This paper investigates the possibilities of optimizing existing protograph low-density parity-check (PLDPC) codes and designing optimal PLDPC codes on both AWGN and Rayleigh channels under binary modulation with unequal power allocation (UPA) for nonuniform sources. While the binary UPA modulation achieves a power gain, it also results in unequal error protection on the coded bits in systematic codewords during transmission. For irregular codes, it is possible to best protect the information bits by optimizing the classification of variable nodes (VNs). Those VNs represent the coded bits in protograph that allows exploiting jointly the degree irregularity and the power differentiation. An algorithm for UPA-based protograph extrinsic information transfer (UPA-PEXIT) analysis on the Rayleigh channel is proposed with the concept of surrogate channel which circumvents the channel asymmetry problem with UPA. With the RJA code as example, it is shown that classification optimization does improve the decoding threshold when the source entropy is small. To design optimal codes, a UPA-based differential evolution (UPA-DE) algorithm is proposed in conjunction with the UPA-PEXIT analysis. A family of optimized codes are illustrated for three typical nonuniform source distributions and compared with the RJA and NND codes by simulations in error rate performance.
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