On Short Forward Error-Correcting Codes for Wireless Communication Systems

For real-time wireless communications, short forward error-correcting (FEC) codes are indispensable due to the strict delay requirement. In this paper we study the performance of short FEC codes. Reed-Solomon (RS) codes and concatenated zigzag (CZ) codes are chosen as representatives of classical algebraic codes and modern simple iterative decodable codes, respectively. Additionally, we use random binary linear codes as a baseline reference for comparison. Our main results (demonstrated by both simulation and ensemble distance spectrum analysis) are as follows: 1) Short RS codes are as good as random binary linear codes; 2) Carefully designed short low-density parity-check (LDPC) codes are almost as good as random binary linear codes when high decoding complexity can be tolerated; 3) Low complexity belief propagation decoders incur considerable performance loss at short coding lengths.