Analysis of Error Floors of Generalized Non-binary LDPC Codes over q-ary Memoryless Symmetric Channels

In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over the general linear group with those for non-binary LDPC codes over finite field transmitted over the q-ary memoryless symmetric channel under belief propagation decoding. To analyze non-binary LDPC codes defined over both general linear group GL(m, F-2) and finite field F-2m, we investigate non-binary LDPC codes defined over GL(m(3), F-2m4). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the optimized non-binary LDPC codes defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels in the edges which satisfy the condition for the optimization.