Low Density Parity Check Codes with Non-Equiprobable Symbols

In this letter, we analyze how to decode LDPC codes with non-equiprobable binary symbols. For such symbols, we need to modify the conventional Tanner graph, because the message passing from check nodes to information bits and to parity check bits are diverse. In other words, in conventional Tanner graph, the message passing along two directions are identical, while in our case, the message along the forward direction and backward direction are different. A method to optimize signaling constellation which maximizes the channel mutual information is presented as well. In the numerical section, symbols with prior probabilities (0.3,0.7) could gain 0.72 dB in performance if we replace equal space constellation with optimal constellation. Several cases of short LDPC codes (N, K =1024, 512) are explored and gain almost 0.4 dB. The simulation shows that additional gain of only 0.2 dB could be attainable, if optimal source coding is achievable.