In a Maximum A posteriori Probability decoding (MAP decoding), a correlation and a deviation of noise for past and future states which depend on input signal patterns in past N bits and future Q bits are calculated by training by a noise correlation arithmetic operating unit(84) and they are stored. Upon reproduction, in a white noise arithmetic operating unit(91), white noise values for the past and future states in which colored noise is converted into white noise are obtained by using the stored correlation and deviation of the noise . In an input signal arithmetic operating unit(92),an input signal (channel information) Ac(ykS<m>k) of the MAP decoding is calculated from the white noise values and the deviation for the past and future states. A likelihood in the MAP decoding is obtained from the input signal. <IMAGE> <IMAGE>
Information recording and reproducing method and signal decoding circuit