                    
                  
                
              
            
            
              
                e
                
                  g
                  ⁡
                  
                    (
                    
                      
                        v
                        
                          
                            n
                            1
                          
                          →
                          k
                        
                      
                      ,
                      
                        
                      
                      ⁢
                      ...
                      ⁢
                      
                        
                      
                      ,
                      
                        v
                        
                          
                            n
                            
                              i
                              -
                              1
                            
                          
                          →
                          k
                        
                      
                      ,
                      
                        v
                        
                          
                            n
                            
                              i
                              +
                              1
                            
                          
                          →
                          k
                        
                      
                      ,
                      
                        
                      
                      ⁢
                      ...
                      ⁢
                      
                        
                      
                      ,
                      
                        v
                        
                          
                            n
                            i
                          
                          →
                          k
                        
                      
                    
                    )
                  
                
              
              +
              
                e
                
                  v
                  
                    
                      n
                      i
                    
                    →
                    k
                  
                
              
            
          
        
      
    
  
  
    
      
        =
        
          ln
          ⁢
          
            
              1
              +
              
                e
                
                  
                    w
                    
                      k
                      →
                      
                        n
                        i
                      
                    
                  
                  +
                  
                    v
                    
                      
                        n
                        i
                      
                      →
                      k
                    
                  
                
              
            
            
              
                e
                
                  w
                  
                    k
                    →
                    
                      n
                      i
                    
                  
                
              
              +
              
                e
                
                  v
                  
                    
                      n
                      i
                    
                    →
                    k
                  
                
              
            
          
        
      
    
  




Accordingly,




  w
  
    k
    →
    
      n
      i
    
  




can be solved in the following manner:





  
    w
    
      k
      →
      
        n
        i
      
    
  
  =
  
    
      ln
      ⁢
      
        
          
            e
            
              
                v
                
                  
                    n
                    i
                  
                  →
                  k
                
              
              +
              
                γ
                k
              
            
          
          -
          1
        
        
          
            e
            
              
                v
                
                  
                    n
                    i
                  
                  →
                  k
                
              
              -
              
                γ
                k
              
            
          
          -
          1
        
      
    
    -
    
      γ
      k
    
  




The 1n(.) term of the above equation can be obtained using a look-up table LUTx that represents the function in |ex−1| (step 1313). Unlike the other look-up tables LUTf or LUTg, the table LUTx would likely requires as many entries as the number of quantization levels. Once γk is obtained, the calculation of




  w
  
    k
    →
    
      n
      i
    
  




for all ni can occur in parallel using the above equation, per step 1315.

The computational latency of γk is advantageously log2(dc).
FIGS. 14A-14C are graphs showing simulation results of LDPC codes generated in accordance with various embodiments of the present invention. In particular, FIGS. 14A-14C show the performance of LDPC codes with higher order modulation and code rates of 3⁄4 (QPSK, 1.485 bits/symbol), 2⁄3 (8-PSK, 1.980 bits/symbol), and 5⁄6 (8-PSK, 2.474 bits/symbol).
Two general approaches exist to realize the interconnections between check nodes and bit nodes: (1) a fully parallel approach, and (2) a partially parallel approach. In fully parallel architecture, all of the nodes and their interconnections are physically implemented. The advantage of this architecture is speed.
The fully parallel architecture, however, may involve greater complexity in realizing all of the nodes and their connections. Therefore with fully parallel architecture, a smaller block size may be required to reduce the complexity. In that case, for the same clock frequency, a proportional reduction in throughput and some degradation in FER versus Es/No performance may result.
The second approach to implementing LDPC codes is to physically realize only a subset of the total number of the nodes and use only these limited number of “physical” nodes to process all of the “functional” nodes of the code. Even though the LDPC decoder operations can be made extremely simple and can be performed in parallel, the further challenge in the design is how the communication is established between “randomly” distributed bit nodes and check nodes. The decoder 305 (of FIG. 3), according to one embodiment of the present invention, addresses this problem by accessing memory in a structured way, as to realize a seemingly random code. This approach is explained with respect to FIGS. 15A and 15B.
FIGS. 15A and 15B are diagrams of the top edge and bottom edge, respectively, of memory organized to support structured access as to realize randomness in LDPC coding, according to an embodiment of the present invention. Structured access can be achieved without compromising the performance of a truly random code by focusing on the generation of the parity check matrix. In general, a parity check matrix can be specified by the connections of the check nodes with the bit nodes. For example, the bit nodes can be divided into groups of a fixed size, which for illustrative purposes is 392. Additionally, assuming the check nodes connected to the first bit node of degree 3, for instance, are numbered as a, b and c, then the check nodes connected to the second bit node are numbered as a+p, b+p and c+p, the check nodes connected to the third bit node are numbered as a+2p, b+2p and c+2p etc.; where p=(number of check nodes)/392. For the next group of 392 bit nodes, the check nodes connected to the first bit node are different from a, b, c so that with a suitable choice of p, all the check nodes have the same degree. A random search is performed over the free constants such that the resulting LDPC code is cycle-4 and cycle-6 free. Because of the structural characteristics of the parity check matrix of the present invention, the edge information can stored to permit concurrent access to a group of relevant edge values during decoding.
In other words, the approach of the present invention facilitates memory access during check node and bit node processing. The values of the edges in the bipartite graph can be stored in a storage medium, such as random access memory (RAM). It is noted that for a truly random LDPC code during check node and bit node processing, the values of the edges would need to be accessed one by one in a random fashion. However, such a conventional access scheme would be too slow for a high data rate application. The RAM of FIGS. 15A and 15B are organized in a manner, whereby a large group of relevant edges can be fetched in one clock cycle; accordingly, these values are placed “together” in memory, according to a predetermined scheme or arrangement. It is observed that, in actuality, even with a truly random code, for a group of check nodes (and respectively bit nodes), the relevant edges can be placed next to one another in RAM, but then the relevant edges adjacent to a group of bit nodes (respectively check nodes) will be randomly scattered in RAM. Therefore, the “togetherness,” under the present invention, stems from the design of the parity check matrices themselves. That is, the check matrix design ensures that the relevant edges for a group of bit nodes and check nodes are simultaneously placed together in RAM.
As seen in FIGS. 15A and 15B, each box contains the value of an edge, which is multiple bits (e.g., 6). Edge RAM, according to one embodiment of the present invention, is divided into two parts: top edge RAM 1501 (FIG. 15A) and bottom edge RAM 1503 (FIG. 15B). Bottom edge RAM contains the edges between bit nodes of degree 2, for example, and check nodes. Top edge RAM contains the edges between bit nodes of degree greater than 2 and check nodes. Therefore, for every check node, 2 adjacent edges are stored in the bottom edge RAM 1503, and the rest of the edges are stored in the top edge RAM 1501. For example, the size of the top edge RAM 1501 and bottom edge RAM 1503 for various code rates are given in Table 1












TABLE 1







1/2
2/3
3/4
5/6




















Top Edge
400 × 392
440 × 392
504 × 392
520 × 392


RAM


Bottom
160 × 392
110 × 392
 72 × 392
 52 × 392


Edge RAM









Based on Table 1, an edge RAM of size 576×392 is sufficient to store the edge metrics for all the code rates of 1⁄2, 2⁄3, 3⁄4, and 5⁄6.
As noted, under this exemplary scenario, a group of 392 bit nodes and 392 check nodes are selected for processing at a time. For 392 check node processing, q=dc−2 consecutive rows are accessed from the top edge RAM 1501, and 2 consecutive rows from the bottom edge RAM 1503. The value of dc depends on the specific code, for example dc=7 for rate 1⁄2, dc=10 for rate 2⁄3, dc=16 for rate 3⁄4 and dc=22 for rate 5⁄6 for the above codes. Of course other values of dc for other codes are possible. In this instance, q+2 is the degree of each check node.
For bit node processing, if the group of 392 bit nodes has degree 2, their edges are located in 2 consecutive rows of the bottom edge RAM 1503. If the bit nodes have degree d>2, their edges are located in some d rows of the top edge RAM 1501. The address of these d rows can be stored in non-volatile memory, such as Read-Only Memory (ROM). The edges in one of the rows correspond to the first edges of 392 bit nodes, the edges in another row correspond to the second edges of 392 bit nodes, etc. Moreover for each row, the column index of the edge that belongs to the first bit node in the group of 392 can also be stored in ROM. The edges that correspond to the second, third, etc. bit nodes follow the starting column index in a “wrapped around” fashion. For example, if the jth edge in the row belongs to the first bit node, then the (j+1)st edge belongs to the second bit node, (j+2)nd edge belongs to the third bit node, . . . , and (j−1)st edge belongs to the 392th bit node.
In Tables 2-5, the row index and the starting column index of top edge RAM 1501 are specified for every group of 392 bit nodes of degree 3 or larger, for the respective code rates of 2⁄3, 5⁄6, 1⁄2, and 3⁄4. Each row in the Tables 2-5 represents a group of 392 bit nodes. The first number denotes the row index and the second number denotes the starting column index. For example in Table 2, the first row completely determines the addresses of adjacent edges for the first group of 392 bit nodes of degree 13. Specifically, the entry 0/0 indicates that the first adjacent edges for all of the 392 bit nodes are stored in row number 0. Moreover in that row, the column indexed 0 carries the information for the first adjacent edge of the first bit node, column indexed 1 carries the information for the first adjacent edge of the second bit node etc., and finally column indexed 391 carries the information for the first adjacent edge of the 392th bit node.
Similarly the entry 433/323 specifies that the second adjacent edges for all of the 392 bit nodes are stored in row number 433. Moreover in that row, the column indexed 323 carries the information for the second adjacent edge of the first bit node, column indexed 324 carries the information for the second adjacent edge of the second bit node etc. The column indexed 322 carries the information for the second adjacent edge of the 392th bit node.
Similarly, other entries in the first row of Table 2 determine the addresses of the remaining adjacent edges for the first group of 392 bit nodes. Likewise, the entries in the second row of Table 2 determine the addresses of the adjacent edges for the second group of 392 bit nodes, etc.







TABLE 2





Row Index/Starting Column Index (Rate 2/3)



























 0/0
433/323
242/150
 91/117
323/112
147/93
 35/105
227/232
196/311
292/180
 52/244
180/250
 20/335


 8/0
121/326
178/109
299/157
195/338
 99/232
251/107
411/263
364/199
 28/218
276/370
108/80
 84/130


 16/0
281/359
 18/112
 83/180
115/264
163/149
355/321
 11/206
268/100
436/79
252/316
420/280
380/335


 24/0
345/122
146/365
107/40
283/363
123/368
379/340
 3/156
124/15
220/187
356/127
188/71
156/82


 32/0
425/177
234/46
267/219
 67/224
171/275
219/306
387/87
372/56
140/31
 36/339
116/36
316/288


 40/0
417/214
122/188
339/58
235/72
187/26
 75/302
 19/362
164/285
132/109
148/189
 60/65
412/303


 48/0
 89/312
362/214
 43/21
419/219
427/378
395/10
347/167
 68/221
260/310
396/54
308/268
388/176


 56/0
 73/69
434/266
155/277
435/360
363/183
 51/165
331/181
 12/232
404/193
172/175
324/349
348/98


 64/0
177/354
 34/172
243/141
139/362
259/151
179/166
307/56
 76/367
244/121
100/299
428/12
284/133


 72/0
145/264
194/335
131/362
403/326
315/180
275/137
203/86
204/303
 4/5
228/360
300/76
 92/17


 80/0
377/382
394/243
 27/109
 59/237
371/175
211/358
291/353
340/161
212/94
332/333
 44/117
236/200


 88/0
 65/365
378/142


 96/0
 57/285
226/108


104/0
 97/161
250/133


112/0
129/184
114/44


120/0
337/130
 50/178


128/0
401/389
170/258


136/0
 25/330
 82/372


144/0
321/309
162/170


152/0
185/38
386/128


160/0
 49/376
 90/331


168/0
265/293
314/166


176/0
297/86
282/193


184/0
217/117
 42/210


192/0
201/124
306/86


200/0
313/377
138/97


208/0
193/247
202/163


216/0
209/377
186/212


224/0
233/238
 26/22


232/0
329/152
410/271


240/0
 9/245
106/170


248/0
409/190
 58/289


256/0
113/375
154/44


264/0
 33/232
274/268


272/0
153/339
218/145


280/0
289/319
 98/4


288/0
 41/209
130/23


296/0
385/42
210/267


304/0
 17/7
258/227


312/0
169/166
290/330


320/0
241/107
 66/111


328/0
137/39
418/182


336/0
249/137
354/218


344/0
161/73
 2/79


352/0
105/280
266/282


360/0
257/69
298/51


368/0
 81/185
338/118


376/0
369/228
370/202


384/0
225/71
 74/136


392/0
 1/314
346/289


400/0
353/286
322/166


408/0
305/81
330/301


416/0
273/170
402/282


424/0
393/227
 10/312


432/0
361/379
426/364


 5/0
350/140
263/166


 13/0
102/110
 87/335


 21/0
174/333
215/219


 29/0
422/227
 31/273


 37/0
406/168
175/11


 45/0
254/42
279/201


 53/0
230/347
 47/291


 61/0
214/139
 55/92


 69/0
358/131
199/344


 77/0
 86/374
183/298


 85/0
118/118
407/25


 93/0
318/221
 39/66


101/0
 54/256
 79/202


109/0
374/195
119/162


117/0
238/89
207/243


125/0
366/78
 95/96


133/0
 46/216
351/9


141/0
326/99
127/87


149/0
134/75
319/102


157/0
158/154
 15/65


165/0
286/158
143/362


173/0
190/146
191/205


181/0
 62/4
343/262


189/0
 94/239
271/38


197/0
198/207
231/297


205/0
 22/32
167/205


213/0
246/385
303/246


221/0
390/368
439/220


229/0
334/207
247/262


237/0
398/378
 63/211


245/0
150/340
359/100


253/0
294/75
415/189


261/0
222/321
391/78


269/0
166/343
159/105


277/0
126/93
239/166


285/0
110/113
151/373


293/0
302/144
 71/18


301/0
262/368
111/193


309/0
414/332
375/389


317/0
142/256
103/242


325/0
278/22
 7/154


333/0
342/192
423/330


341/0
 14/181
431/16


349/0
 38/367
383/16


357/0
270/91
223/195


365/0
182/211
287/313


373/0
310/170
135/230


381/0
 78/15
295/220


389/0
430/353
335/91


397/0
 30/141
367/216


405/0
382/36
311/98


413/0
206/377
255/372


421/0
438/225
399/148


429/0
 70/182
327/105


437/0
 6/277
 23/94
















TABLE 3





Row Index/Starting Column Index (Rate 5/6)



























 0/0
221/158
442/14
503/323
283/150
104/117
384/112
165/93
 45/105
266/232
226/311
347/180
 67/244


 20/0
101/369
162/326
323/359
 23/112
124/180
144/264
205/149
405/321
 6/206
306/100
507/79
287/316


 40/0
201/285
302/12
 63/134
243/68
264/238
344/375
105/259
345/213
246/75
 66/148
327/100
167/220


 60/0
381/141
422/112
443/125
223/47
204/375
504/214
145/188
385/58
206/72
166/26
 87/302
 7/362


 80/0
461/383
 82/80
143/61
463/106
284/196
 4/94
 85/104
285/235
386/3
426/218
 27/38
107/161


100/0
 41/310
482/66
343/376
403/166
324/265
404/236
245/230
445/63
186/343
486/88
427/202
267/362


120/0
 61/31
502/317
123/25
163/139
424/269
164/309
 25/56
505/260
406/279
346/148
367/315
 47/382


140/0
421/362
462/206
263/297
 83/384
244/287
184/132
225/140
125/14
506/216
106/311
447/87
487/264


160/0
441/191
382/360
423/282
203/2
 84/58
 64/347
425/249
 5/267
466/232
 46/275
127/385
187/26


180/0
501/296
222/324
 3/73
 43/6
364/319
444/204
185/82
 65/259
 26/90
286/155
307/181
147/366


200/0
301/325
102/119
383/285
103/84
304/121
484/352
365/102
485/107
 86/9
366/76
387/229
467/52


220/0
341/331
322/242
483/275
303/293
464/166
 44/283
305/232
465/86
126/193
146/184
207/38
407/117


240/0
 21/314
362/289
363/211
183/120
 24/286
224/166
325/186
265/144
446/81
326/301
227/4
247/199


260/0
161/91
142/78


280/0
241/209
 2/119


300/0
141/87
342/147


320/0
281/55
 42/46


340/0
261/213
182/145


360/0
181/264
 62/88


380/0
 1/96
262/184


400/0
361/30
282/126


420/0
 81/202
202/206


440/0
481/156
242/263


460/0
401/170
 22/126


480/0
321/42
402/21


500/0
121/272
122/337


 8/0
289/369
190/223


 28/0
369/313
130/127


 48/0
189/92
290/241


 68/0
509/124
210/56


 88/0
489/23
430/101


108/0
309/208
510/162


128/0
349/147
330/242


148/0
 29/263
490/54


168/0
 69/312
250/377


188/0
249/315
270/116


208/0
 49/176
170/58


228/0
109/337
 10/55


248/0
469/65
110/187


268/0
209/105
470/362


288/0
229/164
150/80


308/0
 9/293
410/374


328/0
329/122
310/152


348/0
149/124
390/382


368/0
389/160
230/92


388/0
169/357
370/368


408/0
449/296
 90/377


428/0
269/32
 70/212


448/0
409/59
450/257


468/0
 89/291
 30/234


488/0
429/130
350/95


508/0
129/276
 50/38


 11/0
292/349
133/372


 31/0
492/271
253/248


 51/0
192/149
273/378


 71/0
352/265
153/37


 91/0
332/244
293/199


111/0
152/354
393/243


131/0
312/144
213/184


151/0
 92/219
173/11


171/0
392/182
473/325


191/0
232/219
193/30


211/0
372/157
 13/63


231/0
 12/108
333/359


251/0
112/33
513/88


271/0
 72/207
413/9


291/0
272/100
 93/357


311/0
432/166
233/272


331/0
412/265
 33/210


351/0
132/155
493/50


371/0
512/292
453/214


391/0
172/387
 53/114


411/0
 32/233
433/177


431/0
252/113
373/52


451/0
212/347
353/90


471/0
 52/89
 73/198


491/0
452/285
313/233


511/0
472/103
113/84


 14/0
 55/43
 36/361


 34/0
355/70
116/287


 54/0
115/137
196/57


 74/0
 95/161
416/206


 94/0
295/273
336/209


114/0
255/184
296/287


134/0
435/11
376/38


154/0
155/356
 16/379


174/0
135/251
 76/10


194/0
235/314
256/293


214/0
 75/296
216/326


234/0
275/314
356/116


254/0
455/133
156/165


274/0
375/292
436/283


294/0
515/227
456/337


314/0
315/111
176/155


334/0
175/98
276/334


354/0
335/7
476/87


374/0
415/161
136/15


394/0
395/338
496/98


414/0
495/82
396/269


434/0
195/312
516/187


454/0
475/100
 56/356


474/0
 15/163
316/195


494/0
 35/197
 96/145


514/0
215/301
236/381


 17/0
 18/321
459/4


 37/0
398/236
139/8


 57/0
338/117
439/84


 77/0
438/97
499/93


 97/0
298/292
 19/215


117/0
218/224
419/275


137/0
 98/229
299/27


157/0
378/133
339/232


177/0
118/191
359/271


197/0
478/272
159/386


217/0
498/262
119/219


237/0
418/282
519/297


257/0
238/33
379/339


277/0
258/230
179/350


297/0
158/27
 59/188


317/0
518/249
399/229


337/0
278/333
279/330


357/0
138/276
239/49


377/0
178/34
219/304


397/0
458/344
199/181


417/0
 58/312
479/158


437/0
358/377
259/364


457/0
 78/157
319/380


477/0
318/75
 99/57


497/0
 38/296
 79/26


517/0
198/115
 39/342
















TABLE 4





Row Index/Starting Column Index (Rate 1/2)






















240/0
306/249
387/194
 98/132
268/80
219/33
 64/252
108/54


245/0
146/169
 37/233
183/243
233/207
 9/336
 54/91
363/391


250/0
196/123
242/31
 63/103
118/277
344/177
339/46
173/219


255/0
216/36
287/288
318/43
 83/327
 34/28
354/114
 53/84


260/0
316/69
377/8
323/110
308/250
314/209
214/101
298/134


265/0
256/186
257/166
 23/196
 68/68
234/41
144/249
333/11


270/0
201/192
 32/38
213/255
203/124
 84/285
264/12
263/134


275/0
 36/100
247/220
388/286
273/339
 89/334
154/192
223/148


280/0
396/141
132/112
283/125
163/47
 79/375
 14/214
138/188


285/0
 31/189
 82/65
 18/303
313/92
299/317
129/18
373/356


290/0
381/332
332/312
258/214
 43/21
364/219
274/378
198/10


295/0
121/66
217/124
338/346
 48/380
189/155
199/79
278/224


300/0
 71/260
 22/248
193/240
288/248
284/237
224/268
 38/263


305/0
 46/232
282/193
293/175
378/349
169/98
184/165
168/31


310/0
156/116
 87/62
208/390
113/287
 69/354
269/172
343/141


315/0
311/12
192/133
143/43
 58/75
124/176
324/24
383/346


320/0
 16/118
372/259
368/265
133/59
309/321
289/272
104/80


325/0
336/114
 7/90
123/190
228/181
114/324
319/240
244/246


330/0
226/71
112/218
358/348
398/83
179/121
119/366
394/197


335/0
 21/383
142/80
158/61
218/106
329/196
 4/94
 49/104


340/0
221/97
 2/252
178/174
 13/190
164/166
 99/130
204/9


345/0
126/76
 67/120
 78/183
243/53
134/140
149/197
359/239


350/0
 96/221
392/290
 28/163
353/297
279/147
294/343
374/314


355/0
176/230
367/63
 73/343
393/88
174/202
259/362
249/256


360/0
241/60
202/21
348/66
328/351
139/144
 94/258
384/41


365/0
 26/374
262/54
303/391
153/132
254/145
209/307
 74/126


370/0
 91/25
382/139
238/269
128/309
239/56
 24/260
369/279


375/0
151/213
317/133
253/161
188/92
399/371
194/116
 39/302


380/0
296/140
307/14
 93/216
148/311
389/87
334/264
109/335


385/0
286/76
222/17
 33/116
 8/191
304/360
 19/282
379/2


390/0
106/217
212/188
103/68
248/264
 29/48
 44/174
349/274


395/0
281/269
162/333
 3/243
 88/320
159/75
 59/300
229/136


 0/0
346/176
157/302


 5/0
171/47
 42/1


 10/0
 86/124
267/2


 15/0
321/291
197/8


 20/0
236/149
147/50


 25/0
 1/168
347/191


 30/0
386/257
252/12


 35/0
301/64
397/176


 40/0
341/340
272/97


 45/0
101/201
122/134


 50/0
136/201
 57/343


 55/0
131/169
292/299


 60/0
166/389
352/216


 65/0
 76/132
297/33


 70/0
211/261
167/45


 75/0
161/323
 12/150


 80/0
116/93
107/105


 85/0
246/180
322/244


 90/0
261/190
342/297


 95/0
366/385
177/103


100/0
391/240
 77/328


105/0
266/327
182/182


110/0
181/73
 47/322


115/0
191/126
 72/135


120/0
251/115
227/161


125/0
276/85
172/213


130/0
371/17
327/236


135/0
 66/326
 62/109


140/0
141/232
357/107


145/0
271/218
207/370


150/0
 56/252
127/20


155/0
 61/143
 97/305


160/0
 11/383
237/214


165/0
376/359
337/112


170/0
186/149
277/321


175/0
206/79
 92/316


180/0
291/315
362/135


185/0
 51/93
232/326


190/0
 6/197
102/103


195/0
331/142
187/122


200/0
361/363
 27/368


205/0
326/15
152/187


210/0
111/82
 52/214


215/0
 41/385
312/150


220/0
356/387
137/254


225/0
 81/175
302/84


230/0
351/11
 17/303


235/0
231/55
117/265
















TABLE 5





Row Index/Starting Column Index (Rate 3/4)



























 0/0
113/334
100/308
423/175
493/163
 32/370
116/20
467/48
243/275
370/284
356/114
 77/201
 7/214


 14/0
 29/350
 44/366
185/335
 3/40
494/155
144/324
383/185
229/96
230/376
188/182
427/304
385/269


 28/0
435/215
366/165
101/329
 17/221
 46/276
 74/130
341/4
313/169
314/11
272/267
 21/376
273/122


 42/0
155/306
240/253
353/325
451/355
312/33
 88/27
 47/23
327/90
286/87
 34/201
483/221
175/39


 56/0
197/263
492/185
283/223
367/316
 60/241
228/91
145/175
439/3
454/168
202/98
133/214
203/82


 70/0
463/384
352/298
269/9
129/294
256/303
214/387
 5/316
285/257
 90/282
 48/376
399/317
329/102


 84/0
 1/159
170/317
409/245
255/173
270/11
438/179
271/224
 89/131
300/144
328/199
343/321
231/338


 98/0
211/266
450/256
199/279
171/358
242/192
466/378
187/100
 19/70
 62/98
384/313
 35/382
245/164


112/0
141/386
128/357
 87/172
465/64
424/35
354/238
117/300
257/174
146/154
496/182
161/232
 91/355


126/0
 15/196
296/183
395/218
 73/356
452/367
158/342
173/70
131/251
258/268
 76/176
455/172
119/109


140/0
 57/265
 58/45
437/175
 59/369
284/357
102/53
103/286
 33/318
412/49
160/25
105/120
371/188


154/0
323/272
198/11
 31/140
227/330
410/150
298/113
 61/249
495/207
244/190
426/233
 63/30
189/283


168/0
477/41
408/85
311/63
 45/301
326/13
200/292
159/218
481/99
 20/171
174/192
217/102
315/178


182/0
 43/340
212/289
381/152
115/273
172/111
368/2
 75/34
369/291
132/92
482/375
413/195
301/219


196/0
225/338
436/232
479/161
339/50
340/372
396/293
355/218
397/80
468/212
342/375
497/351
259/314


210/0
253/84
 30/254
297/89
241/165
382/65
 18/60
299/186
425/104
440/255
398/62
441/191
469/14


224/0
449/109
478/333
325/82
143/94
186/39
130/44
453/22
411/329
 6/168
118/357
287/119
357/258


238/0
169/152
310/308
213/159
157/365
480/361
 4/64
201/245
215/92
104/185
216/189
147/125
 49/310


252/0
267/180
380/44


266/0
 71/132
184/228


280/0
281/48
268/91


294/0
393/59
254/241


308/0
379/129
 86/21


322/0
127/319
114/57


336/0
 85/227
282/298


350/0
491/101
324/74


364/0
309/378
226/317


378/0
239/220
 2/201


392/0
407/135
156/221


406/0
365/360
394/114


420/0
183/335
422/129


434/0
421/105
464/120


448/0
295/245
142/160


462/0
351/37
338/29


476/0
337/16
 72/305


490/0
 99/220
 16/347


 8/0
 23/384
346/305


 22/0
415/118
444/373


 36/0
 65/28
 24/211


 50/0
261/130
 80/113


 64/0
275/316
220/366


 78/0
205/109
206/255


 92/0
 51/110
 38/74


106/0
373/262
304/363


120/0
345/250
472/134


134/0
 37/173
388/301


148/0
359/272
430/234


162/0
429/71
150/189


176/0
 93/332
 94/299


190/0
163/385
416/307


204/0
289/144
164/50


218/0
457/140
290/145


232/0
 79/42
360/26


246/0
387/59
262/196


260/0
233/93
 66/21


274/0
303/116
136/28


288/0
121/176
276/279


302/0
485/235
332/69


316/0
443/336
178/353


330/0
499/298
458/45


344/0
191/240
234/244


358/0
 9/13
248/94


372/0
219/36
402/112


386/0
331/192
 52/58


400/0
471/294
500/144


414/0
317/186
318/150


428/0
107/69
108/346


442/0
149/139
486/346


456/0
135/170
192/65


470/0
401/2
 10/281


484/0
177/326
374/2


498/0
247/143
122/242


 11/0
474/49
433/281


 25/0
292/134
335/294


 39/0
404/29
265/296


 53/0
320/345
111/194


 67/0
208/221
 13/84


 81/0
264/133
419/95


 95/0
 54/157
 83/51


109/0
166/363
195/303


123/0
194/389
377/15


137/0
460/36
447/169


151/0
306/23
279/311


165/0
 40/133
153/233


179/0
236/53
 27/257


193/0
446/121
293/259


207/0
250/350
167/310


221/0
 68/104
209/119


235/0
334/224
251/323


249/0
432/83
503/117


263/0
180/192
125/201


277/0
362/183
391/267


291/0
110/347
405/288


305/0
222/22
223/10


319/0
502/80
489/249


333/0
 12/100
139/370


347/0
390/229
321/44


361/0
376/295
 97/70


375/0
124/166
 69/108


389/0
418/73
349/223


403/0
 96/321
237/242


417/0
 26/23
181/237


431/0
 82/7
 55/264


445/0
348/347
461/381


459/0
138/244
 41/239


473/0
488/356
475/320


487/0
278/80
307/248


501/0
152/153
363/334









With the organization shown in FIGS. 15A and 15B, speed of memory access is greatly enhanced during LDPC coding.
FIG. 16 illustrates a computer system upon which an embodiment according to the present invention can be implemented. The computer system 1600 includes a bus 1601 or other communication mechanism for communicating information, and a processor 1603 coupled to the bus 1601 for processing information. The computer system 1600 also includes main memory 1605, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 1601 for storing information and instructions to be executed by the processor 1603. Main memory 1605 can also be used for storing temporary variables or other intermediate information during execution of instructions to be executed by the processor 1603. The computer system 1600 further includes a read only memory (ROM) 1607 or other static storage device coupled to the bus 1601 for storing static information and instructions for the processor 1603. A storage device 1609, such as a magnetic disk or optical disk, is additionally coupled to the bus 1601 for storing information and instructions.
The computer system 1600 may be coupled via the bus 1601 to a display 1611, such as a cathode ray tube (CRT), liquid crystal display, active matrix display, or plasma display, for displaying information to a computer user. An input device 1613, such as a keyboard including alphanumeric and other keys, is coupled to the bus 1601 for communicating information and command selections to the processor 1603. Another type of user input device is cursor control 1615, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to the processor 1603 and for controlling cursor movement on the display 1611.
According to one embodiment of the invention, generation of LDPC codes is provided by the computer system 1600 in response to the processor 1603 executing an arrangement of instructions contained in main memory 1605. Such instructions can be read into main memory 1605 from another computer-readable medium, such as the storage device 1609. Execution of the arrangement of instructions contained in main memory 1605 causes the processor 1603 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the instructions contained in main memory 1605. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions to implement the embodiment of the present invention. Thus, embodiments of the present invention are not limited to any specific combination of hardware circuitry and software.
The computer system 1600 also includes a communication interface 1617 coupled to bus 1601. The communication interface 1617 provides a two-way data communication coupling to a network link 1619 connected to a local network 1621. For example, the communication interface 1617 may be a digital subscriber line (DSL) card or modem, an integrated services digital network (ISDN) card, a cable modem, or a telephone modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 1617 may be a local area network (LAN) card (e.g. for EthernetTM or an Asynchronous Transfer Model (ATM) network) to provide a data communication connection to a compatible LAN. Wireless links can also be implemented. In any such implementation, communication interface 1617 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information. Further, the communication interface 1617 can include peripheral interface devices, such as a Universal Serial Bus (USB) interface, a PCMCIA (Personal Computer Memory Card International Association) interface, etc.
The network link 1619 typically provides data communication through one or more networks to other data devices. For example, the network link 1619 may provide a connection through local network 1621 to a host computer 1623, which has connectivity to a network 1625 (e.g. a wide area network (WAN) or the global packet data communication network now commonly referred to as the “Internet”) or to data equipment operated by service provider. The local network 1621 and network 1625 both use electrical, electromagnetic, or optical signals to convey information and instructions. The signals through the various networks and the signals on network link 1619 and through communication interface 1617, which communicate digital data with computer system 1600, are exemplary forms of carrier waves bearing the information and instructions.
The computer system 1600 can send messages and receive data, including program code, through the network(s), network link 1619, and communication interface 1617. In the Internet example, a server (not shown) might transmit requested code belonging to an application program for implementing an embodiment of the present invention through the network 1625, local network 1621 and communication interface 1617. The processor 1603 may execute the transmitted code while being received and/or store the code in storage device 169, or other non-volatile storage for later execution. In this manner, computer system 1600 may obtain application code in the form of a carrier wave.
The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to the processor 1603 for execution. Such a medium may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 1609. Volatile media include dynamic memory, such as main memory 1605. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 1601. Transmission media can also take the form of acoustic, optical, or electromagnetic waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, CDRW, DVD, any other optical medium, punch cards, paper tape, optical mark sheets, any other physical medium with patterns of holes or other optically recognizable indicia, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave, or any other medium from which a computer can read.
Various forms of computer-readable media may be involved in providing instructions to a processor for execution. For example, the instructions for carrying out at least part of the present invention may initially be borne on a magnetic disk of a remote computer. In such a scenario, the remote computer loads the instructions into main memory and sends the instructions over a telephone line using a modem. A modem of a local computer system receives the data on the telephone line and uses an infrared transmitter to convert the data to an infrared signal and transmit the infrared signal to a portable computing device, such as a personal digital assistance (PDA) and a laptop. An infrared detector on the portable computing device receives the information and instructions borne by the infrared signal and places the data on a bus. The bus conveys the data to main memory, from which a processor retrieves and executes the instructions. The instructions received by main memory may optionally be stored on storage device either before or after execution by processor.
Accordingly, the various embodiments of the present invention provide an approach for generating structured Low Density Parity Check (LDPC) codes, as to simplify the encoder and decoder. Structure of the LDPC codes is provided by restricting the parity check matrix to be lower triangular. Also, the approach can advantageously exploit the unequal error protecting capability of LDPC codes on transmitted bits to provide extra error protection to more vulnerable bits of high order modulation constellations (such as 8-PSK (Phase Shift Keying)). The decoding process involves iteratively regenerating signal constellation bit metrics into an LDPC decoder after each decoder iteration or several decoder iterations. The above approach advantageously yields reduced complexity without sacrificing performance.
While the present invention has been described in connection with a number of embodiments and implementations, the present invention is not so limited but covers various obvious modifications and equivalent arrangements, which fall within the purview of the appended claims.

## Claims

1. A method comprising:
storing a first edge value in a first segment of memory; and
storing a second edge value in a second segment of memory, wherein the edge values are associated with a structured parity check matrix used to generate a low density parity check coded signal, the edge values specifying relationship of bit nodes and check nodes, wherein the first segment is contiguous with the second segment, and the first edge value and the second edge value are read during a single processor clock cycle for decoding the low density parity check coded signal.

2. A method according to claim 1, wherein the memory is partitioned according to degrees of the bit nodes.

3. A method according to claim 2, wherein edge values having bit nodes of n degrees are stored in a first portion of the memory, and edge values having bit nodes of greater than n degrees are stored in a second portion of the memory, n being an integer.

4. A method according to claim 1, wherein addresses of the memory is stored in a Read-Only memory.

5. A method according to claim 1, wherein M bit nodes or M check nodes correspond to the edge values, and M parallel processing engines are utilized to decode the low density parity check coded signal.

6. A computer-readable storage medium bearing instructions that are arranged, upon execution, to cause one or more processors to perform the method of claim 1.

7. A memory device comprising:
a first segment configured to store a first edge value; and
a second segment contiguous with the first segment and configured to store a second edge value, wherein the edge values are associated with a structured parity check matrix used to generate a low density parity check coded signal, the edge values specifying relationship of bit nodes and check nodes, wherein the first edge value and the second edge value are read during a single processor clock cycle for decoding the low density parity check coded signal.

8. A device according to claim 7, wherein the memory is partitioned according to degrees of the bit nodes.

9. A device according to claim 8, wherein edge values having bit nodes of n degrees are stored in a first portion of the memory, and
edge values having bit nodes of greater than n degrees are stored in a second portion of the memory, n being an integer.

10. A device according to claim 7, wherein addresses of the memory is stored in a Read-Only memory.

11. A device according to claim 7, wherein M bit nodes or M check nodes correspond to the edge values, and M parallel processing engines are utilized to decode the low density parity check coded signal.

12. A system comprising:
a memory including,
a first segment configured to store a first edge value, and
a second segment contiguous with the first segment and configured to store a second edge value, wherein the edge values are associated with a structured parity check
matrix used to generate a low density parity check coded signal, the edge values specifying relationship of bit nodes and check nodes; and
a plurality of processing engines configured to read the edge values during a single clock cycle for decoding the low density parity check coded signal.

13. A system according to claim 12, wherein the memory is partitioned according to degrees of the bit nodes.

14. A system according to claim 13, wherein edge values having bit nodes of n degrees are stored in a first portion of the memory, and edge values having bit nodes of greater than n degrees are stored in a second portion of the memory, n being an integer.

15. A system according to claim 12, wherein addresses of the memory is stored in a Read-Only memory.

16. A method comprising:
reading, during a single processor clock cycle, a first edge value stored in a first segment of memory; and
reading, during the single processor clock cycle, a second edge value in a second segment of memory, wherein the edge values are associated with a structured parity check matrix used to generate a low density parity check coded signal, the edge values specifying relationship of bit nodes and check nodes, wherein the first segment is contiguous with the second segment for decoding the low density parity check coded signal.

17. A method according to claim 16, wherein the memory is partitioned according to degrees of the bit nodes.

18. A method according to claim 17, wherein edge values having bit nodes of n degrees are stored in a first portion of the memory, and edge values having bit nodes of greater than n degrees are stored in a second portion of the memory, n being an integer.

19. A method according to claim 16, wherein addresses of the memory is stored in a Read-Only memory.

20. A method according to claim 16, wherein M bit nodes or M check nodes correspond to the edge values, and M parallel processing engines are utilized to decode the low density parity check coded signal.

21. A computer-readable storage medium bearing instructions that are arranged, upon execution, to cause one or more processors to perform the method of claim 16.