Simplified check node processing in nonbinary LDPC decoders

This paper deals with low-complexity algorithms for the check node processing in nonbinary LDPC decoders. After a review of the state-of-the-art, we focus on an original solution to significantly reduce the order of complexity of the Extended Min-Sum decoder at the elementary check node level. The main originality of the so-called Bubble Check algorithm is the two-dimensional strategy for the check node processing, which leads to a reduction of the number of comparisons. The simulation results obtained for the Bubble Check show that this complexity reduction does not introduce any performance loss and that it is even possible to further reduce the number of comparisons. This motivated the search of a simplified architecture and led to the L-Bubble Check, which is the main contribution of the paper. The implementation of a forward/backward check node as a systolic architecture of L-Bubble elementary checks is also described. Finally, some FPGA synthesis results of a whole GF(64)-LDPC decoder implementation are presented.