Patent ID: 8732545

Claim:
An encoding method of generating a low-density parity check convolutional code of a coding rate of ⅓ and a time varying period of 3 from a low-density parity check convolutional code of a coding rate of ½ and a time varying period of 3, the low-density parity check convolutional code of the coding rate of ½ and the time varying period of 3 being defined based on: a first parity check polynomial in which (a1%3, a2%3, a3%3) and (b1%3, b2%3, b3%3) are any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1) and (2, 1, 0) of a parity check polynomial represented by equation 1-1; a second parity check polynomial in which (A1%3, A2%3, A3%3) and (B1%3, B2%3, B3%3) are any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0) and (2, 0, 1), (2, 1, 0) of a parity check polynomial represented by equation 1-2; and a third parity check polynomial in which (α1%3, α2%3, α3%3) and (β1%3, β2%3, β3%3) are any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1) and (2, 1, 0) of a parity check polynomial represented by equation 1-3, wherein c % d (where c and d are any integers) represents a remainder after dividing c by d, the method comprising the steps of: inserting, using an encode circuit, known information into 3k pieces of information Xj (where j's are any indexes of 6i, 6i+1, 6i+2, . . . , 6(i+k−1)+3, 6(i+k−1)+4, 6(i+k−1)+5, and j's are different from each other) of 6 k bits of information X 6i , X 6i+1 , X 6i+2 , X 6i+3 , X 6i+4 , X 6i+5 , . . . , X 6(i+k−1) , X 6(i+k−1)+1 , X 6(i+k−1)+2 , X 6(i+k−1)+3 , X 6(i+k−1)+4 , X 6(i+k−1)+5 such that, of remainders after dividing values of the 3k different indexes j's by 3, the number of remainders which become 0 is k, the number of remainders which become 1 is k and the number of remainders which become 2 is k, the 6k bits of information made by extracting information from information part of one period of encoded outputs including the information part and parity part, and by arranging the extracted information in output order of the encoded outputs, the one period of the encoded outputs composed of 12k (k is a natural number) bits of the information part and the parity part which are the encoded outputs using the low-density parity check convolutional code of a coding rate of ½; and obtaining, using the encode circuit, the parity part from the information including the known information, wherein: the equation 1-1 is ( D a1 +D a2 +D a3 ) X ( D )+( D b1 +D b2 +D b3 ) P ( D )=0, the equation 1-2 is ( D A1 +D A2 +D A3 ) X ( D )+( D B1 +D B2 +D B3 ) P ( D )=0; and the equation 1-3 is ( D α1 +D α2 +D α3 ) X ( D )+( D β1 +D β2 +D β3 ) P ( D )=0, where: X(D) is a polynomial representation of information X and P(D) is a parity polynomial representation; a1, a2 and a3 are integers (where a1≠a2≠a3) and b1, b2 and b3 are integers (where b1≠b2≠b3); A1, A2 and A3 are integers (where A1≠A2≠A3) and B1, B2 and B3 are integers (where B1≠B2≠B3); and α1, α2 and α3 are integers (where α1≠α2≠α3) and β1, β2 and β3 are integers (where β1≠β2≠β3).