An Iterative Error Patterns Library Formation Method for the Decoding of Product Codes

Abstract

Product codes are preferred in high data rate wireless communication systems to achieve good error performance. In this paper, the problem of twodimensional syndrome-norm decoding of product codes based on a library of error patterns is considered. In product coding, sequence code is first transformed into a code matrix, and then the row and column check code are calculated. In the decoder, the error position of the two-dimensional can be obtained by the operations that first calculate the syndromes and norms, then match with the error patterns in the existing library. The error pattern library is stored in the memory and generated by the subset of the error pattern. This paper proposed a mathematical model for fast generating a library based on the iterative expansion of the error patterns, which makes it possible to shorten the computational complexity in comparison with the known approaches.