Reliable communications over power lines through coded modulation schemes

Single-tone frequency shift keying (FSK) modulation with permutation codes has been found to be useful in establishing reliable communications over power lines. This dissertation is devoted to the study of generalizations to this coded modulation scheme. In the first part of this dissertation, we extend this coded modulation scheme based on permutation codes to general block codes and establish the conditions for correct decoding over a power line communications (PLC) channel. In the process, we introduce a new parameter to measure the performance against narrowband noise. As a result, we define a new class of codes, namely, equitable symbol weight codes, which are optimal with respect to this measure. Simulation results validating the relevance of this new parameter are given. Hence, we investigate the possible sizes of equitable symbol weight codes. Using an Elias-type bound, we determine the asymptotic size of equitable symbol weight codes under certain conditions. Using both classical coding and computational methods, we also tabulate the possible lower and upper bounds of an optimal equitable code for certain parameters. However, the exact size of optimal equitable symbol codes is only known in a limited number of instances. Generalizing a class of combinatorial objects called generalized balanced tournament designs introduced by Lamken and Vanstone (1989), we define a class of combinatorial objects called generalized balanced tournament packings and establish a connection to equitable symbol weight codes. As a result, we construct new infinite families of optimal equitable symbol weight codes whose narrowband noise error-correcting capability to code length ratios are bounded away for zero. Unfortunately, this general coded modulation scheme usually requires the use of a codebook and does not have an efficient decoding algorithm. Hence, we propose the use of multitone FSK and codes defined over binary matrices in the final part of this dissertation. Adopting techniques from classical concatenation, we construct infinite families of efficiently decodable matrix codes with rates and relative distances bounded away from zero. Simulation results demonstrating the merits of multitone FSK modulation scheme are also given.​Doctor of Philosophy (SPMS