The design of advanced wireless communication systems has been one of the most important research areas in recent years. High performance error correction schemes and high speed data services are at the heart of these systems. Due to the excellent performance of Low-Density Parity-Check (LDPC) codes, they are good candidates for many new wireless communication standards. However, complexity, latency scalability and flexibility remain a challenge. This thesis is concerned with investigating a new approach to coding and decoding LDPC codes based on Parallel Concatenated Gallager Code (PCGCs) using multiple constituent codes. These are a class of concatenated codes built from the direct parallel concatenation of LDPC codes without interleave...