Design and Analysis of Coupled Graphs for Error Correction and Multiuser Communications
The work of this PhD thesis is dedicated to the design of graph-based systems and signal processing algorithms on graphs which improve error correction and multi-user interference cancellation performance of modern communication systems. New ensembles of low-density parity-check codes based on connecting coupled graphs ensembles are studied and analyzed. We propose a technique to analyze the thresholds of the resulting connected ensembles and formulate new ensemble design guidelines. We propose a new encoding algorithm for staircase codes which lends itself to improved low-power hardware implementation for high-throughput optical communication systems. An analysis of the decoding process of staircase codes is proposed explaining the mis-correction properties of these codes. Finally, we propose and study a window-based detection/decoding algorithm for coupled information transmission multi-user communication system and propose a novel design of a self-coupled random-access communication system.