Reducing a decoding error floor by post-processing codewords encoded by binary symmetry-invariant product codes

Abstract

A decoder performs iterative decoding of a codeword encoded by a binary symmetry-invariant product code, such as a half product code or quarter product code. In response to the iterative decoding reaching a stopping set, the decoder determines by reference to an ambient error graph formed from the stopping set whether or not the stopping set is correctable by post-processing. If not, the decoder outputs the uncorrected codeword and signals a decoding failure. In response to determining that the stopping set is correctable by post-processing, the decoder inverts all bits of the codeword corresponding to edges of the ambient error graph, applies an additional round of iterative decoding to the codeword to obtain a corrected codeword, and outputs the corrected codeword. Post-processing in this manner substantially lowers an error floor associated with the binary symmetry-invariant product code.