# Patent

## Title
LDPC (low density parity check) code size adjustment by shortening and puncturing

## Abstract

LDPC (Low Density Parity Check) code size adjustment by shortening and puncturing. A variety of LDPC coded signals may be generated from an initial LDPC code using selected shortening and puncturing. Using LDPC code size adjustment approach, a single communication device whose hardware design is capable of processing the original LDPC code is also capable to process the various other LDPC codes constructed from the original LDPC code after undergoing appropriate shortening and puncturing. This provides significant design simplification and reduction in complexity because the same hardware can be implemented to accommodate the various LDPC codes generated from the original LDPC code. Therefore, a multi-LDPC code capable communication device can be implemented that is capable to process several of the generated LDPC codes. This approach allows for great flexibility in the LDPC code design, in that, the original code rate can be maintained after performing the shortening and puncturing.

## Background
CROSS REFERENCE TO RELATED PATENTS/PATENT APPLICATIONS
Provisional Priority Claims
The present U.S. Utility Patent Application claims priority pursuant to 35 U.S.C. § 119(e) to the following U.S. Provisional Patent Application which is hereby incorporated herein by reference in its entirety and made part of the present U.S. Utility Patent Application for all purposes:
1. U.S. Provisional Application Ser. No. 60/757,358, entitled “LDPC (Low Density Parity Check) code size adjustment by shortening and puncturing,” filed Monday, Jan. 9, 2006 (Jan. 9, 2006) pending.


BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
The invention relates generally to communication systems; and, more particularly, it relates to encoding and decoding signals employed within such communication systems.
2. Description of Related Art
Data communication systems have been under continual development for many years. One such type of communication system that continues to be of significant interest is that which employs iterative error correction codes. Of particular interest is a communication system that employs LDPC (Low Density Parity Check) code. Communications systems with iterative codes are often able to achieve lower BER (Bit Error Rate) than alternative codes for a given SNR (Signal to Noise Ratio).
The use of LDPC coded signals continues to be explored within many newer application areas. Some examples of possible communication systems that may employ LDPC coded signals include communication systems employing 4 wire twisted pair cables for high speed Ethernet applications (e.g., 10 Gbps (Giga-bits per second) Ethernet operation according to the IEEE 802.3an (10 GBASE-T) emerging standard) as well as communication systems operating within a wireless context (e.g., in the IEEE 802.11 context space including the IEEE 802.11n emerging standard). In general, LDPC coding can be applied to any type of communication system in which data is sent from one place to another where error correction capability is desired.
For any of these particular communication system application areas, near-capacity achieving error correction codes are very desirable. The latency constraints, which would be involved by using traditional concatenated codes, simply preclude their use in such applications in very high data rate communication system application areas.
When performing processing of such LDPC signals within communication systems, a designer has quite a degree of freedom by which to implement the hardware to perform such encoding and/or decoding processing. However, in many communication systems, such as wireless LAN and satellite communication system, multiple error correcting codes each possible having different block sizes and different code rates are oftentimes needed. For example, a typical prior art approach is to design and construct multiple LDPC codes to accommodate each of the different block sizes and code rates required for the particular communication system application. For example, in IEEE 802.11n Joint Proposal (depicted further below using reference [d]), twelve (12) distinct codes are constructed for four (4) different code rates. Each code rate has three (3) different block sizes, and every block size has its own code structure. Currently, the typical approach in the art is to employ separate and distinct functional blocks and/or circuitry portions within a communication device to perform the appropriate processing for each of these different LDPC codes. This approach inherently requires more hardware in implementation. In other words, within communication devices that seek to operate on a variety of LDPC codes (i.e., variable code rate and/or modulation type communication devices), the typical design approach is to provision separate functional blocks and/or circuitry for each of the separate LDPC codes which are to be processed.
This can prove to be very expensive in terms of a variety of cost factors including real estate, actual dollar cost, and complexity in terms of the number of gates required within the communication device. With the continual advent of communication devices and communication systems being designed to accommodate multi-code types signals (including multi-code rate and/or multi-modulation types signals whose code rate and/or modulation can vary as frequently as on a symbol by symbol or frame by frame basis), there continues to be a need in the art for better and more efficient LDPC code design as well as the associated hardware that is designed and implemented to support such LDPC codes.
In the art of communication systems and communication devices that employ multiple LDPC code signals, shortening and puncturing can be performed to generate the various LDPC coded signals. However, using the prior art approaches of shortening and puncturing, the LDPC codes resulting there from inherently require the multiple functional block and/or circuitry approach to hardware design, in that, each of the resulting LDPC codes have a different code structure. In addition, many of the prior art approaches to shortening and puncturing require a particular shortening and puncturing ratio which also inherently narrows the type of LDPC codes which can be selected and designed while still complying with those particular shortening and puncturing approaches.
The following 5 references describe some prior art approaches to multiple LDPC code design, some of which employ prior art approaches to shortening and puncturing.
[a] PHY Advanced Coding “ad hoc” team, “Motion JP-K043: Low-Density Parity Check (LDPC) Code and Encoding Procedure Definition,” 7 pages.
[b] Motorola, “Column weight distribution,” Nov. 15, 2005, 5 pages.
[c] Huaning Niu and Chiu Ngo, Samsung, “Performance evaluation of different shortening schemes puncturing patens,” Nov. 29, 2005, 23 pages.
[d] Syed Aon Mujtaba, Agere Systems Inc., “TGn Sync Proposal Technical Specification,” doc.: IEEE 802.11-04/0889r7, IEEE P802.11 Wireless LANs, 133 pages.
[e] Michael Livshits, Nortel Networks Limited, “Shortening and puncturing performance analysis,” Dec. 7, 2005, 4 pages.
BRIEF SUMMARY OF THE INVENTION
The present invention is directed to apparatus and methods of operation that are further described in the following Brief Description of the Several Views of the Drawings, the Detailed Description of the Invention, and the claims. Other features and advantages of the present invention will become apparent from the following detailed description of the invention made with reference to the accompanying drawings.



BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
FIG. 1 is a diagram illustrating various possible embodiments of a communication system.
FIG. 2 illustrates an embodiment of LDPC encoding system.
FIG. 3 illustrates an embodiment of a method for shortening and puncturing.
FIG. 4 illustrates an embodiment of an apparatus that is operable to perform encoding and/or decoding of multiple LDPC coded signals using shortening and puncturing.
FIG. 5 illustrates an embodiment of a communication device employing common functional block and/or circuitry for encoding and decoding, respectively, of multiple LDPC coded signals.
FIG. 6 illustrates an embodiment of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 1296.
FIG. 7 illustrates an embodiment of a performance comparison of LDPC codes having different shortening and puncturing ratios.
FIG. 8 illustrates an embodiment of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 648 with code rates of 1/2.
FIG. 9 illustrates an embodiment of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 1296 with code rates of 5/6.



DETAILED DESCRIPTION OF THE INVENTION
The goal of digital communications systems is to transmit digital data from one location, or subsystem, to another either error free or with an acceptably low error rate. As shown in FIG. 1, data may be transmitted over a variety of communications channels in a wide variety of communication systems: magnetic media, wireless, fiber, copper, and other types of media as well.
FIG. 1 is a diagram illustrating various possible embodiments of a communication system 100.
Referring to FIG. 1, this embodiment of a communication system 100 is a communication channel 199 that communicatively couples a communication device 110 (including a transmitter 112 having an encoder 114 and including a receiver 116 having a decoder 118) situated at one end of the communication channel 199 to another communication device 120 (including a transmitter 126 having an encoder 128 and including a receiver 122 having a decoder 124) at the other end of the communication channel 199. In some embodiments, either of the communication devices 110 and 120 may only include a transmitter or a receiver. There are several different types of media by which the communication channel 199 may be implemented (e.g., a satellite communication channel 130 using satellite dishes 132 and 134, a wireless communication channel 140 using towers 142 and 144 and/or local antennae 152 and 154, a wired communication channel 150, and/or a fiber-optic communication channel 160 using electrical to optical (E/O) interface 162 and optical to electrical (O/E) interface 164)). In addition, more than one type of media may be implemented and interfaced together thereby forming the communication channel 199.
In general, the various coding principles presented herein may be applied to any system that performs encoding of digital information to be transmitted across a communication channel or that performs decoding of a signal that has digital information encoded therein. Additional application areas include the storage and retrieval of information within media storage devices (e.g., hard disk drives) in which encoding and/or decoding of digital information is performed.
To reduce transmission errors that may undesirably be incurred within a communication system, error correction and channel coding schemes are often employed. Generally, these error correction and channel coding schemes involve the use of an encoder at the transmitter side of the communication channel and a decoder at the receiver side of the communication channel.
Encoding and Decoding with Shortening:
Let a binary LDPC code has block size n and k information bits. Then its code rate is r=k/n. Consider a systematic encoder of this LDPC code, which generates k input bits, b0, . . . , bk−1 to a size n codeword c0, . . . , cn−1, where ci=bi, i=0, . . . ,k−1. Let s be the shortening length and j1, . . . , js are shortening positions. Let i0<i1< . . . <ikl−1, where kl=k−s be the ordered numbers of the set {0, . . . ,k−1}/{jl, . . . , js}. Then shortening with these given positions in encoding of kl data bits b0, . . . , bkl−1, can be realized by inputting b0, . . . ,bk−1 with bjl=0, l=1, . . . ,kl and bil= bl, l=1, . . . , kl−1 to the LDPC encoder. Let ck, . . . , cn−1 be the redundancy (or check) bits of the LDPC encoder. Then the output of the shortened codeword is bi0, bi1, . . . , bik−1, ck, . . . , cn−1. Moreover, the code rate of the shortened codeword is (k−s)/(n−s).
In decoding side, the bit metric of the positions i0, . . . , ikl, k, . . . , n−1 are obtained as usually from the received signals. However, since the decoder knows that in position jl, . . . , js the inputted bits are 0, the decoder assigns a fixed value to those metric (e.g. assign a maximal or minimal value depends on the decoding approach being employed).
Encoding and Decoding with Puncturing:
Suppose a binary LDPC code has block size n and k information bits. Then its code rate is r=k/n. Consider a systematic encoder of this LDPC code, which generates k input bits, b0, . . . ,bk−1 to a size n codeword c0, . . . , cn−1, where ci=bi, i=0, . . . ,k−1. Let p be the puncturing length and jl, . . . , jp are puncturing positions. Let i0<i1< . . . <irl−1, where rl=n−k−p be the ordered numbers of the set {k, . . . ,n−k−1}/{jl, . . . , jp}. Then puncturing with these given positions in encoding with the data bits b0, . . . , bk−1 can be realized by inputting b0, . . . ,bk−1 to the LDPC encoder and replacing the original check bits ck, . . . , cn−1 by ci0, . . . , cirl−1. Moreover, the code rate of the punctured codeword is k/(n−p).
In decoding side, the bit metric of the positions 0, . . . ,k−1,i0, . . . , irl−1 are obtained as usually from the received signals. However, since the decoder does not know what is the real value of position jl, . . . , jp, the decoder assigns a neutral value (e.g., 0) to those metrics.
Adjusting Codeword Size with Shortening and Puncturing:
Suppose a binary LDPC code has block size N and K information bits. Moreover, suppose K=kq and N=nq. Then, the code rate of the code is K/N=k/n. By shortening kt positions and puncturing (n−k)t positions of an LDPC codeword, one can obtain a codeword with a reduced block size N−nt=n(q−t) and rate (K−kt)/(n(q−t))=k/n. The encoding and decoding of this codeword can be operated by combining the operations in the two sections above, namely, “Encoding and decoding with shortening” and “Encoding and decoding with puncturing”.
Consider LDPC codes proposed in 802.11n JP codes the [a] reference depicted above, there are 4 code rates, namely, the 4 LDPC codes having code rates of 1/2, 2/3, 3/4 and 5/6 and having 3 different block sizes, namely 1944, 1296, and 648. In the proposal of the [a] reference, the low density parity check matrix, H, of the codes are constructed by sub-matrices. Block size 1944 code has sub-matrices size 81, block size 1296 has sub-matrices size 54 and block size 648 has sub-matrices size 27.
EXAMPLE 1
Consider rate 1/2 block size 1944 LDPC code in the [a] reference. Let q=81. Then N=24, q=1944, K=12, q=972, i.e. n=24 and k=12. Let t=27, then by shortening kt=324 bits and by puncturing (n−k)t=324 bits from a block size 1944 codeword, one can obtain a block size 1296 rate 1/2 codeword. Let t=54, then shortening kt=648 bits and puncturing (n−k)t=648 bits from a block size 1944 codeword, one can obtain a block size 1296 rate 1/2 codeword.
EXAMPLE 2
Consider rate 5/6 block size 1944 LDPC code in the [a] reference. Let q=81. Then N=24, q=1944, K=4, q=324, i.e. n=24 and k=20. Let t=27, then by shortening kt=540 bits and by puncturing (n−k)t=108 bits from a block size 1944 codeword, one can obtain a block size 1296 rate 5/6 codeword. Let t=54, then shortening kt=1080 bits and puncturing (n−k)t=216 bits from a block size 1944 codeword, one can obtain a block size 648 rate 5/6 codeword.
A novel and improved approach to shortening and puncturing is presented below which allows for a greater flexibility in the LDPC codes that can be selected, allows for a singular functional block and/or circuitry portion to perform encoding processing (or decoding processing) according to a variety of LDPC codes.
FIG. 2 illustrates an embodiment of an LDPC encoding system 200. Information bits 205 and zero valued bits (i.e., shortened bits or 0s) 207 are provided to an LDPC encoder 210 that is operable to generate an LDPC codeword (or LDPC code block) 220 there from. When considering a systematic LDPC code, the LDPC codeword 220 includes the actual ‘real’ information bits 222 (which are the same as the information bits 205 provided to the LDPC encoder 210), zero valued bits (i.e., shortened bits or 0s) 224, redundancy bits 226, and punctured redundancy bits 228. If desired, as depicted using reference numeral 214, the information bits 207 can be provided directly as part of the LDPC codeword 220, in that, they need not be taken as output from the LDPC encoder 210. Since the information bits are explicitly represented within the LDPC codeword 220, they can be provided directly to the LDPC codeword 220. It is noted that any shortened bits 224 and any punctured redundancy bits 228 are not transmitted. In addition, it is noted that the shortened bits 224 may be distributed throughout various portions of the original information bits within the original LDPC codeword 220 (i.e., before any shortening is performed). Analogously, it is noted that the punctured redundancy bits 228 may be distributed throughout various portions of the original redundancy bits within the original LDPC codeword 220 (i.e., before any puncturing is performed).
The LDPC encoder 210 performs shortening of a desired number of bits, as shown using reference numeral 212, for the particular shortening and puncturing being performed when encoding according to the appropriate LDPC code. In addition, to generate the zero valued bits (i.e., shortened bits or 0s) 224 within the LDPC codeword 220, the LDPC encoder 210 can simply place or force those positions to 0, since they are known beforehand, as shown using reference numeral 215.
The novel shortening and puncturing approach presented herein also allows for a broader range of LDPC codes to be generated that is possible using prior art shortening and puncturing approaches. As one example of the increased flexibility of LDPC code design available by using this new approach, the shortening and puncturing ratio required according to many prior art approaches is obviated by the novel approach to shortening and puncturing presented herein. This novel shortening and puncturing approach allows for a shortening and puncturing ratio of 1, thereby allowing for easy maintenance of the same code rate for each of the different LDPC codes generated using this novel shortening and puncturing approach.
Moreover, while this novel approach provides a great simplicity in terms of complexity and hardware in implementation, this novel approach to shortening and puncturing does not suffer a significant degradation in performance when compared to prior art shortening and puncturing approaches.
Consider irregular LDPC codes with its low density parity check matrix, H, consists of sub-matrix such as




  
    
      
        H
        =
        
          [
          
            
              
                
                  S
                  
                    0
                    ,
                    0
                  
                
              
              
                
                  S
                  
                    0
                    ,
                    1
                  
                
              
              
                ⋯
              
              
                
                  S
                  
                    0
                    ,
                    
                      n
                      -
                      1
                    
                  
                
              
            
            
              
                
                  
                
              
              
                
                  
                
              
              
                ⋯
              
              
                
                  
                
              
            
            
              
                
                  S
                  
                    l
                    ,
                    0
                  
                
              
              
                
                  S
                  
                    l
                    ,
                    1
                  
                
              
              
                ⋯
              
              
                
                  S
                  
                    l
                    ,
                    
                      n
                      -
                      1
                    
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        
          EQ
          ⁢
          
            
          
          ⁢
          1
        
        )
      
    
  




where Si,j is an m×m sub-matrix, which is either all 0 matrix (i.e., all entries are 0) or a CSI (Cyclic Shifted Identity) matrix (or permutation matrix). If the number of non-zero sub-matrices in all rows of the low density parity check matrix, H, is the same as the number of non-zero sub-matrices in all columns of the low density parity check matrix, H, then the LDPC codes generated thereby are regular; otherwise, the LDPC codes generated thereby are irregular. Moreover, the block size of the LDPC code is N, where N=nm.
The base matrix, Hbase, of the low density parity check matrix, H, depicted by (EQ 1) is provided as




  
    
      
        
          H
          base
        
        =
        
          [
          
            
              
                
                  b
                  
                    0
                    ,
                    0
                  
                
              
              
                
                  b
                  
                    0
                    ,
                    1
                  
                
              
              
                ⋯
              
              
                
                  b
                  
                    0
                    ,
                    
                      n
                      -
                      1
                    
                  
                
              
            
            
              
                
                  
                
              
              
                
                  
                
              
              
                ⋯
              
              
                
                  
                
              
            
            
              
                
                  b
                  
                    l
                    ,
                    0
                  
                
              
              
                
                  b
                  
                    l
                    ,
                    1
                  
                
              
              
                ⋯
              
              
                
                  b
                  
                    l
                    ,
                    
                      n
                      -
                      1
                    
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        
          EQ
          ⁢
          
            
          
          ⁢
          2
        
        )
      
    
  




where bi,j=1 if the sub-matrix, Si,j, is a non-zero matrix, and 0 otherwise.
For example, when considering a 6×8 low density parity check matrix, H, that is composed of 2×2 sub-matrices as follows:




  
    
      
        
          H
          =
          
            [
            
              
                
                  
                    [
                    
                      
                        
                          1
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          1
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          1
                        
                      
                      
                        
                          1
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
              
              
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          1
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          1
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          1
                        
                      
                      
                        
                          1
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          1
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          1
                        
                      
                    
                    ]
                  
                
              
              
                
                  
                    [
                    
                      
                        
                          1
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          1
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          1
                        
                      
                      
                        
                          1
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
                
                  
                    [
                    
                      
                        
                          0
                        
                        
                          1
                        
                      
                      
                        
                          1
                        
                        
                          0
                        
                      
                    
                    ]
                  
                
              
            
            ]
          
        
        ,
      
    
    
      
        (
        
          EQ
          ⁢
          
            
          
          ⁢
          3
        
        )
      
    
  




then base matrix of this matrix depicted above in (EQ 3) is shown as follows:




  
    
      
        
          H
          base
        
        =
        
          
            [
            
              
                
                  1
                
                
                  0
                
                
                  1
                
                
                  0
                
              
              
                
                  0
                
                
                  1
                
                
                  1
                
                
                  1
                
              
              
                
                  1
                
                
                  1
                
                
                  0
                
                
                  1
                
              
            
            ]
          
          .
        
      
    
    
      
        (
        
          EQ
          ⁢
          
            
          
          ⁢
          4
        
        )
      
    
  




The following relationships are employed below: N=nm and K=km. Some special sub-classes of irregular (n,k) LDPC codes have their low density parity check matrix, H, defined by H=[H1, H2] such that H1 is a (n−k)×k matrix and H2 is a (n−k)×(n−k) matrix. Each of these matrices, H1 and H2, is composed of special sub-matrices as described below. Again, the block size of the LDPC code is N, where N=nm, and K is the dimension of the LDPC code, where K=km.
There are at least 4 such classes, listed as follows with respect to their H2 matrix component:
Class 1:




  
    
      
        
          H
          2
        
        =
        
          [
          
            
              
                I
              
              
                0
              
              
                ⋯
              
              
                0
              
              
                0
              
            
            
              
                I
              
              
                I
              
              
                
                  
                
              
              
                0
              
              
                0
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋰
              
              
                ⋮
              
              
                ⋮
              
            
            
              
                0
              
              
                0
              
              
                
                  
                
              
              
                I
              
              
                0
              
            
            
              
                0
              
              
                0
              
              
                ⋯
              
              
                I
              
              
                I
              
            
          
          ]
        
      
    
    
      
        
      
    
  




where I is an m×m identity matrix and 0 is an m×m zero-matrix (i.e., all entries are value 0).
Class 2:




  
    H
    2
  
  =
  
    [
    
      
        
          I
        
        
          0
        
        
          ⋯
        
        
          0
        
        
          
            I
            ⁡
            
              (
              
                -
                1
              
              )
            
          
        
      
      
        
          I
        
        
          I
        
        
          
            
          
        
        
          0
        
        
          0
        
      
      
        
          ⋮
        
        
          ⋮
        
        
          ⋰
        
        
          ⋮
        
        
          ⋮
        
      
      
        
          0
        
        
          0
        
        
          
            
          
        
        
          I
        
        
          0
        
      
      
        
          0
        
        
          0
        
        
          ⋯
        
        
          I
        
        
          I
        
      
    
    ]
  




where I(−1) is an m×m matrix obtained by left cyclic shifting one position of the identity matrix, I.
Class 3:




  
    H
    2
  
  =
  
    [
    
      
        
          I
        
        
          0
        
        
          ⋯
        
        
          0
        
        
          D
        
      
      
        
          I
        
        
          I
        
        
          
            
          
        
        
          0
        
        
          0
        
      
      
        
          ⋮
        
        
          ⋮
        
        
          ⋰
        
        
          ⋮
        
        
          ⋮
        
      
      
        
          0
        
        
          0
        
        
          
            
          
        
        
          I
        
        
          0
        
      
      
        
          0
        
        
          0
        
        
          ⋯
        
        
          I
        
        
          I
        
      
    
    ]
  




where D is obtained by replacing the first row of I(−1) by an all zero-valued vector, i.e.,




  D
  =
  
    [
    
      
        
          0
        
        
          0
        
        
          ⋯
        
        
          0
        
      
      
        
          1
        
        
          0
        
        
          
            
          
        
        
          0
        
      
      
        
          
            
          
        
        
          1
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          ⋰
        
        
          
            
          
        
      
      
        
          0
        
        
          0
        
        
          ⋯
        
        
          1
        
      
    
    ]
  




Class 4:
H2=└H2,0, H2,1┘ where H2,0 is a [(n−k)m]×[(n−k−1)m] matrix and H2,1 is a [(n−k)m]×m matrix such that




  
    
      H
      
        2
        ,
        0
      
    
    =
    
      [
      
        
          
            I
          
          
            0
          
          
            ⋯
          
          
            0
          
          
            0
          
        
        
          
            I
          
          
            I
          
          
            
              
            
          
          
            0
          
          
            0
          
        
        
          
            ⋮
          
          
            ⋮
          
          
            ⋰
          
          
            ⋮
          
          
            ⋮
          
        
        
          
            0
          
          
            0
          
          
            
              
            
          
          
            I
          
          
            0
          
        
        
          
            0
          
          
            0
          
          
            ⋯
          
          
            I
          
          
            I
          
        
      
      ]
    
  
  ,
  and




and

H2,1=[I(t) 0 . . . 0 I 0 . . . 0 I(t)]T, where “T” indicates transpose.
where I(t) is an m×m matrix obtained by right cyclic shifting m positions of the identity matrix, I.
One prior art approach to shortening and puncturing is referred to as the “text book” approach (sometimes referred to in the various diagrams as TBSP). This “text book” approach involves shortening of s bits being performed by shortening the first (or last) s consecutive information bits. This “text book” approach involves puncturing of p bits being performed puncturing the last p consecutive redundancy bits.
In the [b] reference and the [c] reference depicted above, contributors from Motorola and Samsung suggest 2 other possible shortening methods, namely, “evenly distribute s zeros to information bit position” and “cycle through the block columns”, i.e., └s/k┘ zeros in every information block columns (i.e., every column j, Si,j for all i=0, . . . ,l (EQ 1)), the remainder in the first s−k └s/k┘ information block columns, where k is the base matrix information size.
In the [c] reference and the [d] reference depicted above, the “text book” puncturing method (i.e., puncturing the last consecutive bits) is suggested. In [c], another approach is discussed which involves puncturing the alternate parity bits, and it is shown that the “text book” approach outperforms the alternate parity bits approach.
A novel approach to performing shortening and puncturing is presented below.
An low density parity check matrix, H, of an (n,k) LDPC code is composed of m×m sub-matrices, Si,j.




  
    
      
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The shortened and punctured code is obtained from this original LDPC code. A codeword from the original LDPC code is depicted below.

C=(c0,c1, . . . ,cn−1)  (EQ 6)

Each element of the codeword is depicted below.

ci=(ci,0,ci,1, . . . ,ci,m−1)  (EQ 7)

FIG. 3 illustrates an embodiment of a method 300 for shortening and puncturing. Before the method 300 is described in greater detail, some definitions are also provided. Suppose a designer wishes to perform shortening of s positions and puncturing of p positions. Then, the following denotations can be employed Bs=└s/m┘ (where “└ ┘ ” denotes the floor or rounded down integer value of the ratio calculated therein), Bp=└p/m┘, Rs=s−mBs, and Rp=s−mBp.
The method 300 begins by first carefully selecting an information position, a, among 0, 1, . . . , k−1, where a=Bs+┌Rs/m┐ (where “┌ ┐” denotes the ceiling or rounded up integer value of the ratio calculated therein) and the selected information positions columns in the base matrix as shown in a block 310 can be depicted as below.

i1, . . . , iaε{0, . . . ,k−1}  (EQ 8)

Then, the method 300 continues by selecting a redundancy position, b, among k, . . . ,n−1, where b=Bp+|Rp/m | and the selected redundancy columns in the base matrix as shown in a block 320 can be depicted as below.

j1, . . . ,jbε{0, . . . ,k−1}  (EQ 9)

One possible approach to determine which are the best or optimal a=Bs+┌Rs/m┐ information columns to select, and which are the best or optimal b=Bp+|Rp/m| redundancy columns to select, to select is to perform searching through all of the possible combinations thereof to determine which provides for the best performance, as shown using reference numeral 305.
For example, this could be performed by going “brute force” through all of the possible combinations, performing simulations on the various combinations, and selecting the best option there from.
The method 300 then continues by shortening all entries ci1, ci2, . . . , ciBs (shown as i in FIG. 3) from the original LDPC codeword, C, in (EQ 6), and shortening Rs consecutive positions in the cia component of the original LDPC codeword, C, if
Rs≠0, as shown in a block 330. More specifically, the shortening of the elements, (cia,0,cia,1, . . . ,cia,Rs−1), is performed with respect to the original LDPC codeword, C, and this can be denoted as below.

c′ia=(cia,Rs,cia,Rs+1, . . . , cia,m−1)  (EQ 10)

In addition, the method 300 then continues by puncturing all entries cj1, cj2, . . . , cjBp. (shown as CJ in FIG. 3) from the original LDPC codeword, C, in (EQ 6), and puncturing Rp consecutive positions in the cjb component of the original LDPC codeword, C, if Rp≠0, as shown in a block 340. More specifically, the puncturing of the elements, (cjb,0,cjb,1, . . . ,cjb,Rp−1), is performed with respect to the original LDPC codeword, C, and this can be denoted as below.

c′jb=(cjb,Rp,cjb,Rp+1, . . . ,cjb,m−1)  (EQ 11)

The following denotations can also be employed.

{u1,u2, . . . , uk−Bs}={0, . . . ,k−1}\{i1, . . . ,iBs}  (EQ 12)

with u1<u2< . . . <uk−Bs. When Rs≠0, then one of u1,u2, . . . ,uk−Bs is ia.
Furthermore, the following denotations can also be employed.

{v1,v2, . . . , vn−k−Bp}={k, . . . ,n−1}\{j1, . . . , jBp}  (EQ 13)

with v1<v2< . . . <vn−k−Bp. When Rp≠0, then one of v1,v2, . . . ,vn−k−Bp is ib.
Then the LDPC codeword of the new LDPC code, Cnew, (after undergoing the shortening and puncturing) can be depicted as below.

Cnew=(c′u1,c′u2, . . . ,c′uk=Bs,c′v1,c′v2, . . . ,c′vn−k−Bp)  (EQ 14)

such that c′r=cr if r≠ia when Rs≠0 and if r≠jb when Rp≠0.
In implementation within a communication device that is operable to perform encoding of information bits according to the original LDPC code (i.e., before undergoing any shortening and puncturing), then the very same encoder can at least one perform encoding of information bits according to the new LDPC code as described below.
Suppose the information bits of a codeword of the new LDPC code are depicted as below.

b=(b0, . . . ,bk−1)  (EQ 15)

Then let (c′u1, c′u2, . . . ,c′uk−Bs)=b and let the rest of the components in the LDPC codeword (i.e., (c′0,c′1, . . . ,c′k−1)) be 0 (i.e., zero), where c′i consists of m components. Then the encoder of the original LDPC code can be employed to encode (c′0,c′1,c′k−1).
The encoder then outputs the redundant bits as c′k, . . . ,c′n−1. From there, only the components (c′v1,c′v2, . . . ,c′vn−k−Bp) are taken to be the redundant bits for the new LDPC code. Therefore, the LDPC codeword of the new LDPC code, Cnew, (after undergoing the shortening and puncturing) can be depicted as below.

Cnew=(b,c′v1,c′v2, . . . ,c′vn−k−Bp)  (EQ 16)

It is noted also that a first shortening and puncturing and a second shortening and puncturing can be generated using the principles described herein, such that each of the first shortening and puncturing and the second shortening and puncturing can then employ the very same original low density parity check matrix, H, to generate a first LDPC coded signal and a second LDPC coded signal. Also, because of the unique nature of this novel approach to shortening and puncturing presented herein, the very same LDPC matrix can then be employed to decode two different signals that have been generated using the first shortening and puncturing and the second shortening and puncturing, respectively. For example, a communication device can encode information bits according to the first shortening and puncturing and the second shortening and puncturing to generate a first LDPC coded signal and a second LDPC signal. In addition, a communication device can employ the very same low density parity check matrix, H, to decode a third LDPC coded signal (that has been generated using the first shortening and puncturing) and a fourth LDPC coded signal (that has been generated using the second shortening and puncturing).
FIG. 4 illustrates an embodiment of an apparatus 400 that is operable to construct at least one parity check matrix corresponding to at least one LDPC code. The apparatus 400 includes a processing module 420, and a memory 410. The memory 410 is coupled to the processing module, and the memory 410 is operable to store operational instructions that enable the processing module 420 to perform a variety of functions. The processing module 420 (serviced by the memory 420) can be implemented as an apparatus capable to perform any of the functionality of any of the various modules and/or functional blocks described herein. For example, the processing module 420 (serviced by the memory 420) can be implemented as an apparatus capable to perform LDPC code construction and processing of an LDPC coded signal using any of the various embodiments described herein.
The processing module 420 can be implemented using a shared processing device, individual processing devices, or a plurality of processing devices. Such a processing device may be a microprocessor, micro-controller, digital signal processor, microcomputer, central processing unit, field programmable gate array, programmable logic device, state machine, logic circuitry, analog circuitry, digital circuitry, and/or any device that manipulates signals (analog and/or digital) based on operational instructions. The memory 410 may be a single memory device or a plurality of memory devices. Such a memory device may be a read-only memory, random access memory, volatile memory, non-volatile memory, static memory, dynamic memory, flash memory, and/or any device that stores digital information. Note that when the processing module 420 implements one or more of its functions via a state machine, analog circuitry, digital circuitry, and/or logic circuitry, the memory storing the corresponding operational instructions is embedded with the circuitry comprising the state machine, analog circuitry, digital circuitry, and/or logic circuitry.
If desired in some embodiments, the apparatus 400 can be any of a variety of communication devices 430, or any part or portion of any such communication device 430. Any such communication device that includes the apparatus 400 can be implemented within any of a variety of communication systems 440 as well.
If desired in some embodiments, the parity check matrix of the LDPC code can be provided from the apparatus 400 to the communication system 440 that is operable to employ and perform error correcting coding using that LDPC code. The parity check matrix of the LDPC code can also be provided from the apparatus 400 to any of a variety of communication devices 430 implemented within the communication system 440 as well. This way, a completely integrated means is provided by which the parity check matrix of the LDPC code can be constructed in hardware and provided to one or more the communication devices 430 implemented within a communication system 440 to employ that LDPC code. If desired, the apparatus 420 can be designed to generate multiple parity check matrices corresponding to multiple LDPC codes as well. In some embodiments, the apparatus 420 can selectively provide different information (corresponding to different LDPC codes) to different communication devices and/or communication systems. That way, different communication links between different communication devices can employ different error correcting coding. Clearly, the apparatus 420 can also provide the same information (corresponding to a singular LDPC code) to each of different communication devices and/or communication systems as well without departing from the scope and spirit of the invention.
FIG. 5 illustrates an embodiment of a communication device 500 employing common functional block and/or circuitry for encoding and decoding, respectively, of multiple LDPC coded signals. Using the novel approach to shortening and puncturing presented herein, the various LDPC codes constructed thereby have a common structure and can thereby be processed (e.g., encoding or decoding processing) using a common functional block and/or circuitry portion.
Looking at the communication device 510, the communication device 510 includes an LDPC encoder (implemented using a singular functional block and/or circuitry portion) 520 and an LDPC decoder (implemented using a singular functional block and/or circuitry portion) 530. The LDPC encoder 520 is operable to encode information bits according to the same low density parity check matrix, H, but according to a wide variety of shortening and puncturing approaches applied to the same low density parity check matrix, H. For example, the LDPC encoder is operable to perform encoding to generate a first LDPC coded signal (using first shortening and puncturing), as shown in a block 521; the LDPC encoder 520 is also operable to perform encoding to generate a second LDPC coded signal (using second shortening and puncturing), as shown in a block 522.
In addition, the LDPC decoder 530 is operable to decode at least two separate LDPC coded signals using the very same low density parity check matrix, H. The LDPC decoder 530 is operable to perform decoding of a first LDPC coded signal using a low density parity check matrix, H, as shown in a block 531; the LDPC decoder 532 is also operable to perform decoding of a second LDPC coded signal using the very same low density parity check matrix, H, as shown in a block 532.
Again, it is noted that, thanks to the novel shortening and puncturing approach presented herein, the LDPC encoder 520 is operable to employ a common/single functional block and/or circuitry portion capable to encode multiple LDPC coded signals that all can be generated according to the very same low density parity check matrix, H, but with different shortening and puncturing applied thereto, as shown using reference numeral 529.
Analogously, thanks to the novel shortening and puncturing approach presented herein, the LDPC decoder 530 is operable to employ a common/single functional block and/or circuitry portion capable to decode multiple LDPC coded signals that all have been generated according to the very same low density parity check matrix, H, but with different shortening and puncturing applied thereto, as shown using reference numeral 539. In addition, because of the novel shortening and puncturing approach presented herein, different shortening and puncturing can be employed to generate two different LDPC coded signals, yet each of the LDPC coded signals can still have the very same code rate. Clearly, more than two LDPC codes may be employed for each of the LDPC encoder 520 and the LDPC decoder 530, respectively, while still using a common/single functional block and/or circuitry portion.
In this disclosure, a performance diagram is described in the context of BLER (Block Error Rate) versus Eb/No (ratio of energy per bit Eb to the Spectral Noise Density No). BLER is oftentimes used in the context of wireless communications where if any one bit in a block is determined to be in error, then the entire block is determined to be in error. In some other communication system application, performance may be viewed in terms of BER (Bit Error Rate) vs. Eb/No. This term Eb/No is the measure of SNR (Signal to Noise Ratio) for a digital communication system. When looking at these performance curves, the BLER may be determined for any given Eb/No (or SNR) thereby providing a relatively concise representation of the performance of the coding approach.
FIG. 6 illustrates an embodiment 600 of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 1296.
EXAMPLE 3
Consider rate 1/2 block size 1944 LDPC code in the [a] reference depicted above, where the low density parity check matrix, H, is defined below.
The following table consists of a plurality of entries such that every entry represents a 81×81 sub-matrix, where an actual number in the entry location indicates the shift position that is used to construct the CSI sub-matrix (e.g., right cyclic shifting of the identity matrix by that number of positions), and an empty space indicates an all zero-valued (i.e., all elements are 0) 81×81 sub-matrix. The table is depicted using two paragraphs because of its width. The entire Table includes 12 rows and 24 columns. The first Table portion includes columns 1-12 and the second Table portion includes columns 13-24.












Rows 1-12, Columns 1-12


















57



50

11

50

79



3

28

0



55
7


30



24
37


56
14


62
53


53


3
35


40


20
66


22
28


0



8

42

50


8


69
79
79



56

52


65



38
57


72

27


64



14
52


30

32



45

70
0



77
9


2
56

57
35





12


24

61

60


27
51


16







Rows 1-12, Columns 13-24


















1
0













0
0




0
0





0
0






0
0







0
0


0





0
0









0
0










0
0











0
0












0
0


1










0









As can be seen, there are 24 columns and 12 rows in the base matrix. Again, each sub-matrix is a 81×81 sub-matrix. The modification of this low density parity check matrix, H, can be performed by shortening 324 positions as well as puncturing 324 positions for 16 QAM (Quadrature Amplitude Modulation) when considering a Rayleigh fading communication channel (e.g., see Example 1).
Then, Bs=4, Rs=0, Bp=4, Rp=0. The information base columns are ordered from left to right by 0 to 11, and the redundancy base columns are ordered from left to right by 0 to 11 (for a total of 24 columns). Then, one possible optimal selection of shortening base columns is 5, 8, 9, 10, and one possible optimal selection of puncturing base columns is 1, 3, 7, 9.
With this novel shortening and puncturing selection (shown as NSP 630), a gain of 0.5 dB in terms of BLER (Block Error Rate) can be achieved when compared to the prior art “text book” shortening and puncturing (shown as TBSP 620) which is described and referenced above. This performance improvement is depicted in the diagram (FIG. 6).
FIG. 6 also provides additional information. There is only approximately a 0.175 dB loss when compared to the block size 1296 LDPC code in the [a] reference (shown as JP 1296 rate 1/2 610). It is noted that the block size 1296 LDPC code in the [a] reference has sub-matrices of a different size and also has a different structure. In addition, the puncturing positions that are selected are very important and largely determinative of the overall performance. If an improper or “not best” selection is made, a performance loss of more than 1 dB may undesirably be realized; this can be seen be considering reference numeral 640, which corresponds to performing the same shortening (S) as the novel shortening and puncturing approach, but with a modified puncturing.
The [a] reference, the [d] reference, and the [e] reference (all depicted above) suggest the shortening and puncturing (SP) ratio should not be less than 1.2. However, based on the novel approach to shortening and puncturing presented herein, it seems evident that this prior art prescribed SP ratio may not be correct at all. Furthermore, by requiring this limitation, an LDPC code designer is unduly prohibited from and restricted from choosing and designing certain LDPC codes.
FIG. 7 illustrates an embodiment 700 of a performance comparison of LDPC codes having different shortening and puncturing ratios. FIG. 7 shows that an LDPC code generated with the novel approach presented herein and with an SP ratio of 1 (shown by ratio 1.0, size 1296 NSP from 1/2 JP 1944 (324, 324) 740) actually outperforms an LDPC code having an SP ratio of 1.2 (shown by ratio 1.2, size 1296 TBSP from 1/2 JP 1944 (354, 294) 720), and that is generated using the prior art “text book” approach to shortening and puncturing presented above, by approximately 0.2 dB at a BLER=1e-3 (1×10−3). Both of the LDPC codes being compared have the same length.
The LDPC code generated with the novel approach presented herein and with an SP ratio of 1 (reference numeral 740) also provides a better performance than an LDPC code having an SP ratio of 1.4 (shown by ratio 1.4, size 1296 TBSP from 1/2 JP 1944 (378, 270) 730), and that is generated using the prior art “text book” approach to shortening and puncturing presented above, at a BLER below 1 e−3 (10−1). One of the very evident and important advantages of being able to employ a SP ratio of 1 is that it does not change the code rate. This flexibility and capability can be very desirable when designing a communication device to accommodate a variety of LDPC codes.
Another LDPC code which is compared is depicted as a shortening and puncturing ratio 1.2 LDPC code (shown by ratio 1.2, size 1296 TBSP from 1/2 JP 1944 (390, 324) 710). As can be seen, the LDPC code generated with the novel approach presented herein and with an SP ratio of 1 (reference numeral 740) also provides significantly better performance than this LDPC code at a BLER below 1 e−3 (1×10−3).
FIG. 8 illustrates an embodiment 800 of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 648 with code rates of 1/2.
EXAMPLE 4
Consider the rate 1/2 block size 1944 LDPC code in the [a] reference depicted above that is employed in Example 3. Consider shortening 648 positions as well as puncturing 648 positions for 16 QAM and Rayleigh fading channel, see Example 1 above.
Then Bs=8, Rs=0, Bp=8, Rp=0. The information base columns are ordered from left to right by 0 to 11, and the redundancy base columns are ordered from left to right by 0 to 11 (for a total of 24 columns). Then, one possible optimal selection of shortening base columns is 0, 1, 3, 5, 6, 8, 10, 11, and one possible optimal selection of puncturing base columns is 0, 2, 4, 5, 7, 8, 9, 10. The performance curve of the novel shortening and puncturing approach is depicted using NSP from 1944 820. With this shortening and puncturing selection, a 2 dB gain can be obtained at BLER=1e−3 (1×10−3) when compared to the “text book” using the SP ratio of 1.2 (shown by TBSP from 1944 830), and a 3 dB gain is achieved when compared to cyclic approach performed through the block columns as suggested in the [b] reference and the [c] reference (e.g., see FIG. 8) (shown by cyclic interleave S and TBP from 1944 840). FIG. 8 also shows there is only approximately a 0.38 dB loss when compared to the block size 648 LDPC code in the [a] reference (shown by JP 648 1/2 16 QAM 810). Again, it is noted that the block size 1296 LDPC code in the [a] reference has sub-matrices of a different size and also has a different structure. Therefore, when employing the LDPC codes corresponding to the performance curves of the reference numerals 830 and 840, there is an inherent requirement for different hardware (e.g., functional blocks and/or circuitries) to accommodate each of the different LDPC codes being processed within such a communication system and/or communication device.
FIG. 9 illustrates an embodiment 900 of a performance comparison of LDPC codes generated by shortening and puncturing from an LDPC code having block size 1944 to LDPC codes having block sizes 1296 with code rates of 5/6.
Example 5 Take the rate 5/6 block size 1944 LDPC code in the [a] reference that has a low density parity check matrix, H, as depicted in the following table.
The following table consists of a plurality of entries such that every entry represents a 81×81 sub-matrix, where an actual number in the entry location indicates the shift position that is used to construct the CSI sub-matrix (e.g., right cyclic shifting of the identity matrix, I, by that number of positions), and an empty space indicates an all zero-valued (i.e., all elements are 0) 81×81 sub-matrix. The table is depicted using two paragraphs because of its width. The entire Table includes 4 rows and 24 columns. The first Table portion includes columns 1-12 and the second Table portion includes columns 13-24.












Rows 1-4, Columns 1-12


















13
48
80
66
4
74
7
30
76
52
37
60


69
63
74
56
64
77
57
65
6
16
51


51
15
0
80
24
25
42
54
44
71
71
9


16
29
36
41
44
56
59
37
50
24

65







Rows 1-4, Columns 13-24



















49
63
31
74
73
23

1
0




64

68
9
48
62
54
27

0
0


67
35

58

29

53
0

0
0


4
65
52

4

73
52
1


0









As can be seen, there are 24 columns and 4 rows in the base matrix. Again, each sub-matrix is a 81×81 sub-matrix. The modification of this low density parity check matrix, H, can be performed by shortening 540 positions as well as puncturing 108 positions for 16 QAM when considering a Rayleigh fading communication channel. Then, Bs=6, Rs=54, Bp=1, Rp=27. The information base columns are ordered from left to right by 0 to 19, and the redundancy base columns are ordered from left to right by 0 to 3 (for 24 columns total).
Then, one possible optimal selection of shortening base columns is 0, 1, 2, 5, 6, 11, and 16. In the base column 16, only the first 54 bits are shortened, and one possible optimal selection of puncturing base columns is 0, 1. Also, in base column 1, only the first 27 bits are punctured. With this novel shortening and puncturing selection approach (shown using block size 1296 NSP, rate 5/6 940), a gain of 0.6 dB can be achieved at BLER=1e-3 (1×10−3) when compared to the “text book” (shown using block size 1296 TBSP, rate 5/6 920 and whose extrapolated value is depicted using reference numeral 921) (e.g., see FIG. 9). FIG. 9 also shows that there is only approximately a 0.15 dB loss when compared to the block size 1296 LDPC code in the [a] reference (shown using JP block size 1296, rate 5/6 910). Again, it is noted that the block size 1296 LDPC code in the [a] reference has sub-matrices of a different size and also has a different structure.
As can be seen, a novel approach to performing shortening and puncturing is presented herein that has many ancillary benefits including providing for significantly more flexibility in terms of implementing an actual communication device when compared to prior art approaches to shortening and puncturing. For example, the novel shortening and puncturing presented herein allows for construction of multiple LDPC codes all having a generally similar structure, thereby allowing for a communication device to have single functional block and/or circuitry portion that is capable to perform encoding (or decoding) processing according to all of the LDPC codes generated using this novel shortening and puncturing approach. This can provide for a significant reduction in hardware, complexity, real estate consumption, and overall cost of a communication device designed to accommodate processing of signals that comport with multiple LDPC coded signals. According to various aspects of the invention, each of the codes has a common structure (e.g., there is only one structure of the codes), and this can provide for many of the savings enumerated above.
In addition, the novel shortening and puncturing approach presented herein provides comparable performance (e.g., not much loss in terms of SNR as a function of a given BLER) than other prior art shortening and puncturing approaches. It is noted that these prior art shortening and puncturing approaches generate their multiple respective LDPC codes that have different structures, and therefore require the use of multiple functional blocks and/or circuitries in a communication device capable to process them all. Moreover, these prior art shortening and puncturing approaches have unnecessary design limitations (e.g., shortening and puncturing ratio of 1.2) that inherently limit the type of LDPC codes that can be employed within a communication system and/or communication device in which it is desirable to operate using multiple LDPC codes. The novel the novel shortening and puncturing approach presented herein allows for a shortening and puncturing ratio of 1.0, thereby allowing for greater design flexibility including the ability to maintain a common code rate for each of the LDPC codes generated thereby.
It is also noted that the methods described within the preceding figures may also be performed within any appropriate system and/or apparatus designs (e.g., communication systems, communication devices, communication transmitters, communication receivers, communication transceivers, and/or functionality described herein) without departing from the scope and spirit of the invention.
In view of the above detailed description of the invention and associated drawings, other modifications and variations will now become apparent. It should also be apparent that such other modifications and variations may be effected without departing from the spirit and scope of the invention.

## Claims

1. An apparatus, comprising:
a processing module; and
a memory, coupled to the processing module, that is operable to store operational instructions that enable the processing module to:
select first information positions among a plurality of information columns of an LDPC (Low Density Parity Check) matrix corresponding to an LDPC code;
select first redundancy positions among the plurality of information columns of the LDPC matrix;
shorten a first plurality of components of an LDPC codeword that corresponds to the LDPC code based on the first selected information positions;
puncture a second plurality of components of the LDPC codeword based on the first selected redundancy positions;
select second information positions among the plurality of information columns of the LDPC matrix;
select second redundancy positions among the plurality of information columns of the LDPC matrix;
shorten a third plurality of components of the LDPC codeword based on the second selected information positions;
puncture a fourth plurality of components of the LDPC codeword based on the second selected redundancy positions, wherein:
the first information positions and the first redundancy positions correspond to a first shortening and puncturing; and
the second information positions and the second redundancy positions correspond to a second shortening and puncturing;

encode first information bits using the LDPC matrix according to the first shortening and puncturing thereby generating a first LDPC coded signal; and
encode a second information bits using the LDPC matrix according to the second shortening and puncturing thereby generating a second LDPC coded signal; and wherein:

a number of columns within the first information position is a sum composed of a first term and a second term;
the first term is a floor of a ratio whose numerator is a number of shorten positions and whose denominator is a size of a sub-matrix within the LDPC matrix; and
the second term is a ceiling of a ratio whose numerator is a difference, generated by subtracting a product that is generated by multiplying the size of the sub-matrix and the first term from a number of shorten positions or a number of puncture positions, and whose denominator is the size of the sub-matrix.

2. The apparatus of claim 1, wherein:
the second information bits are the first information bits.

3. The apparatus of claim 1, wherein:
the apparatus is a communication device; and
the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.

4. The apparatus of claim 1, wherein:
the apparatus is a communication device; and
the communication device is a transceiver.

5. The apparatus of claim 1, wherein:
the apparatus is an encoder that is operable to employ a common circuitry portion to:
encode the first information bits using the LDPC matrix according to the first shortening and puncturing thereby generating the first LDPC coded signal; and
encode the second information bits using the LDPC matrix according to the second shortening and puncturing thereby generating the second LDPC coded signal.

6. The apparatus of claim 1, wherein:
the first LDPC coded signal has a code rate; and
the second LDPC coded signal has the code rate.

7. The apparatus of claim 1, wherein:
the apparatus is a decoder that is operable to:
receive a third LDPC coded signal that has been generated using the LDPC matrix according to the first shortening and puncturing;
receive a fourth LDPC coded signal that has been generated using the LDPC matrix according to the second shortening and puncturing;
employ the LDPC matrix to decode the third LDPC coded signal thereby making a best estimate of an information bit encoded therein; and
employ the LDPC matrix to decode the fourth LDPC coded signal thereby making a best estimate of an information bit encoded therein.

8. The apparatus of claim 7, wherein:
the third LDPC coded signal has a code rate; and
the fourth LDPC coded signal has the code rate.

9. The apparatus of claim 7, wherein:
the decoder is operable to employ a common circuitry portion to:
decode the third LDPC coded signal thereby making the best estimate of the information bit encoded therein; and
decode the fourth LDPC coded signal thereby making the best estimate of the information bit encoded therein.

10. An apparatus, comprising:
a circuitry portion that is operable to:
encode first information bits using an LDPC (Low Density Parity Check) matrix, that corresponds to an LDPC code, according to a first shortening and puncturing thereby generating a first LDPC coded signal; and
encode second information bits using the LDPC matrix according to a second shortening and puncturing thereby generating a second LDPC coded signal; and wherein:

the first shortening is performed on the first information bits thereby generating first shortened information bits that undergo LDPC encoding within the circuitry portion thereby generating first LDPC coded bits that undergo puncturing thereby generating the first LDPC coded signal; and
the second shortening is performed on the second information bits thereby generating second shortened information bits that undergo LDPC encoding within the circuitry portion thereby generating second LDPC coded bits that undergo puncturing thereby generating the second LDPC coded signal.

11. The apparatus of claim 10, wherein:
the second information bits are the first information bits.

12. The apparatus of claim 10, wherein:
the first LDPC coded signal has a code rate; and
the second LDPC coded signal has the code rate.

13. The apparatus of claim 10, wherein:
the apparatus is operable to:
select first information positions among a plurality of information columns of the LDPC matrix;
select first redundancy positions among the plurality of information columns of the LDPC matrix;
shorten a first plurality of components of an LDPC codeword that corresponds to the LDPC code based on the first selected information positions;
puncture a second plurality of components of the LDPC codeword based on the first selected redundancy positions;
select second information positions among the plurality of information columns of the LDPC matrix;
select second redundancy positions among the plurality of information columns of the LDPC matrix;
shorten a third plurality of components of the LDPC codeword based on the second selected information positions;
puncture a fourth plurality of components of the LDPC codeword based on the second selected redundancy positions, wherein:
the first information positions and the first redundancy positions correspond to the first shortening and puncturing; and
the second information positions and the second redundancy positions correspond to the second shortening and puncturing.

14. The apparatus of claim 10, further comprising:
at least one additional circuitry portion that is operable to:
employ the LDPC matrix to decode a third LDPC coded signal, that has been generated using the LDPC matrix according to the first shortening and puncturing, thereby making best estimates of the information bits encoded therein; and
employ the LDPC matrix to decode the fourth LDPC coded, that has been generated using the LDPC matrix according to the second shortening and puncturing, thereby making best estimates of the information bits encoded therein.

15. The apparatus of claim 14, wherein:
the third LDPC coded signal has a code rate; and
the fourth LDPC coded signal has the code rate.

16. A method, comprising:
selecting first information positions among a plurality of information columns of an LDPC (Low Density Parity Check) matrix corresponding to an LDPC code;
selecting first redundancy positions among the plurality of information columns of the LDPC matrix;
shortening a first plurality of components of an LDPC codeword that corresponds to the LDPC code based on the first selected information positions;
puncturing a second plurality of components of the LDPC codeword based on the first selected redundancy positions;
selecting second information positions among the plurality of information columns of the LDPC matrix;
selecting second redundancy positions among the plurality of information columns of the LDPC matrix;
shortening a third plurality of components of the LDPC codeword based on the second selected information positions;
puncturing a fourth plurality of components of the LDPC codeword based on the second selected redundancy positions, wherein:
the first information positions and the first redundancy positions correspond to a first shortening and puncturing; and
the second information positions and the second redundancy positions correspond to a second shortening and puncturing;

encoding first information bits using the LDPC matrix according to the first shortening and puncturing thereby generating a first LDPC coded signal; and
encoding second information bits using the LDPC matrix according to the second shortening and puncturing thereby generating a second LDPC coded signal; and wherein:
a number of columns within the first information position is a sum composed of a first term and a second term;
the first term is a floor of a ratio whose numerator is a number of shorten positions and whose denominator is a size of a sub-matrix within the LDPC matrix; and
the second term is a ceiling of a ratio whose numerator is a difference, generated by subtracting a product that is generated by multiplying the size of the sub-matrix and the first term from a number of shorten positions or a number of puncture positions, and whose denominator is the size of the sub-matrix.

17. The method of claim 16, wherein:
the second information bits are the first information bits.

18. The method of claim 16, wherein:
the first LDPC coded signal has a code rate; and
the second LDPC coded signal has the code rate.

19. The method of claim 16, further comprising:
receiving a third LDPC coded signal that has been generated using the LDPC matrix according to the first shortening and puncturing;
receiving a fourth LDPC coded signal that has been generated using the LDPC matrix according to the second shortening and puncturing;
employing the LDPC matrix to decode the third LDPC coded signal thereby making best estimates of the information bits encoded therein; and
employing the LDPC matrix to decode the fourth LDPC coded signal thereby making best estimates of the information bits encoded therein.

20. The method of claim 19, wherein:
the third LDPC coded signal has a code rate; and
the fourth LDPC coded signal has the code rate.