Abstract: An encoder and a decoder employ an encoding scheme corresponding to a parity check matrix which is derivable from a bipartite protograph formed of variable nodes and check nodes, with each variable node corresponding to a codeword symbol position. The protograph has a plurality of groups of nodes, each group of nodes comprising both variable nodes and check nodes. Each of the check nodes in a group is of degree 2 and has connections to two variable nodes in the same group. The protograph also has a plurality of check nodes of degree n, where n is the number of said plurality of groups, wherein each of the plurality of check nodes has a connection to a variable node in each group such that the symbol positions in a codeword are interleaved between the groups of nodes.

Abstract: A decoding apparatus for performing decoding processing of encoded data by using non-binary LDPC codes, includes: a logarithmic Fourier transform processing section, a variable node processing section, an edge coefficient processing section, and a check node processing section, wherein the logarithmic Fourier transform processing section performs Fourier transform processing and logarithmization processing on a probability vector of a symbol of an encoded frame data to output an initial value of logarithmic Fourier domain probability vector, and the variable node processing section, the edge coefficient processing section, and the check node processing section perform iteration processing by using a logarithmic Fourier domain probability vector.

Abstract: A decoding apparatus for performing decoding processing of encoded data by using non-binary LDPC codes, includes: a logarithmic Fourier transform processing section, a variable node processing section, an edge coefficient processing section, and a check node processing section, wherein the logarithmic Fourier transform processing section performs Fourier transform processing and logarithmization processing on a probability vector of a symbol of an encoded frame data to output an initial value of logarithmic Fourier domain probability vector, and the variable node processing section, the edge coefficient processing section, and the check node processing section perform iteration processing by using a logarithmic Fourier domain probability vector.

Abstract: An encoder and a decoder employ an encoding scheme corresponding to a parity check matrix which is derivable from a bipartite protograph formed of variable nodes and check nodes, with each variable node corresponding to a codeword symbol position. The protograph has a plurality of groups of nodes, each group of nodes comprising both variable nodes and check nodes. Each of the check nodes in a group is of degree 2 and has connections to two variable nodes in the same group. The protograph also has a plurality of check nodes of degree n, where n is the number of said plurality of groups, wherein each of the plurality of check nodes has a connection to a variable node in each group such that the symbol positions in a codeword are interleaved between the groups of nodes.