Low-complexity decoding for non-binary LDPC codes in high order fields

In this paper, we propose a new implementation of the Extended Min-Sum (EMS) decoder for non-binary LDPC codes. A particularity of the new algorithm is that it takes into accounts the memory problem of the non-binary LDPC decoders, together with a significant complexity reduction per decoding iteration. The key feature of our decoder is to truncate the vector messages of the decoder to a limited number n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> of values in order to reduce the memory requirements. Using the truncated messages, we propose an efficient implementation of the EMS decoder which reduces the order of complexity to ¿(n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ). This complexity starts to be reasonable enough to compete with binary decoders. The performance of the low complexity algorithm with proper compensation is quite good with respect to the important complexity reduction, which is shown both with a simulated density evolution approach and actual simulations.