Encoding method, encoding device, decoding method and decoding device for low density generator matrix codes

An encoding device for Low Density Generator matrix Codes, LDGC, comprising:

• basic matrix storing means, for storing a uniform basic matrix Gbuniform of an LDGC mother code set constructed using P LDGC, wherein P denotes there are total P LDGC in the LDGC mother code set, with code rate R0 and different code lengths, wherein R0=kb/nb, kb denotes the number of rows in the basic matrix, and nb denotes the number of columns in the basic matrix;
• matrix parameter computing means, for computing length L of a intermediate variant according to the relation between length K of an information bit sequence to be encoded in the LDGC mother code set and the length L of the intermediate variant, computing an expanding factor Zk for processing the basic matrix using the length L of the intermediate variant and the number kb of rows of the basic matrix, and performing modifying and expanding computation on the basic matrix to obtain a generator matrix Gldgc using the expanding factor Zk;
• bit filling means, for adding L−K known bits to the information bit sequence to be encoded to generate an information bit sequence m with the length L;
• pre-coding means, for obtaining, according to a formula I×Gldgc (1:L,1:L)=m, the intermediate variant I using a square matrix Gldgc (1:L,1:L) composed of L rows and the front L columns of the generator matrix and the information bit sequence m with the length L;
• block code encoding means, for encoding the intermediate variant using a matrix Gldgc (1:L, 1:N+L−K) composed of L rows and the front N+L−K columns of the generator matrix to generate a first encoding result with length N+L−K, wherein N denotes the length of the encoded information, K denotes the length of the information bit sequence;
• and
• bit deleting means, for deleting L−K known bits from the first encoding result with the length N+L−K to generate a second encoding result with length N.

A decoding method executed by a decoding device for Low Density Generator matrix Codes, LDGC, comprising the following steps:

• step 1, obtaining a reception generator matrix Gldgc, (:r1, r2, . . . ri,), wherein i is a positive integer which satisfies L≦i≦N+L−K, by modifying and expanding a basic matrix Gbuniform using an expanding factor Zk used in an encoding process by using a processor;
• step 2, filling L−K known bits in encoded LDGC having passed an erasure channel to obtain LDGC C(r1, r2, . . . ri)=[Cr1, Cr2, Cr3, . . . , Cri], wherein C(r1, r2, . . . ri) is an input signal stream, to be decoded, wherein i is a positive integer which satisfies L≦i≦N+L−K, L is the length of an intermediate variant used in the encoding process, N is the length of encoded LDGC having not passed the erasure channel, K is the length of LDGC before encoding;
• step 3, according to a formula C(:,r1, r2, . . . ri)=I*Gidgc (:,r1, r2, . . . ri), obtaining 1*L reception intermediate vector I using the reception generator matrix and the LDGC to be decoded;
• step 4, according to a formula I*Gldgc (1:L,1:L)=m, obtaining a decoding result m with length L using a square matrix Gldgc (1:L,1:L) composed of L rows and the front L columns of the reception generator matrix and the reception intermediate vector;
• and
• step 5, obtaining a decoding result with length K by deleting the L−K known bits from the decoding result m with the length L.

A decoding device for Low Density Generator matrix Codes, LDGC, comprising:

• basic matrix storing means, for storing a uniform basic matrix Gbuniform of an LDGC mother code set constructed by using P LDGC, wherein P denotes there are total P LDGC in the LDGC mother set, with code rate R0 and different code lengths, wherein R0=kb/nb , kb denotes the number of rows in the basic matrix, and nb denotes the number of columns in the basic matrix;
• matrix parameter computing means, for obtaining a reception generator matrix Gldgc (:,r1, r2, . . . ri), wherein i is a positive integer which satisfies L ≦i≦N+L−K, by modifying and expanding the basic matrix Gbuniform using an expanding factor Zk used in an encoding process;
• bit filling means, for filling L−K known bits in an encoded LDGC having passed an erasure channel to obtain LDGC C(r1, r2, . . . ri)=[Cr1, Cr2, Cr3, . . . , Cri], wherein C(r1, r2, . . . ri) is an input signal stream, to be decoded, wherein i is a positive integer which satisfies L≦i≦N+L−K is the length of an intermediate variant used in the encoding process, N is the length of encoded LDGC having not passed the erasure channel, K is the length of the LDGC before encoding;
• upper triangular matrix computing means, for performing row permutation, column permutation, and/or row elimination operation on the reception generator matrix Gldgc (:,r1, r2, . . . ri) , using Gaussian elimination method to obtain a matrix comprising L*L upper triangular matrix;
• intermediate variant computing means, for obtaining, according to a formula C(:,r1, r2, . . . ri)=I*Gldgc (:,r1, r2, . . . ri), 1*L reception intermediate vector I using the matrix comprising L*L upper triangular matrix and the LDGC to be decoded;
• block code decoding means, for obtaining, according to a formula I*Gldgc (1:L,1:L)=m, a decoding result m with length L using a square matrix Gldgc (1:L,1:L) composed of L rows and the front L columns of the reception generator matrix and the reception intermediate vector;
• and
• bit deleting means, for obtaining a decoding result with length K by deleting the L−K known bits from the decoding result m with the length L.