Encoding method, and decoding method

摘要

An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. The first parity check matrix corresponds to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials. The second parity check matrix is generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix. An eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressible by using a predetermined mathematical formula.

主权项

1. An encoding method comprising
generating an encoded sequence comprising: n−1 information sequences denoted as X1 through Xn−1; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number, wherein the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e%m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as(Db⁢⁢1,i+1)⁢P⁡(D)+∑k=1n-1⁢{(1+∑j=1r⁢⁢k⁢Da⁢⁢k,i,j)⁢Xk⁡(D)}=0(Math.⁢1) where b1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed asP⁡(D)+∑k=1n-1⁢{(1+∑j=1r⁢⁢k⁢Dak,(α-1)⁢5⁢m,j)⁢Xk⁡(D)}=0(Math.⁢2)where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than rp, and rp denotes an integer no less than three, D denotes a delay operator, Xp(D) denotes a polynomial representation of an information sequence Xp among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and ap,i,q denotes a natural number, and when x and y are integers no less than one and no greater than rp and satisfy x≠y, ap,i,x≠ap,i,y holds true for all x and y,where, in Math. 1 and Math. 2,
Xk(D) has no less than four terms, a1,g,1%m=v1,1 and a1,g,2%m=v1,2, where v1,1 and v1,2 are fixed numbers, hold true for all g, where g is an integer no less than zero and no greater than m−1, and a greatest common divisor of vs,1 and m is one, and a greatest common divisor of vs,2 and m is one, where s is an integer no less than one and no greater than n−1, and vs,1 and vs,2 are integers no less than one and no greater than m−1.