Decoding by iterative detection (DECIDET): Soft-in/soft-out decoding of arbitrary linear block codes over arbitrary finite fields

This paper presents a framework for an error correction decoding algorithm which can perform soft-input/soft-output decoding on arbitrary linear block codes over arbitrary finite fields. The algorithm produces estimates of individual symbols by detecting the symbol as a scalar multiple of a column of the generator matrix for the code, with other columns forming an interfering “noise” which is probabilistically modeled. Only the generator matrix is used for the decoder; the parity check matrix is not employed. The posterior probability so obtained is iteratively fed back as a prior input for turbo-like operation. Methods of incorporating statistical dependence among symbols are presented. The decoder can be used for channels with arbitrary noise distributions. Computation over larger fields is achieved through the use of an extended Hadamard transform, which is used to compute the distribution of arbitrary linear combinations of random variables distributed over the field. Results are presented for some codes of various lengths and design distances.