# Patent

## Title
Channel coding, modulating and mapping method for hybrid automatic repeat request of low density parity check code

## Abstract

The present invention discloses a method for channel coding and modulation mapping in HARQ of the LDPC code, comprising: performing structured LDPC encoding of an information bit sequence with a length of K input by a channel encoder, and sending a generated codeword to a HARQ buffer; rearranging codeword bits of a LDPC HARQ mother code in the HARQ buffer, and sequentially selecting codeword bits to generate a binary sequence of a HARQ packet; mapping codeword bits of the HARQ packet to a constellation, and high-significant bits in encoding blocks of the HARQ packet being mapped to high reliability bits in the constellation. The present invention provides the LDPC codeword with the maximal constellation gain, so that the LDPC HARQ channel encoding has the optimal performance.

## Background
CROSS REFERENCE RELATED APPLICATIONS
This application is a national phase of PCT/CN2008/000408 filed Feb. 28, 2008, which claims priority to China Application Serial No.200710126103.2, filed Jun. 12, 2007, both of which are entirely incorporated herein by reference.
TECHNICAL FIELD
The present invention relates to hybrid automatic repeat request (HARQ) of the low density parity check (LDPC) code, and more specifically, to a method for the channel encoding and modulation mapping therein.
BACKGROUND OF THE INVENTION
All digital communication systems need channel encoders, as shown in FIG. 1. The channel coder is used to resist various noises and interferences during a transmission process, by manually adding redundant information so that the system is capable of automatic error correction, and thereby reliability of digital transmission can be guaranteed. The low density parity check (LDPC) code is a type of linear block code that can be defined by a very sparse parity check matrix or bipartite graph, and since it is initially discovered by Gallager, it is referred to as Gallager code. Over decades of silence, with the development of computer hardware and relevant theories, MacKay and Neal rediscovered it and proved that it has a property of approximating to the Shannon limit. Latest research shows that the low density parity check code has characteristics of low decoding complexity, capability of linear-time encoding, having a property of approximating to the Shannon limit, capability of parallel decoding, and having a performance better than that of Turbo code in the case of a long code length.
The LDPC code is a linear block code based on a sparse check matrix, and utilizing the sparseness of its check matrix, low complexity encoding and decoding can be implemented, so that the LDPC code becomes practical. The Gallager code mentioned previously is a regular LDPCC, while Luby and Mitzenmacher et al extended the Gallager code and proposed an irregular LDPCC. The LDPC code has plenty of decoding algorithms, wherein, the Message Passing algorithm or the Belief Propagation algorithm (BP algorithm) is a mainstream and basic algorithm of the LDPC code, and so far a lot of improved effective decoding algorithms have emerged.
The graphical form of a LDPC parity check matrix is a bipartite graph. There is a one-to-one correspondence between the bipartite graph and the check matrix, and an M*N parity check matrix H defines a constraint that each codeword of N bits satisfies M parity check sets. A bipartite graph comprises N variable nodes and M parity check nodes. If the mth check relates to the nth bit, that is, for the element Hm at the mth row and nth column in H, n=1, there will be a line connecting the check node m and the variable node n. In a bipartite graph, there will be no connection between any nodes of the same type, and the total number of sides in the bipartite graph is equal to the number of non-zero elements in the check matrix.
A special type of LDPC code gradually becomes a mainstream application due to its structured characteristics. Supposing the parity check matrix H of this type of LDPC code is a (M×z)×(N×z) matrix consisting of M×N block matrices, each of which is a different power of a z×z basic permutation matrix, and if the basic permutation matrix is an identity matrix, the block matrices are all cyclic shift matrices of the identity matrix (right shift by default in this disclosure). It has a form as follows:
If the power hijb=−1, then Phijb=0. If hijb is an integer no less than 0, it is defined




  H
  =
  
    [
    
      
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
      
      
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
      
      
        
          0
        
        
          0
        
        
          1
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
      
      
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
      
      
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
      
      
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
        
          0
        
        
          1
        
        
          0
        
        
          1
        
        
          0
        
        
          0
        
      
    
    ]
  




Phijb=(P)hijb, herein P is a standard z×z permutation matrix shown as follows:




  P
  =
  
    [
    
      
        
          0
        
        
          1
        
        
          0
        
        
          ⋯
        
        
          0
        
      
      
        
          0
        
        
          0
        
        
          1
        
        
          ⋯
        
        
          0
        
      
      
        
          ⋯
        
        
          ⋯
        
        
          ⋯
        
        
          ⋯
        
        
          ⋯
        
      
      
        
          0
        
        
          0
        
        
          0
        
        
          ⋯
        
        
          1
        
      
      
        
          1
        
        
          0
        
        
          0
        
        
          ⋯
        
        
          0
        
      
    
    ]
  




With such a power hijb, each block matrix can be uniquely identified, and the power of the identity matrix can be represented by 0, and a zero matrix is generally represented by −1. As such, if each block matrix of H is replaced with its power, a mb×nb power matrix Hb can be acquired. Here, Hb is defined as the base matrix of H, and H is referred to as the expanded matrix of Hb. In practical encoding, z=code length/the number of columns nb of the base matrix is referred to as the expand factor.




  H
  =
  
    
      [
      
        
          
            
              P
              
                h
                00
                b
              
            
          
          
            
              P
              
                h
                01
                b
              
            
          
          
            
              P
              
                h
                02
                b
              
            
          
          
            ⋯
          
          
            
              P
              
                h
                
                  0
                  ⁢
                  
                    n
                    b
                  
                
                b
              
            
          
        
        
          
            
              P
              
                h
                10
                b
              
            
          
          
            
              P
              
                h
                11
                b
              
            
          
          
            
              P
              
                h
                12
                b
              
            
          
          
            ⋯
          
          
            
              P
              
                h
                
                  1
                  ⁢
                  
                    n
                    b
                  
                
                b
              
            
          
        
        
          
            ⋯
          
          
            ⋯
          
          
            ⋯
          
          
            ⋯
          
          
            ⋯
          
        
        
          
            
              P
              
                h
                
                  
                    m
                    b
                  
                  ⁢
                  0
                
                b
              
            
          
          
            
              P
              
                h
                
                  
                    m
                    b
                  
                  ⁢
                  1
                
                b
              
            
          
          
            
              P
              
                h
                
                  
                    m
                    b
                  
                  ⁢
                  2
                
                b
              
            
          
          
            ⋯
          
          
            
              P
              
                h
                
                  
                    m
                    b
                  
                  ⁢
                  
                    n
                    b
                  
                
                b
              
            
          
        
      
      ]
    
    =
    
      P
      
        H
        b
      
    
  




For example, the matrix H can be acquired by expanding a 2×4 base matrix Hb with the following parameter z:




  z
  =
  
    
      3
      ⁢
      
        
      
      ⁢
      and
      ⁢
      
        
      
      ⁢
      
        H
        b
      
    
    =
    
      [
      
        
          
            0
          
          
            1
          
          
            0
          
          
            
              -
              1
            
          
        
        
          
            2
          
          
            1
          
          
            2
          
          
            1
          
        
      
      ]
    
  




Therefore, it can also be said that the LDPC code encoder of the present invention is uniquely generated by a base matrix Hb, an expand factor z and a selected basic permutation matrix.
If a base matrix is utilized for each LDPC code with a different expand factor, then for each different code length, said LDPC code encoder needs to store a base matrix, and if there are plenty of code lengths, plenty of basic matrices have to be stored, which will bring problems of representation and storage. Therefore, if it is needed to implement a variable code length, LDPC codes with different code lengths within a certain range and the same code rate will use a uniform base matrix which we define as a uniform base matrix Hbuniform. If a code length is different, a parity check matrix H can be obtained by modifying and extending the Hbuniform, and as a result, the generated codec can apply to a variable code length.
The modification is a modification of the non-negative values in the base matrix Hb utilizing an expand factor with a different code length, and the value of the modified element should be less than the value of the expand factor with the code length. There are a lot of modification algorithms, for example, mod, scale+floor, scale+round or the like can be utilized. Supposing Pij is a non-negative element of 1 at the ith row and jth column of the base matrix Nb, Pij′ is a non-negative element of 1 at the ith row and jth column of the modified matrix Hbmodified, then:
With the mod method,




  
    P
    ij
    ′
  
  ≡
  
    
      P
      ij
    
    ⁢
    
      
    
    ⁢
    mod
    ⁢
    
      
    
    ⁢
    z
  
  ≡
  
    
      P
      ij
    
    ⁢
    
      
    
    ⁢
    mod
    ⁢
    
      
    
    ⁢
    
      N
      
        n
        b
      
    
  




With the scale+floor method,




  
    P
    ij
    ′
  
  =
  
    
      ⌊
      
        
          P
          ij
        
        ×
        
          z
          
            z
            max
          
        
      
      ⌋
    
    =
    
      ⌊
      
        
          P
          ij
        
        ×
        
          N
          
            N
            max
          
        
      
      ⌋
    
  




With the scale+round method:




  
    P
    ij
    ′
  
  =
  
    
      Round
      ⁢
      
        
      
      ⁢
      
        (
        
          
            P
            ij
          
          ×
          
            z
            
              z
              max
            
          
        
        )
      
    
    =
    
      Round
      ⁢
      
        
      
      ⁢
      
        (
        
          
            P
            ij
          
          ×
          
            N
            
              N
              max
            
          
        
        )
      
    
  




Wherein, z is the expand factor corresponding to the current code length, i.e. the number of rows or columns of the block matrix; zmax is the expand factor corresponding to the maximum code length supported. mod is a modulus operation, └ ┘ is a flooring operation and Round is a rounding operation.
In IEEE802.16e, the LDPC code supports code rates of 1⁄2, 2⁄3, 3⁄4 and 5⁄6, so there are four base matrices, and it becomes difficult to use a unique encoder/decoder to implement encoding and decoding with different code rates; if the four code rates need four codec, hardware cost will become an application bottleneck. But this type of LDPC code with a specific code rate and variable code length has a uniform base matrix, and only one encoder/decoder needs to be used. Wherein, the encoding method and encoder can be acquired with reference to a Chinese patent application of which the application number is 200710072808.0 and the patent name is “an apparatus and method for encoding the LDPC code supporting incremental redundancy HARQ”.
HARQ is an extremely important link adaptation technology in a wireless communication system.
The HARQ method will be briefly described below. The method comprises two parts: a transmission method of a transmitter and a reception method of a receiver, and the method should be universal.
The transmission method of the transmitter comprises:
a. The transmitter sends the first HARQ packet in a specified HARQ channel, a new HARQ transmission starts, and the retransmission counter is set to 1;
b. The transmitter waits for an ACK/NAK sent by the receiver;
c. After a certain delay (depending on whether it is synchronous mode or asynchronous mode, the delay is decided by the system), if the transmitter receives the ACK, then the packet is correctly received and this HARQ transmission ends; otherwise, the retransmission counter is added by 1, and whether the number of retransmissions exceeds the maximum number of retransmissions permitted is determined, if yes, then this HARQ transmission ends, otherwise, proceeds to d;
d. The transmitter tries another HARQ in the HARQ channel of this HARQ transmission, the sending time can be selected by the system, and returns to b.
The reception method of the receiver comprises:
a. Receive a HARQ packet, and determine whether the received packet is the first HARQ attempt, if yes, proceed to b; otherwise proceed to d;
b. Discard all the HARQ attempts previously received in this HARQ channel;
c. Decode the packet, and proceed to e;
d. The decoder of the receiver combines the originally error and retransmitted encoding packets according to a specific combination method;
e. If the decoding is correct, then after a certain delay, send the ACK in a feedback channel which is allocated by the system; otherwise, send the NAK and store the HARQ packet.
In the step d of the above reception method, the combination method may comprise full incremental redundancy, partial incremental redundancy and Chase combination.
How to support the HARQ based on the LDPC code supporting any code length and any code rate and make the LDPC HARQ channel encoding have the optimal performance is a problem to be researched and solved at present.
SUMMARY OF THE INVENTION
The technical problem to be solved by the present invention is to provide a method for channel encoding and modulation mapping in hybrid automatic repeat request of the low density parity check code, so as to provide the LDPC codeword with the maximal constellation gain, so that the LDPC HARQ channel encoding has the optimal performance.
In order to solve the above technical problem, the present invention provides a method for channel coding and modulation mapping in hybrid automatic repeat request of a low density parity check code, comprising the following steps of:
(a) performing structured low density parity check encoding of an information bit sequence with a length of K input by a channel encoder, and sending a generated codeword to a hybrid automatic repeat request buffer;
(b) rearranging codeword bits of a low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer, and sequentially selecting codeword bits to generate a binary sequence of a hybrid automatic repeat request packet;
(c) mapping codeword bits of the hybrid automatic repeat request packet to a constellation, and high-order bits in encoding blocks of the hybrid automatic repeat request packet being mapped to high reliability bits in the constellation.
Furthermore, said step (a) further divides into the following sub-steps of:
(a1) determining a mother code set of low density parity check codes, said mother code set consisting of a finite number of low density parity check codes with different code lengths and the same code rate R0, and said mother code set having a uniform base matrix Hbuniform with a size of mb×nb, and kb=nb−mb;
(a2) determining an expand factor zk according to a matching information group length, and determining parameters and a matrix required by an encoder according to the expand factor and the base matrix Hbuniform;
(a3) according to the parameters and matrix required for encoding, the encoder encoding the input K bit information group, and generating and outputting an NFIR bit codeword.
Furthermore, the uniform base matrix Hbuniform of the mother code set with the code rate R0=1⁄2 utilized in said step (a1) is as follows:




  
    H
    b
    uniform
  
  =
  
    
      
        605
      
      
        173
      
      
        110
      
      
        
          -
          1
        
      
      
        274
      
      
        
          -
          1
        
      
      
        8
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        108
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        194
      
      
        77
      
      
        265
      
      
        571
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        242
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        246
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
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          -
          1
        
      
      
        
          -
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          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        63
      
      
        0
      
      
        538
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        194
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        358
      
      
        
          -
          1
        
      
      
        
          -
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          1
        
      
      
        411
      
      
        
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        23
      
      
        271
      
      
        260
      
      
        166
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
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          1
        
      
      
        348
      
      
        
          -
          1
        
      
      
        
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        566
      
      
        
          -
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        238
      
      
        241
      
      
        574
      
      
        
          -
          1
        
      
      
        466
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
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        111
      
      
        
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          -
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          -
          1
        
      
      
        
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          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
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          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
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          -
          1
        
      
      
        
          -
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          -
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          -
          1
        
      
      
        
          -
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        601
      
      
        442
      
      
        474
      
      
        218
      
      
        
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          1
        
      
      
        
          -
          1
        
      
      
        321
      
      
        
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          1
        
      
      
        
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          1
        
      
      
        
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          -
          1
        
      
      
        446
      
      
        
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          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
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          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
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          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        56
      
      
        148
      
      
        618
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        363
      
      
        
          -
          1
        
      
      
        485
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        454
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        495
      
      
        178
      
      
        459
      
      
        270
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        112
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        193
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        611
      
      
        380
      
      
        170
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        241
      
      
        346
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        135
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        343
      
      
        255
      
      
        353
      
      
        405
      
      
        317
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        436
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        630
      
      
        42
      
      
        282
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        436
      
      
        
          -
          1
        
      
      
        552
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        96
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        194
      
      
        479
      
      
        621
      
      
        170
      
      
        
          -
          1
        
      
      
        567
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        12
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        352
      
      
        158
      
      
        73
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        471
      
      
        187
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        218
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        524
      
      
        595
      
      
        329
      
      
        185
      
      
        
          -
          1
        
      
      
        532
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        501
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        573
      
      
        48
      
      
        108
      
      
        
          -
          1
        
      
      
        452
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        195
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        536
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        0
      
    
    
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
    
      
        293
      
      
        5
      
      
        409
      
      
        9
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        285
      
      
        
          -
          1
        
      
      
        
          -
          552
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        
          -
          1
        
      
      
        0
      
    
  




Furthermore, if a code rate r to be utilized in the encoding is less than R0, said step (a2) divides into the following sub-steps of:
a2A1) utilizing




  
    Δ
    ⁢
    
      
    
    ⁢
    m
  
  =
  
    ⌈
    
      
        
          k
          b
        
        r
      
      -
      
        n
        b
      
    
    ⌉
  




to determine Δm, adding Δm rows and Δm columns respectively after the last row and last column of the base matrix Hbuniform to extend the base matrix Hbuniform into a (mb+Δm)×(nb+Δm) extended base matrix Hbuniform—extension, the extended base matrix consisting of a system bits part, that is, an information bits part, a punctured check bits part and an extended check bits part, and ┌ ┐ representing ceiling;

a2A2) utilizing an expand factor formula




  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




to determine an expand factor zt, supposing zt having a relationship of zk−1<zt≦zk with elements in an Zset, wherein zk−1, zk are two adjacent elements in values in the Zset, then the expand factor required by the encoder being zk;

a2A3) based on the extended uniform base matrix Hbuniform—extension and the expand factor zk, modifying the Hbuniform—extension according to a preset modification algorithm, and calculating a modified extension base matrix Hbmodified—extension with a size of (N=(nb+Δm)×zk,K=kb×zk) required for the low density parity check encoding, the modified extension base matrix being the matrix required for the encoding, and parameters of the expand factor and the matrix size being the parameters required for the encoding;
if the code rate r to be utilized in the encoding is no less than R0, the following sub-steps are performed in step (a2):
a2B1) utilizing an expand factor formula




  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




to determine an expand factor zt, supposing zt having a relationship of zk−1<zt≦zk with elements in an Zset, wherein zk−1, zk are two adjacent elements in values in the Zset, then the expand factor required by the encoder being zk;

a2B2) based on the uniform base matrix Hbuniform and the expand factor zk, calculating a modified base matrix with a matrix size of (mb×zk, nb×zk) required for the encoding according to a preset modification algorithm and the expand factor, the modified base matrix being the matrix required for the encoding, and parameters of the expand factor and the matrix size being the parameters required for the encoding;
Furthermore, a particular extension method in step a2A1) is as follows:
for a row index i=mb+1 in the newly-added matrix part in Hbuniform—extension, there are always:

Hbuniform—extension(i,i−mb)=0

Hbuniform—extension(i,i−mb+1)=0

Hbuniform—extension(i,i−mb+nb)=0

for any row index i satisfying mb+2≦i≦mb+Δm, there are:

Hbuniform—extension(i,i−mb+1)=0

Hbuniform—extension(i,i−mb+nb−1)=0

Hbuniform—extension(i,i−mb+nb)=0

other elements in the newly-added matrix part is −1.
Furthermore, step (a3) further divides into the following steps of:
a31) adding x=kb·zk−K zero bits before the K information bits to form a kb·zk information group required for the encoding; and then performing (N=(nb+Δm)×zk,K=kb×zk) low density parity check encoding to form (nb+Δm)×zk encoding codeword bits;
a32) from said encoding codeword, deleting the x zero bits added, and if the number of codeword bits after the deletion does not match the group size NFIR required, then continuing to delete y=(mb+Δm)×zk−NFIR+K bits from the codeword after deleting the zero bits, to form a encoding codeword with the length of NFIR.
Furthermore, in step a32), said NFIR has the following definition:




  
    N
    FIR
  
  =
  
    {
    
      
        
          
            N
            BUF
          
        
        
          
            
              N
              max
            
            ≥
            
              N
              BUF
            
          
        
      
      
        
          
            N
            max
          
        
        
          
            
              N
              max
            
            <
            
              N
              BUF
            
          
        
      
    
  




herein, Nmax=K+nb·┌K/kb┐; NBUF is the maximum value of received soft bit information that can be stored in a virtual buffer, and the value is determined by an upper-level signaling in each HARQ transmission.
Furthermore, the method further comprises:
when the codeword bits of the low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer is rearranged in step (b), rearranging the codeword bits of the low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer, while maintaining sequences of the information bits and extended check bits unchanged, and changing a sequence of the punctured check bits, that is, letting codeword bits before arrangement be A0, A1, . . . , ANFIR−1 and codeword bits after arrangement be B0, B1, . . . , BNFIR−1, then a formula for the arrangement being defined as:




  
    B
    k
  
  =
  
    {
    
      
        
          
            A
            k
          
        
        
          
            k
            <
            
              K
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              k
            
            ≥
            
              
                
                  n
                  b
                
                ·
                
                  z
                  k
                
              
              -
              x
            
          
        
      
      
        
          
            A
            
              
                
                  (
                  
                    k
                    +
                    x
                  
                  )
                
                ⁢
                mod
                ⁢
                
                  
                
                ⁢
                
                  z
                  k
                
              
              +
              
                
                  PV
                  ⁡
                  
                    (
                    
                      
                        ⌊
                        
                          
                            (
                            
                              k
                              +
                              x
                            
                            )
                          
                          /
                          
                            z
                            k
                          
                        
                        ⌋
                      
                      -
                      
                        k
                        b
                      
                    
                    )
                  
                
                ×
                
                  z
                  k
                
              
            
          
        
        
          
            k
            ⁢
            
              
            
            ⁢
            is
            ⁢
            
              
            
            ⁢
            any
            ⁢
            
              
            
            ⁢
            other
            ⁢
            
              
            
            ⁢
            value
          
        
      
    
  




wherein └ ┘ represents flooring, k=0,1, . . . , NFIR−1, PV is a punctured pattern vector comprising mb elements and consisting of integers from kb to nb−1, and PV(l) is an index of the punctured vector PV and has l elements;
by deforming the above formula, the arrangement formula having a equivalent form as follows:




  
    B
    k
  
  =
  
    {
    
      
        
          
            A
            k
          
        
        
          
            
              k
              <
              K
            
            ⁢
            
              
            
            ,
            
              
            
            ⁢
            
              
                or
                ⁢
                
                  
                
                ⁢
                k
              
              ≥
              
                K
                +
                
                  
                    m
                    b
                  
                  ×
                  z
                
              
            
          
        
      
      
        
          
            A
            
              
                
                  (
                  
                    k
                    -
                    K
                  
                  )
                
                ⁢
                mod
                ⁢
                
                  
                
                ⁢
                z
              
              +
              
                
                  PV
                  ⁡
                  
                    (
                    
                      
                        ⌊
                        
                          
                            (
                            
                              k
                              -
                              K
                            
                            )
                          
                          /
                          z
                        
                        ⌋
                      
                      -
                      
                        k
                        b
                      
                    
                    )
                  
                
                ×
                z
              
              +
              K
            
          
        
        
          else
        
      
    
  




Furthermore, the method further comprises:
when codeword bits are sequentially selected from the codeword of the rearranged hybrid automatic repeat request mother code in step (b), starting from a first system bit in a first transmission, a starting position of each transmission afterwards following an ending position of a previous transmission, so that a binary sequence of a hybrid automatic repeat request packet is generated, and a formula being:

Ck,i=B(Ltotal(k−1)+i)mod(NFIR)

Wherein k represents an index of hybrid automatic repeat request sub-packets, when hybrid automatic repeat request is applied, k=0 represents the first transmission, and the index of a sub-packet transmitted subsequently is incremented by one, and so forth, when hybrid automatic repeat request is not applied, k=0; Lk represents a length of a kth sub-packet,




  
    
      L
      total
    
    ⁡
    
      (
      k
      )
    
  
  =
  
    
      ∑
      
        j
        =
        0
      
      
        k
        -
        1
      
    
    ⁢
    
      
    
    ⁢
    
      L
      j
    
  




and Ltotal(−1) is supposed to be zero, Ck,0, Ck,1, . . . , Ck,Lk−1 are codeword bits of the kth sub-packet, and B0, B1, . . . , BNFIR−1 is the codeword of the hybrid automatic repeat request mother code.

Furthermore, the method further comprises:
when the codeword bits of the hybrid automatic repeat request packet are mapped to the constellation in step (c), firstly performing interleaving, and then performing mapping, and step (c) comprising the following steps of:
(c1) utilizing an interleaver to interleave the codeword bits of the hybrid automatic repeat request packet, reading in by rows and reading out by columns, and guaranteeing that the high-order bits in the encoding blocks of the hybrid automatic repeat request packet are mapped to high reliability bits in the constellation;
(c2) sequentially mapping said codeword bits to the constellation, and for binary phase shift keying, quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation, or 64 quadrature amplitude modulation, modulating a group of input bits bm−1, . . . , b0 into a complex symbol.
Furthermore, in said step (c1), an Ncpc×L row-column interleaver is utilized, and for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation, Ncpc is respectively 2, 6, 4 and 6; L=2Ncbps/Ncpc, wherein an interleaving length Ncbps is equal to a length Lk of a kth hybrid automatic repeat request packet, and the interleaving is represented by the following arrangement formula:
codeword bits before arrangement are C0, C1, . . . , CNcbps−1,
codeword bits after arrangement are D0, D1, . . . , DNcbps−1,
the formula is defined as:

Dk=C(Ncpc/2)·k mod L+└k/L┘ L=2Ncbps/Ncpc, k=0,1, . . . , Ncbps−1

in said step (c2), each m=log 2(M) bits of said codeword bits D0, D1, . . . , DNcbps−1 starting from zero form a group and are mapped to a modulation symbol, and M represents a modulation order.
Furthermore, step (c) comprises the following steps:
letting the encoded bit sequence before modulation be D0, D1, . . . , DNcbps−1, and a complex symbol sequence after modulation be S0, S1, . . . , SNsym−1, a kth symbol Sk corresponding to a binary sequence (bm−l,k, . . . , b0,k), and Sk comprising a real part SkI and an imaginary part SkQ,
modulation orders for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation being respectively 2, 3, 4 and 6, then the input binary data D0, D1, . . . , DNcbps−1 for modulation being mapped to the constellation according to the following formulas:
if the modulation is quadrature phase shift keying:

(b1,k,b0,k)=(D2k,D2k+1) k=0,1, . . . , Ncbps/2−1

if the modulation is 8 phase shift keying:

(b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/3,Dk+2·Ncbps/3) k=0,1, . . . Ncbps/3−1

if the modulation is 16 quadrature amplitude modulation:

(b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/4,Dk+Ncbps/2,Dk+3·Ncbps/4) k=0,1, . . . Ncbps/4−1

if the modulation is 64 quadrature amplitude modulation:

(b5,k,b4,k,b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/6,Dk+Ncbps/3,Dk+Ncbps/2,Dk+2·Ncbps/3,Dk+5·Ncbps/6). k=0,1, . . . , Ncbps/6−1

Another problem to be solved by the present invention is to provide a method for modulation mapping in hybrid automatic repeat request of the low density parity check code, which can provide the LDPC codeword acquired by structured LDPC encoding with the maximal constellation gain.
In order to solve the above technical problem, the present invention provides a method for modulation mapping in hybrid automatic repeat request of a low density parity check code, comprising:
(c1) utilizing an interleaver to interleave codeword bits in an hybrid automatic repeat request packet acquired through structured low density parity check encoding, reading in by rows and reading out by columns, and guaranteeing that high-order bits in encoding blocks of the hybrid automatic repeat request packet are mapped to high reliability bits in a constellation;
(c2) sequentially mapping said codeword bits to the constellation, and for binary phase shift keying, quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation, or 64 quadrature amplitude modulation, modulating a group of input bits bm−1, . . . , b0 into a complex symbol.
Furthermore, in said step (c1), an Ncpc×L row-column interleaver is utilized, and for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation, Ncpc is respectively 2, 6, 4 and 6;L=2Ncbps/Ncpc, wherein an interleaving length Ncbps is equal to a length Lk of a kth hybrid automatic repeat request packet, and the interleaving is represented by the following arrangement formula:
codeword bits before arrangement are C0, C1, . . . , CNcbps−1,
codeword bits after arrangement are D0, D1, . . . , DNcbps−1,
the formula is defined as:

Dk=C(Ncpc/2)·k mod L+└k/L┘ L=2Ncbps/Ncpc, k=0,1, . . . , Ncbps−1

in said step (c2), each m=log 2(M) bits of said codeword bits D0, D1, . . . , DNcbps−1 starting from zero form a group and are mapped to a modulation symbol, and M represents a modulation order.
In order to solve the above technical problem, the present invention also provides a method for modulation mapping in hybrid automatic repeat request of a low density parity check code, comprising:
letting a bit sequence encoded through structured low density parity check encoding before modulation be D0, D1, . . . , DNcbps−1, and a complex symbol sequence after modulation be S0, S1, . . . , SNsym−1, a kth symbol Sk corresponding to a binary sequence (bm−1,k, . . . , b0,k), and Sk comprising a real part SkI and an imaginary part SkQ,
modulation orders for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation being respectively 2, 3, 4 and 6, then the input binary data D0, D1, . . . , DNcbps−1 for modulation being mapped to a constellation according to the following formulas:
if the modulation is quadrature phase shift keying:

(b1,k,b0,k)=(D2k,D2k+1) k=0,1, . . . , Ncbps/2−1

if the modulation is 8 phase shift keying:

(b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/3,Dk+2·Ncbps/3) k=0,1, . . . Ncbps/3−1

if the modulation is 16 quadrature amplitude modulation:

(b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/4,Dk+Ncbps/2,Dk+3·Ncbps/4) k=0,1, . . . Ncbps/4−1

if the modulation is 64 quadrature amplitude modulation:

(b5,k,b4,k,b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/6,Dk+Ncbps/3,Dk+Ncbps/2,Dk+2·Ncbps/3,Dk+5·Ncbps/6). k=0,1, . . . , Ncbps/6−1

It can be seen that, the processing chain of the method for channel encoding and modulation mapping in the HARQ of the LDPC code proposed by the present invention comprises LDCP coding, codeword arrangement, bits selection, channel interleaving, and modulation mapping. According to the code structure of the LDPC code, the present invention also provides a new channel interleaver which makes the high-order bits of the encoding blocks of HARQ sub-packets be mapped to the high-order bits of a constellation, thus the high-order bit mapping of the encoding blocks of the HARQ sub-packets gets a more reliable protection, while the low-order bits of the encoding blocks get a protection of low reliability. Ultimately, the channel interleaver provides the LDPC codeword with the maximal constellation gain and guarantees that the LDPC HARQ channel encoding chain has the optimal performance.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of the system where the apparatus of the present invention resides;
FIG. 2 is a schematic diagram of the channel encoding processing chain of the HARQ based on the LDPC code in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of the extension base matrix proposed by the present invention;
FIG. 4 is a schematic diagram of the interleaving by the channel interleaver proposed by the present invention;
FIGS. 5(a), 5(b), 5(c) and 5(d) are respectively constellations of QPSK, 8PSK, 16QAM and 64QAM in accordance with an embodiment of the present invention.



PREFERRED EMBODIMENTS OF THE PRESENT INVENTION
The basic idea of the present invention is to support HARQ based the LDPC code supporting any code length and any code rate, and the codeword arrangement guarantees that the codeword generated by the bits selection has the optimal puncturing distribution, and the codeword selection can be implemented with a very simple cyclic buffer, and the channel interleaving and modulation mapping can incorporate the characteristics of the LDPC codeword to provide the codeword with maximal constellation gain.
The present invention will be described in further detail in conjunction with figures and particular embodiments.
The processing chain of the method for channel encoding and modulation mapping in the HARQ of the structured LDPC code supporting any code rate/code length in this embodiment comprises LDPC encoding, codeword arrangement, bits selection, channel interleaving, and modulation mapping. As shown in FIG. 2, said method specifically comprises the following steps:
1) LDPC encoding, which encodes an information bit sequence with an arbitrary length of K input by a channel encoder, then outputs a codeword bit sequence with an arbitrary length of NFIR, and sends the generated codeword to an HARQ buffer, wherein the length of check bits is M=NFIR−K, and the code rate is r=K/NFIR;
2) Codeword arrangement, which rearranges codeword bits of the LDPC HARQ mother code in the HARQ buffer, maintains the sequences of information bits and extended check bits unchanged, and changes the sequence of punctured check bits;
3) Bits selection, which sequentially selects codeword bits from the rearranged codeword of the HARQ mother code, that is, the first transmission starts from the first system bit, and the starting position of each transmission afterwards follows the ending position of the previous transmission, so that a binary sequence of an HARQ packet is generated;
4) Channel interleaving, in which a Ncpc×L row-column interleaver interleaves the codeword bits of the HARQ packet, reading in by rows and reading out by columns. This arrangement guarantees that the high-order bits of the encoding blocks of the HARQ packet are mapped to high reliability bits in a constellation;
5) Modulation mapping, which sequentially maps the above codeword bits to a constellation, and for BPSK, QPSK, 8PSK, 16QAM or 64QAM, a group of input bits bb−1, . . . , b0 are modulated into a complex symbol.
In the above channel encoding chain of the LDPC code, the step 1), i.e. the LDPC encoding step, can further divide into the following three sub-steps:
(1) Determine a mother code set of structured LDPC codes, said mother code set consists of a finite number of LDPC codes with different code lengths and the same code rate R0, and said mother code set has a uniform base matrix Hbuniform;
Said LDPC mother code set defines P (N=z×nb, K=z×kb) LDPC codes with different code lengths and the same code rate R0 (Herein, N represents the LDPC codeword length and K represents the length of the information group, and for a LDPC code, the number of its check bits is M, and the size of its parity check matrix H is M*N). Wherein, Zset is a set of expand factors, and the expand factor z can be any element in Zset which is a set consisting of P positive integers z1<z2< . . . <zk−1<zk< . . . <zP larger than zero, and P is an integer larger than 1, and the code rate R0 of the base matrix Hbuniform satisfies:




  
    R
    0
  
  =
  
    
      (
      
        
          n
          b
        
        -
        
          m
          b
        
      
      )
    
    
      n
      b
    
  




Wherein, nb is the total number of columns in the base matrix and it is a certain integer larger than 2; mb is the number of rows in the base matrix and also the number of columns in the check bits part of the base matrix, and it is a certain integer larger than 1; kb is the number of columns in the information bits (also referred to as system bits) part of the base matrix, and kb=nb−mb.
(12) Determine an expand factor according to a matching information group length, and determine the parameters and matrix required by the encoder according to the expand factor and the base matrix Hbuniform;
This step further divides into the following two cases:
A, if determining by comparison that the code rate r to be utilized in later encoding is less than R0, the following sub-steps are performed in calculating the parameters and matrix required for the encoding:
12A1) Utilize




  
    Δ
    ⁢
    
      
    
    ⁢
    m
  
  =
  
    ⌈
    
      
        
          k
          b
        
        r
      
      -
      
        n
        b
      
    
    ⌉
  




to determine Δm, and add Δm rows and Δm columns respectively after the last row and the last column of the base matrix Hbuniform to extend it into a (mb+Δm)×(nb+Δm) extension base matrix Hbuniform—extension; here ┌ ┐ represents ceiling;

The detailed extension method is as follows:
For a row index i=mb+1 in the newly-added matrix part in Hbuniform—extension, there are always:

Hbuniform—extension(i,i−mb)=0

Hbuniform—extension(i,i−mb+1)=0

Hbuniform—extension(i,i−mb+nb)=0

As shown in FIG. 3, three zero elements in the first row of the extension part in the extension base matrix are defined here, and the other elements are −1.
For any row index i satisfying mb+2≦i≦mb+Δm, there are:

Hbuniform—extension(i,i−mb+1)=0

Hbuniform—extension(i,i−mb+nb−1)=0

Hbuniform—extension(i,i−mb+nb)=0

As shown in FIG. 3, three zero elements in the second, third, fourth, . . . rows of the extension part in the extension base matrix are defined here, and the other elements are −1.
Herein, both the row index and the column index start from 1, and by columns, the extension base matrix can be divided into a system bits part, i.e. information bits part (the number of columns is kb), a punctured check bits part (the number of columns is mb), and an extended check bits part (the number of columns is Δm).
12A2) Utilize the expand factor formula




  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




to determine the expand factor zt, supposing zt has a relationship of zk−1<zt≦zk with elements in Zset, wherein zk−1,zk are adjacent elements in values in Zset, then the expand factor required by the encoder is zk;

12A3) Based on the extended uniform base matrix Hbuniform—extension and the expand factor z=zk, modify the Hbuniform—extension according to a preset modification algorithm, a modified extension base matrix Hbmodified—extension with a size of (N=(nb+Δm)×zk,K=kb×zk) required for the LDPC encoding can be calculated. Here, the modified extension base matrix is the matrix required for the encoding, and the expand factor and the matrix size are the parameters required for the encoding.
Said modification of the base matrix can utilize the Scale+floor modification formula, and the object of the modification is the element (hijb)uniform—extension representing the non-zero square in the Hbuniform—extension:




  
    
      (
      
        h
        ij
        b
      
      )
    
    modified_extension
  
  =
  
    ⌊
    
      
        
          (
          
            h
            ij
            b
          
          )
        
        uniform_extension
      
      ×
      
        z
        
          z
          max
        
      
    
    ⌋
  




Wherein: zmax is the maximum expand factor in Zset, e.g., it can be 640, and └ ┘ represents flooring.
B, if determining by comparison that the code rate r to be utilized in later encoding is no less than R0, the following sub-steps are performed in calculating the parameters and matrix required for the encoding:
12B1) Utilize the expand factor formula




  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




to determine the expand factor zt, supposing zt has a relationship of zk−1<zt≦zk with elements in Zset, wherein zk−1,zk are adjacent elements in values in Zset, then the expand factor required by the encoder is zk;

12B2) Based on the uniform base matrix Hbuniform and the expand factor zk, calculate a modified base matrix with a size of (mb×zk,nb×zk) required for the encoding according to a preset modification algorithm and the expand factor. The modified base matrix is the matrix required for the encoding, and the expand factor and the matrix size are the parameters required for the encoding.
Similarly, said modification of the base matrix can utilize the Scale+floor modification formula, and the object of the modification is the element (hijb)uniform representing the non-zero square in the Hbuniform, that is:




  
    
      (
      
        h
        ij
        b
      
      )
    
    modified
  
  =
  
    ⌊
    
      
        
          (
          
            h
            ij
            b
          
          )
        
        uniform
      
      ×
      
        z
        
          z
          max
        
      
    
    ⌋
  




Wherein: zmax is the maximum expand factor in Zset.
(13) According to the parameters and matrix required for the encoding, the encoder encodes the input K bit information group and generates and outputs a NFIR bit codeword.
This step can be implemented by the following sub-steps:
131) Add x=kb·zk−K zero bits before the K information bits to form a kb·zk information group required for the encoding; and then perform (N=(nb+Δm)×zk,K=kb×zk) LDPC encoding to form (nb+Δm)×zk encoding codeword bits;
132) In the above encoding codeword, delete the x zero bits added in step 131), and if the number of codeword bits after the deletion does not match the group size NFIR required, then continue to delete y=(mb+Δm)×zk−NFIR+K bits in the codeword after deleting the zero bits to form a encoding codeword with a length of NFIR.
In this embodiment, said NFIR has the following definition:




  
    N
    FIR
  
  =
  
    {
    
      
        
          
            N
            BUF
          
        
        
          
            
              N
              max
            
            ≥
            
              N
              BUF
            
          
        
      
      
        
          
            N
            max
          
        
        
          
            
              N
              max
            
            <
            
              N
              BUF
            
          
        
      
    
  




Here, Nmax=K+nb·┌K/kb┐; NBUF is the maximum value of received soft bit information that can be stored in a virtual buffer, and the value is determined by an upper-level signaling in each HARQ transmission. Therefore, NBUF represents the maximum number of encoding bits into which the K bits can be encoded in the case of full incremental redundancy.
In deleting the above y bits, this embodiment deletes y bits at the end of the codeword, but bits at the other positions may also be deleted, as long as the system performance is not affected.
Content of the above steps can also be acquired with reference to the Chinese patent application of which the application number is 200710072808.0 and the patent name is “an apparatus and method for encoding the LDPC code supporting incremental redundancy HARQ”.
In the above channel encoding chain of the LDPC code, in step (2), i.e., in the codeword arrangement step, it is required to rearrange codeword bits of the LDPC HARQ mother code in the HARQ buffer, maintain the sequences of information bits and extended check bits unchanged, and change the sequence of punctured check bits.
Let the codeword bits before the arrangement be A0, A1, . . . , ANFIR−1, and the codeword bits after the arrangement be B0, B1, . . . , BNFIR−1, then the arrangement formula is defined as follows:




  
    B
    k
  
  =
  
    {
    
      
        
          
            A
            k
          
        
        
          
            k
            <
            
              K
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              k
            
            ≥
            
              
                
                  n
                  b
                
                ·
                
                  z
                  k
                
              
              -
              x
            
          
        
      
      
        
          
            A
            
              
                
                  (
                  
                    k
                    +
                    x
                  
                  )
                
                ⁢
                mod
                ⁢
                
                  
                
                ⁢
                
                  z
                  k
                
              
              +
              
                
                  PV
                  ⁡
                  
                    (
                    
                      
                        ⌊
                        
                          
                            (
                            
                              k
                              +
                              x
                            
                            )
                          
                          /
                          
                            z
                            k
                          
                        
                        ⌋
                      
                      -
                      
                        k
                        b
                      
                    
                    )
                  
                
                ×
                
                  z
                  k
                
              
            
          
        
        
          
            k
            ⁢
            
              
            
            ⁢
            is
            ⁢
            
              
            
            ⁢
            any
            ⁢
            
              
            
            ⁢
            other
            ⁢
            
              
            
            ⁢
            value
          
        
      
    
  




Wherein, └ ┘ represents flooring, k=0,1, . . . , NFIR−1, and PV is a punctured pattern vector comprising mb elements and consisting of integers from kb to nb−1, and PV(l) is the index of the punctured vector PV and has l elements.
In the above channel encoding chain of the LDPC code, in the step 3), i.e., in the bits selection step, codeword bits are sequentially selected from the rearranged codeword of the HARQ mother code, that is, the first transmission starts from the first system bit, and the starting position of each transmission afterwards follows the ending position of the previous transmission, so that a binary sequence of an HARQ packet is generated;
The codeword bits selection rule can be a selection based on the following formula:

Ck,i=B(Ltotal(k−1)+i)mod(NFIR)

Wherein, k represents the index of HARQ sub-packets, and when HARQ is applied, k=0 represents the first transmission, and the index of the sub-packet transmitted subsequently is incremented by one, and so forth. When HARQ is not applied, k=0. Lk represents the length of the kth sub-packet,




  
    
      L
      total
    
    ⁡
    
      (
      k
      )
    
  
  =
  
    
      ∑
      
        j
        =
        0
      
      
        k
        -
        1
      
    
    ⁢
    
      
    
    ⁢
    
      L
      j
    
  




and Ltotal(−1) is supposed to be zero. Ck,0, Ck,1, . . . , Ck,Lk−1 are the codeword bits of the kth sub-packet, and B0, B1, . . . , BNFIR−1 is the codeword of the HARQ mother code.

In the above channel encoding chain of the LDPC code, in the step 4), i.e., in the channel interleaving step, an Ncpc×L interleaver is utilized to interleave the codeword bits of the HARQ packet, reading in by rows and reading out by columns.
Here, for modulation modes of QPSK, 8PSK, 16QAM and 64QAM, Ncpc is respectively 2, 6, 4 and 6, and L=2Ncbps/Ncpc, wherein the interleaving length Ncbps is equal to the length of the kth HARQ packet Lk (i.e. the number of codeword bits). Here, for I or Q mapping codeword bits, high-order bits have higher reliability. For 8PSK as shown in FIG. 5, b2b1 has comparatively high reliability, while b0 has comparatively low reliability, and for 16QAM and 64QAM, b3b1, b5b3b1 have comparatively high reliability, whereas b2b0 and b4b2b0 have comparatively low reliability. This interleaving can be defined with the following one step arrangement formula,
Define Ncpc for QPSK, 8PSK, 16QAM and 64QAM is respectively 2, 6, 4 and 6. An HARQ sub-packet comprises Ncbps codeword bits, and let:
The codeword bits before the arrangement be C0, C1, . . . , CNcbps−1,
and the codeword bits after the arrangement be D0, D1, . . . , DNcbps−1, then the formula is defined as follows:

Dk=C(Ncpc/2)·k mod L+└k/L┘ L=2Ncbps/Ncpc, k=0,1, . . . , Ncbps−1

The interleaving here is combined with the previously described structured LDPC encoding and has special functions and implements a technology of bits priority selection, thereby it is guaranteed that the high-order bits of the encoding blocks of the HARQ packet (for a code block, the left is high order and the right is low order) are mapped to high reliability bits in a constellation.
In the above channel encoding chain of the LDPC code, in the step 5), i.e., in the modulation mapping step, the above interleaved and arranged codeword bits are sequentially mapped to a constellation, and for BPSK, QPSK, 8PSK, 16QAM or 64QAM, a group of input bits bm−b, . . . , b0 are modulated into a complex symbol. That is, each m=log 2(M) bits of the above codeword bits D0, D1, . . . , DNcbps−1 starting from zero form a group and are mapped to a modulation symbol. Herein, M represents a modulation order.
In another embodiment, the above step 4) and 5) can be replaced by the following step (which are not steps specially for interleaving)
4′) Let the encoded bit sequence before modulation (which is the binary sequence of the generated HARQ packet after the bits selection) be D0, D1, . . . , DNcbps−1, and the complex symbol sequence after modulation be S0, S1, . . . , SNsym−1, wherein the kth symbol Sk corresponds to a binary sequence (bm−1,k, . . . , b0,k), and Sk comprises a real part Skl and an imaginary part SkQ.
The modulation orders for QPSK, 8PSK, 16QAM and 64QAM are respectively 2, 3, 4 and 6. Then the input binary data D0, D1, . . . , DNcbps−1 for modulation is mapped to the constellation according to the following formulas:
If the modulation mode is QPSK:

(b1,k,b0,k)=(D2k,D2k+1) k=0,1, . . . , Ncbps/2−1

If the modulation mode is 8PSK:

(b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/3,Dk+2·Ncbps/3) k=0,1, . . . Ncbps/3−1

If the modulation mode is 16QAM:

(b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/4,Dk+Ncbps/2,Dk+3·Ncbps/4) k=0,1, . . . Ncbps/4−1

If the modulation mode is 64QAM:

(b5,k,b4,k,b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/6,Dk+Ncbps/3,Dk+Ncbps/2,Dk+2·Ncbps/3,Dk+5·Ncbps/6). k=0,1, . . . , Ncbps/6−1

This can achieve the same effect as that of the above steps 4) and 5), that is, it guarantees that the high-order bits of the encoding blocks of the HARQ packet are mapped to high reliability bits of the constellation.
A practical example is used below to further illustrate the technology of the present invention, but the present invention is not limited to this example.
Step 1: firstly, modify a mother code set of LDPC codes and acquire a modified base matrix.
For a mother code set of structured LDPC codes with a specific code rate R0=1⁄2 and multiple code lengths, the size of the uniform base matrix of the mother code set is mb×nb=16×32, and the expand factor of the code set increases from zmin=18 to zmax=640 with a step of 1, denoted by z∈Zset={zmin1:zmax}. Since a specific code length NFIR corresponds to a specific expand factor z, the length of the information group increases from zmin×kb to zmax×nb with a step of kb, denoted by K∈{zmin×kb:kb:zmax×kb}={288:16:10240}.
An illustration of the uniform base matrix Hbuniform of the mother code set with the code rate R0=1⁄2 is as follows:




  
    H
    b
    uniform
  
  =
  
     
    
      
        
          605
        
        
          173
        
        
          110
        
        
          
            -
            1
          
        
        
          274
        
        
          
            -
            1
          
        
        
          8
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          108
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          194
        
        
          77
        
        
          265
        
        
          571
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          242
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          246
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          63
        
        
          0
        
        
          538
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            194
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          411
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          23
        
        
          271
        
        
          260
        
        
          166
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          348
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          566
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          238
        
        
          241
        
        
          574
        
        
          
            -
            1
          
        
        
          466
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          111
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          575
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          601
        
        
          442
        
        
          474
        
        
          218
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          321
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          446
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          56
        
        
          148
        
        
          618
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          363
        
        
          
            -
            1
          
        
        
          485
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          454
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          495
        
        
          178
        
        
          459
        
        
          270
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          112
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          193
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          611
        
        
          380
        
        
          170
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          241
        
        
          346
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          135
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          343
        
        
          255
        
        
          353
        
        
          405
        
        
          317
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          436
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          630
        
        
          42
        
        
          282
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          436
        
        
          
            -
            1
          
        
        
          552
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          96
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          194
        
        
          479
        
        
          621
        
        
          170
        
        
          
            -
            1
          
        
        
          567
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          12
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          352
        
        
          158
        
        
          73
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          471
        
        
          187
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          218
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          524
        
        
          595
        
        
          329
        
        
          185
        
        
          
            -
            1
          
        
        
          532
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          501
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
        
          
            -
            1
          
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          573
        
        
          48
        
        
          108
        
        
          
            -
            1
          
        
        
          452
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          195
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          536
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          0
        
      
      
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
        
          
            
          
        
      
      
        
          293
        
        
          5
        
        
          409
        
        
          9
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          285
        
        
          
            -
            1
          
        
        
          552
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          0
        
      
    
  




However, the definition of Hbuniform is not limited to this matrix, and can be another matrix.
In order to implement the encoding and decoding of the (z×nb,z×kb) LDPC code, it is required to modify the uniform base matrix Hbuniform with some modification operation as described previously and the expand factor z, to acquire the modified base matrix Hbmodified, and based on the Hbmodified and z, the parity check matrix can be acquired. This example utilizes the Scale+floor modification formula to modify the uniform base matrix, and the object of the modification is the element (hijb)uniform representing the non-zero square of the Hbuniform, herein zmax=640:




  
    
      (
      
        h
        ij
        b
      
      )
    
    modified
  
  =
  
    
      ⌊
      
        
          
            (
            
              h
              ij
              b
            
            )
          
          uniform
        
        ×
        
          z
          
            z
            max
          
        
      
      ⌋
    
    =
    
      ⌊
      
        
          
            (
            
              h
              ij
              b
            
            )
          
          uniform
        
        ×
        
          z
          640
        
      
      ⌋
    
  




In a case in which the code rate r<R0, based on the mother code set provided in the embodiment, that is,




  
    
      R
      0
    
    =
    
      
        K
        
          N
          FIR
        
      
      =
      
        1
        /
        2
      
    
  
  ,




the encoding method with the LDPC code supporting any length/code rate provided in the present invention is described in detail as follows:

The code rate




  
    r
    =
    
      
        
          K
          
            N
            FIR
          
        
        <
        
          R
          0
        
      
      =
      
        1
        2
      
    
  
  ,




the length of the information group before encoding is K, the codeword length after encoding is NFIR, z is the expand factor of the structured LDPC code, and the number of check bits required is M=NFIR−K.

According to the above encoding method with the LDPC code supporting any code rate/code length, the encoding of the (NFIR,K) LDPC code is implemented, and it comprises the following steps:
Step A1, code rate matching: calculate




  
    
      Δ
      ⁢
      
        
      
      ⁢
      m
    
    =
    
      
        ⌈
        
          
            
              k
              b
            
            r
          
          -
          
            n
            b
          
        
        ⌉
      
      =
      
        ⌈
        
          
            16
            r
          
          -
          32
        
        ⌉
      
    
  
  ,




and add Δm rows and Δm columns respectively after the last row and the last column of Hbuniform to extend it into a base matrix Hbuniform—extension with a size of (mb+Δm)×(nb+Δm)=(16+Δm)×(32+Δm) ; herein ┌ ┐ represents ceiling.

Step A2, code length matching: calculate the expand factor




  
    
      z
      t
    
    =
    
      
        K
        
          k
          b
        
      
      =
      
        K
        16
      
    
  
  ,




supposing zt has a relationship of zk−1<zt≦zk with elements in Zset, wherein zk−1,zk are the two adjacent elements in values in Zset; zk is the expand factor that we ultimately require; based on the extended uniform base matrix Hbuniform—extension and the calculated expand factor zk, the LDPC mother code of (N=(nb+Δm)×zk,K=kb×zk)=((32+Δm)×zk,16×zk) can be acquired.

Step A3, curtailing the encoding: add x=(kb·zk−K)=(16·zk−K) zero bits before the K information bits to construct a 16×zk information group required for encoding; and then perform (N=(nb+Δm)×zk,K=kb×zk)=((32+Δm)×zk16×zk) LDPC encoding to acquire a (nb+Δm)×zk=(32+Δm)×zk bit codeword;
Step A4, symbol deletion: delete the x zero bits added in step B3 from the encoded codeword of the mother code, and if the number of codeword bits after the deletion does not match the group size NFIR required, then delete the last (or other positions) y bits of the codeword after deleting the zero bits, i.e., the y=(mb+Δm)×zk−NFIR+K=(16+Δm)×zk−NFIR+K bits, to finally acquire a codeword with a length of NFIR, wherein the determination of NFIR is as described previously and will not be repeated here.
In another case in which the code rate r≧R0, based on the mother code set provided in the embodiment, that is,




  
    
      (
      
        r
        =
        
          K
          
            N
            FIR
          
        
      
      )
    
    ≥
    
      (
      
        
          R
          0
        
        =
        
          1
          2
        
      
      )
    
  
  ,




the encoding method with the LDPC code supporting any length/code rate provided in the present invention is described in detail as follows:

The code rate




  
    
      (
      
        r
        =
        
          K
          
            N
            FIR
          
        
      
      )
    
    ≥
    
      (
      
        
          R
          0
        
        =
        
          1
          2
        
      
      )
    
  
  ,




the length of the information group before encoding is K, the codeword length after encoding is NFIR, zk is the expand factor of the structured LDPC code, and the number of check bits required is M=NFIR−K.

According to the above encoding method with the LDPC code supporting any code rate/code length, the encoding of the (NFIR,K) LDPC code is implemented, and it comprises the following steps:
Step C1, code rate matching: calculate the expand factor




  
    z
    =
    
      
        ⌈
        
          K
          
            k
            b
          
        
        ⌉
      
      =
      
        ⌈
        
          K
          16
        
        ⌉
      
    
  
  ,




and based on the uniform base matrix Hbuniform and the calculated expand factor z, acquire the LDPC mother code with a size of (nb×z,mb×z)=(32×z,16×z).

Step C2, curtailing the encoding: add x=(kb×z−K)=(16×z−K) zero bits before the K information bits to construct a kb×z=16×z bit information group required for encoding; and then perform the (N=nb×z=32×z,K=kb×z=16×z) LDPC encoding to acquire a nb×z=32×z bit codeword;
Step C3, symbol deletion: delete the x zero bits added in step C2 from the codeword of the mother code, and if the number of the codeword bits after the deletion is not equal to N, continue to delete the last (or other positions) y=mb×z−NFIR+K=16×z−NFIR+K bits of the codeword after deleting the zero bits, to acquire a codeword with a length of NFIR, wherein the determination of NFIR is as described previously and will not be repeated here.
Step 2, rearrange the codeword bits of the LDPC HARQ mother code in the HARQ buffer, maintain the sequences of the information bits and extended check bits unchanged, and change the sequence of the punctured check bits;
The arrangement of the LDPC HARQ codeword bits is: let the codeword bits before the arrangement be A0, A1, . . . , ANFIR−1, and the codeword bits after the arrangement be B0, B1, . . . , BNFIR−1, then the arrangement formula is defined as:




  
    B
    k
  
  =
  
    {
    
      
        
          
            A
            k
          
        
        
          
            k
            <
            
              K
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              k
            
            ≥
            
              
                
                  n
                  b
                
                ·
                z
              
              -
              x
            
          
        
      
      
        
          
            A
            
              
                
                  (
                  
                    k
                    +
                    x
                  
                  )
                
                ⁢
                mod
                ⁢
                
                  
                
                ⁢
                
                  z
                  k
                
              
              +
              
                
                  PV
                  ⁡
                  
                    (
                    
                      
                        ⌊
                        
                          
                            (
                            
                              k
                              +
                              x
                            
                            )
                          
                          /
                          
                            z
                            k
                          
                        
                        ⌋
                      
                      -
                      
                        k
                        b
                      
                    
                    )
                  
                
                ×
                
                  z
                  k
                
              
            
          
        
        
          
            k
            ⁢
            
              
            
            ⁢
            is
            ⁢
            
              
                
              
              ⁢
              
                
              
            
            ⁢
            any
            ⁢
            
              
                
              
              ⁢
              
                
              
            
            ⁢
            other
            ⁢
            
              
            
            ⁢
            value
          
        
      
    
  




Wherein, └ ┘ represents flooring, k=0,1, . . . , NFIR−1, PV is a punctured pattern vector comprising mb elements and consisting of integers from kb to nb−1, supposing:
PV=[17, 19, 21, 23, 25, 27, 29, 31, 18, 24, 22, 28, 30, 20, 26, 16], and PV(l) represents the index of the punctured vector PV and comprises l elements.
Step 3, sequentially select codeword bits from the rearranged codeword of the HARQ mother code, that is, the first transmission starts from the first system bit, and the starting position of each transmission afterwards follows the ending position of the previous transmission, so that a binary sequence of an HARQ packet is generated;
The codeword bits selection rule is a selection based on the following formula:

Ck,i=B(Ltotal(k−1)+i)mod(NFIR)

Wherein, k represents the index of HARQ sub-packets, and when HARQ is applied, k=0 represents the first transmission, and the index of the sub-packet transmitted subsequently is incremented by one, and so forth, when HARQ is not applied, k=0. Lk represents the length of the kth sub-packet,




  
    
      L
      total
    
    ⁡
    
      (
      k
      )
    
  
  =
  
    
      ∑
      
        j
        =
        0
      
      
        k
        -
        1
      
    
    ⁢
    
      L
      j
    
  




and suppose Ltotal(−1) is zero. Let Ck,0, Ck,1, . . . , Ck,Lk−1 be the codeword bits of the kth sub-packet, and B0, B1, . . . , BNFIR−1 be the codeword of the HARQ mother code.

Step 4, as shown in FIG. 4, a block interleaver is used to interleave the codeword bits of the HARQ packet, and the length of the interleaving Ncbps is equal to the length of the kth HARQ packet Lk. This interleaving can be defined by an arrangement formula. This arrangement guarantees that the high-order bits of the codeword are mapped to high reliability bits in a constellation, which will improve the performance of the punctured code. Here, for I or Q mapping codeword bits, the high-order bits have higher reliability. For 8PSK shown in FIG. 5, b2b1 has comparatively high reliability, while b0 has comparatively low reliability, and for 16QAM and 64QAM, b3b1, b5b3b1 have comparatively high reliability, whereas b2b0 and b4b2b0 have comparatively low reliability.
It is defined that for QPSK, 8PSK, 16QAM and 64QAM, Ncpc is respectively 2, 6, 4 and 6. An HARQ sub-packet comprises Ncbps codeword bits, and let the codeword bits before the arrangement be C0, C1, . . . , CNcbps−1 and the codeword bits after the arrangement be D0, D1, . . . , DNcbps−1, then the arrangement formula is defined as:

Dk=C(Ncpc/2)·k mod L+└k/L┘ L=2Ncbps/Ncpc, k=0,1, . . . , Ncbps−1

Step 5, sequentially map the above codeword bits to a constellation, and the constellations for QPSK, 8PSK, 16QAM and 64QAM are shown in FIG. 5.
For QPSK, m=log 2(4)=2, that is, each two bits of the codeword bits D0, D1, . . . , DNcbps−1 starting from index 0 form a group, such as [D0,D1], [D2,D3], . . . , [DNcbps−2DNcbps−1], and are respectively mapped to the constellation points b1b0.
For 8PSK, m=log 2(8)=3, that is, each three bits of the codeword bits D0, D1, . . . , DNcbps−1 starting from index 0 form a group, such as [D0,D1,D2], [D3,D4,D5], . . . , [DNcbps−3DNcbps−2DNcbps−1], and are respectively mapped to the constellation points b2b1b0.
For 16QAM, m=log 2(16)=4, that is, each four bits of the codeword bits D0, D1, . . . , DNcbps−1 starting from index 0 form a group, such as [D0,D1,D2,D3], [D4,D5,D6,D7], . . . , [DNcbps−4DNcbps−3DNcbps−2DNcbps−1], and are respectively mapped to the constellation points b3b2b1b0.
For 64QAM, m=log 2(64)=6, that is, each six bits of the codeword bits D0, D1, . . . , DNcbps−1 starting from index 0 form a group, such as [D0,D1,D2,D3,D4,D5], [D6,D7,D8,D9,D10,D11], . . . , [Dncbps−6DNcbps−5DNcbps−4DNcbps−3DNcbps−2DNcbps−1], and are respectively mapped to the constellation points b5b4b3b2b1b0.
To sum up, the present invention proposes a channel encoding processing chain of the HARQ of the LDPC code, and the chain comprises LDCP coding, codeword arrangement, bits selection, channel interleaving, and modulation mapping, as shown in FIG. 2. According to the code structure of the LDPC code, the present invention also provides a new channel interleaver which makes the high-order bits of the encoding blocks of HARQ sub-packets be mapped to the high-order bits of a constellation, thus the high-order bit mapping of the encoding blocks of the HARQ sub-packets gets a more reliable protection, while the low-order bits of the encoding blocks get a protection of low reliability. Finally, the channel interleaver provides the LDPC codeword with the maximal constellation gain and guarantees that the LDPC HARQ channel encoding chain has the optimal performance.
Here, the present invention has been described in detail with particular embodiments, the description of the above embodiments is provided for those skilled in the art to manufacture or use the present invention, and various modifications of these embodiments are easy to understand for those skilled in the art. The present invention is not limited to these embodiments or some aspects therein. The scope of the present invention will be illustrated in detail by the appended claims.
INDUSTRIAL APPLICABILITY
The present invention proposes a method for channel encoding and modulation mapping in the HARQ of the LDPC code, and the processing chain comprises LDCP coding, codeword arrangement, bits selection, channel interleaving, and modulation mapping. According to the code structure of the LDPC code, the present invention also provides a new channel interleaver which makes the high-order bits of the encoding blocks of HARQ sub-packets be mapped to the high-order bits of a constellation, thus the high-order bit mapping of the encoding blocks of the HARQ sub-packets gets a more reliable protection, while the low-order bits of the encoding blocks get a protection of low reliability. The channel interleaver provides the LDPC codeword with the maximal constellation gain and guarantees that the LDPC HARQ channel encoding chain has the optimal performance.

## Claims

1. A method for channel coding and modulation mapping for hybrid automatic repeat request of a low density parity check code, comprising the following steps of:
(a) performing structured low density parity check encoding of an information bit sequence of length K as the input of a channel encoder, and sending a generated codeword to a hybrid automatic repeat request buffer;
(b) rearranging the said codeword bits of a low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer, and sequentially selecting codeword bits to generate a binary sequence of a hybrid automatic repeat request packet;
(c) mapping the codeword bits of the hybrid automatic repeat request packet to a constellation, wherein the high significant bits in the encoding block of the hybrid automatic repeat request packet are mapped to high reliability bits in the constellation.

2. A method of claim 1, wherein said step (a) further divides into the following sub-steps of:
(a1) determining a mother code set of low density parity check codes, said mother code set consisting of a finite number of low density parity check codes with different code lengths and the same code rate, wherein the code rate is denoted as R0, and said mother code set has a uniform base matrix Hbuniform with a size of mb×nb, and the number of columns of an information bits part in the uniform base matrix is kb=nb−mb;
(a2) determining an expand factor zk according to a matching information group length, and determining parameters and a matrix required by an encoder according to the expand factor and the uniform base matrix Hbuniform;
(a3) according to the parameters and matrix required for encoding, the encoder encoding the input information block of K bits, and generating and outputting a codeword of NFIR bits.

3. A method of claim 2, wherein,
if a code rate r to be used in the encoding is less than R0, said step (a2) divides into the following sub-steps of:
a2A1) determining Δm through a formula





  
    Δ
    ⁢
    
      
    
    ⁢
    m
  
  =
  
    ⌈
    
      
        
          k
          b
        
        r
      
      -
      
        n
        b
      
    
    ⌉
  




adding Δm rows and Δm columns respectively after the last row and last column of the uniform base matrix Hbuniform to extend the base matrix Hbuniform into a (mb+Δm)×(nb+Δm) extension base matrix Hbuniform —extension, the extension base matrix consisting of a system bits part, that is, an information bits part, a punctured check bits part and an extended check bits part, wherein ┌ ┐ represents the ceiling operation;
a2A2) determining an expand factor zt through an expand factor formula





  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




if zt has a relationship of zk−1<zt≦zk with elements in an Zset, wherein Zset is a set of expand factors which are positive integers, and zk−1,zk are two adjacent elements in magnitude in the Zset, then the expand factor required by the encoder being zk;
a2A3) based on the extended uniform base matrix Hbuniform—extension and the expand factor zk, modifying the Hbuniform—extension according to a preset modification algorithm, thereby acquiring a modified extension base matrix Hbmodified—extension with a size of (N=(nb+Δm)×zk,K=kb×zk) required for the low density parity check encoding, wherein N is the codeword length of the low density parity check encoding, and K is the length of the information group, the modified extension base matrix is the matrix required for the encoding, and the expand factor and the matrix size are the parameters required for the encoding;
if the code rate r to be used in the encoding is no less than R0, the following sub-steps are performed in step (a2):
a2B1) determining an expand factor zt through a formula





  
    z
    t
  
  =
  
    K
    
      k
      b
    
  




if zt has a relationship of zk−1<zt≦zk with elements in an Zset, wherein Zset is a set of expand factors which are positive integers, and zk−1,zk are two adjacent elements in magnitude in the Zset, then the expand factor required by the encoder being zk;
a2B2) based on the uniform base matrix Hbuniform and the expand factor zk, calculating a modified base matrix with a matrix size of (mb×zk,nb×zk) required for the encoding according to a preset modification algorithm and the expand factor, the modified base matrix being the matrix required for the encoding, and the expand factor and the matrix size being the parameters required for the encoding;
step (a3) further divides into the following steps of:
a31) adding x=kb·zk−K zero bits before the K information bits to form an information group with the length of kb·zk required for the encoding; and then performing (N=(nb+Δm)×zk,K=kb×zk) low density parity check encoding to form (nb+Δm)×zk encoding codeword bits;
a32) from said encoding codeword, deleting the x zero bits added, and if the number of codeword bits after the deletion does not match the group size NFIR required, then continuing to delete y=(mb+Δm)×zk−NFIR+K bits from the codeword after deleting the zero bits, to form an encoding codeword with the length of NFIR.

4. A method of claim 1, further comprising:
when the codeword bits of the low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer is rearranged in step (b), rearranging the codeword bits of the low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer, while maintaining the sequences of information bits and extended check bits unchanged, and changing the sequence of punctured check bits, that is, if codeword bits before the arrangement are A0, A1, . . . , ANFIR−1 and codeword bits after the arrangement are B0, B1, . . . , BNFIR−1, then a formula for the arrangement is:





  
    B
    k
  
  =
  
    {
    
      
        
          
            A
            k
          
        
        
          
            k
            <
            
              K
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              k
            
            ≥
            
              
                
                  n
                  b
                
                ·
                
                  z
                  k
                
              
              -
              x
            
          
        
      
      
        
          
            A
            
              
                
                  (
                  
                    k
                    +
                    x
                  
                  )
                
                ⁢
                mod
                ⁢
                
                  
                
                ⁢
                
                  z
                  k
                
              
              +
              
                
                  PV
                  ⁡
                  
                    (
                    
                      
                        ⌊
                        
                          
                            (
                            
                              k
                              +
                              x
                            
                            )
                          
                          /
                          
                            z
                            k
                          
                        
                        ⌋
                      
                      -
                      
                        k
                        b
                      
                    
                    )
                  
                
                ×
                
                  z
                  k
                
              
            
          
        
        
          
            k
            ⁢
            
              
            
            ⁢
            is
            ⁢
            
              
                
              
              ⁢
              
                
              
            
            ⁢
            any
            ⁢
            
              
                
              
              ⁢
              
                
              
            
            ⁢
            other
            ⁢
            
              
            
            ⁢
            value
          
        
      
    
  



wherein └ ┘ represents the flooring operation, k=0,1, . . . , NFIR−1, NFIR is the number of the codeword bits of the low density parity check hybrid automatic repeat request mother code in the hybrid automatic repeat request buffer, PV is a punctured pattern vector comprising mb elements and consisting of integers from kb to nb−1, mb is the number of rows of a uniform base matrix, nb is the number of columns of the uniform base matrix, kb is the number of columns of an information bits part in the uniform base matrix and kb=nb−mb, PV(l) is an index of the punctured vector PV and has l elements, x is the number of zero bits added before the K information bits, and zk is the expand factor of the structured low density parity check encoding.

5. A method of claim 1, further comprising:
when codeword bits are sequentially selected from the codeword of the rearranged hybrid automatic repeat request mother code in step (b), starting from a first system bit in a first transmission, a starting position of each transmission afterwards following an ending position of a previous transmission, so that a binary sequence of a hybrid automatic repeat request packet is generated, and a formula being:


Ck,i=B(Ltotal(k−1)+i)mod(NFIR)


wherein k represents an index of a hybrid automatic repeat request sub-packet, when hybrid automatic repeat request is applied, k=0 represents the first transmission, and the index of a sub-packet transmitted subsequently is incremented by one, and so forth, when hybrid automatic repeat request is not applied, k=0; Lk represents a length of a kth sub-packet,





  
    
      L
      total
    
    ⁡
    
      (
      k
      )
    
  
  =
  
    
      ∑
      
        j
        =
        0
      
      
        k
        -
        1
      
    
    ⁢
    
      L
      j
    
  




and Ltotal(−1) is set to zero, i=0,1, . . ., Lk−1, Ck,0, Ck,1, . . . , Ck,Lk−1 are codeword bits of the kth sub-packet, and B0, B1, . . . , BNFIR−1 is the codeword of the hybrid automatic repeat request mother code, NFIR is the number of codeword bits of the hybrid automatic repeat request mother code.

6. A method of claim 1, further comprising:
when the codeword bits of the hybrid automatic repeat request packet are mapped to the constellation in step (c), firstly performing interleaving, and then performing mapping, and step (c) comprising the following steps of:
(c1) utilizing an interleaver to interleave the codeword bits of the hybrid automatic repeat request packet, reading in by rows and reading out by columns, and guaranteeing that the high-order bits in the encoding blocks of the hybrid automatic repeat request packet are mapped to high reliability bits in the constellation;
(c2) sequentially mapping said codeword bits to the constellation, and for binary phase shift keying, quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation, or 64 quadrature amplitude modulation, modulating a group of input bits bm−1, . . . , b0 into a complex symbol, wherein m=log 2(M), and M is a modulation order.

7. A method of claim 6, wherein,
in said step (c1), an Ncpc×L row-column interleaver is utilized, and for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation, Ncpc is respectively 2, 6, 4 and 6; L=2Ncbps/Ncpc, wherein an interleaving length Ncbps is equal to a length Lk of a kth hybrid automatic repeat request sub-packet, and the interleaving is represented by the following arrangement formula:
codeword bits before arrangement are C0, C1, . . . , CNcbps−1,
codeword bits after arrangement are D0, D1, . . . , DNcbps−1,
the formula is defined as:


Dk=C(Ncpc/2)·k mod L+└k/L┘ L=2Ncbps/Ncpc, k=0,1, . . . , Ncbps−1


wherein └ ┘ represents the flooring operation;
in said step (c2), each m=log 2(M) bits of said codeword bits D0, D1, . . . , Dncbps−1 starting from D0 form a group and are mapped to a modulation symbol, wherein M represents a modulation order.

8. A method of claim 1, wherein step (c) comprises the following steps:
if the encoded bit sequence before modulation is D0, D1, . . . , DNcbps−1, and a complex symbol sequence after modulation is S0, S1, . . . , SNsym−1, wherein Ncbps is the number of codeword bits in a hybrid automatic repeat request sub-packet, and Nsym is the number of complex symbols after the modulation of the hybrid automatic repeat request sub-packet, then the kth symbol Sk in the complex symbol sequence corresponding to a binary sequence (bm−1,k, . . . , b0,k), and Sk comprising a real part SkI and an imaginary part SkQ, wherein m=log 2(M), and M is a modulation order,
modulation orders for quadrature phase shift keying, 8 phase shift keying, 16 quadrature amplitude modulation and 64 quadrature amplitude modulation being respectively 2, 3, 4 and 6, then mapping the input binary data D0, D1, . . . , DNcbps−1 for modulation to the constellation according to the following formulas:
if the modulation is quadrature phase shift keying:


(b1,k,b0,k)=(D2k,D2k+1) k=0,1, . . . , Ncbps/2−1


if the modulation is 8 phase shift keying:


(b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/3,Dk+2·Ncbps/3) k=0,1, . . . Ncbps/3−1


if the modulation is 16 quadrature amplitude modulation:


(b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/4,Dk+Ncbps/2,Dk+3·Ncbps/4) k=0,1, . . . Ncbps/4−1


if the modulation is 64 quadrature amplitude modulation:


(b5,k,b4,k,b3,k,b2,k,b1,k,b0,k)=(Dk,Dk+Ncbps/6,Dk+Ncbps/3,Dk+Ncbps/2,Dk+2·Ncbps/3,Dk+5·Ncbps/6). k=0,1, . . . , Ncbps/6−1.