Channel coding provides numerous advantages to digital communications. One of such advantages is error correcting capabilities. This, however, comes at the expense of coding rate, which is a function of the codebook’s cardinality |C| or number of coded information bits and the codeword length M. In order to achieve high coding rate, we hereby report a channel coding approach that is capable of error correction under power line communications (PLC) channel conditions, with permutation coding as the coding scheme of choice. The approach adopts the technique of unequal error correction for binary codes, but with the exception that non-binary permutation codes are employed here. As such, certain parts of the information bits are coded with permutation symbols, while transmitting other parts uncoded. Comparisons with other conventional permutation codes are presented, with the proposed scheme exhibiting a relatively competitive performance in terms of symbol error rate.

Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These Quasi-Cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature.