Decoding apparatus and decoding method

A decoding method for performing decoding processing of encoded frame data which is encoded by using non-binary low density parity check codes, comprising:

• logarithmic Fourier transform processing executed in a processor;
• variable node processing executed in a processor;
• edge coefficient processing executed in a processor;
• and
• check node processing executed in a processor, wherein
• the logarithmic Fourier transform processing comprises performing Fourier transform processing and logarithmization processing on a probability vector of a symbol of the encoded frame data to compute an initial value of a logarithmic Fourier domain probability vector,
• the variable node processing comprises executing variable node processing by convolution operation using the logarithmic Fourier domain probability vector and a fourth message outputted from the edge coefficient processing to compute a first message and update the logarithmic Fourier domain probability vector,
• the edge coefficient processing comprises executing edge coefficient processing on the first message to compute a second message, and to execute edge inverse coefficient processing on a third message to compute the fourth message, and
• the check node processing comprises executing check node processing by addition operation on the second message to compute the third message.