ML vs. BP decoding of binary and non-binary LDPC codes

It has been shown that non-binary LDPC codes have a better error correction performance than binary codes for short block lengths. However, this advantage was up to now only shown under belief propagation decoding. To gain new insights, we investigate binary and non-binary codes under ML decoding. Our analysis includes different modulation schemes and decoding algorithms. For ML decoding under different modulation schemes a flexible integer programming formulation is presented. In this paper, we show that with respect to ML decoding short non-binary LDPC codes are not necessarily superior to binary codes. The decoding gain observed under BP decoding originates mainly in the more powerful non-binary decoding algorithm.