1. A decoding apparatus for performing decoding processing of encoded frame data which are encoded by using non-binary low density parity check codes, comprising: a logarithmic Fourier transform processing section configured to perform Fourier transform processing and logarithmization processing on a probability vector of a symbol of the encoded frame data, and to output an initial value of a logarithmic Fourier domain probability vector; a variable node processing section configured to execute variable node processing by convolution operation using the initial value of the logarithmic Fourier domain probability vector and a fourth message outputted from an edge coefficient processing section to compute a first message, and to update and output the logarithmic Fourier domain probability vector; the edge coefficient processing section configured to execute edge coefficient processing on the first message to compute a second message, and to execute edge inverse coefficient processing on a third message inputted from a check node processing section to compute the fourth message; and the check node processing section configured to execute check node processing by addition operation on the second message to compute the third message.