Soft-input soft-output list-based decoding algorithm

List-based SISO decoding algorithms calculate extrinsic information using a list of codewords. They try to produce a list containing the closest codewords to the soft input by encoding or decoding test sequences. Ideally for each position in the code, there is at least one codeword in the list with a ´1´ in that position and at least one with a ´0´. The extrinsic information must be estimated in positions where there is not. We focus on encoding-based algorithms since they retain performance as the minimum Hamming distance of the code, d_H,min, increases, whereas, decoding-based algorithms generally become increasingly inefficient. We consider product codes with extended BCH component codes. They are transmitted using BPSK over a memoryless additive white Gaussian noise channel. The proposed algorithm can easily be extended to different channel models, modulation schemes and concatenated codes.