| The discovery (and rediscovery) of turbo codes and low density parity check (LDPC) codes has revolutionized the coding research with novel ideas and techniques on code concatenation, iterative decoding and graph-based structure. Although these remarkable codes have demonstrated performance very close to the Shannon limit on memoryless channels, it is fair to say that practice still lags behind theory by some margin due to constructional difficulty, decoding complexity, structural irregularity and/or other implementation issues. This work endeavors to fill some of these gaps concerning the design, analysis, application and evaluation of simple but good codes. The primary interest is to construct a class of bandwidth-efficient and power-efficient “good” codes that are simple to construct, implement and analyze, and to investigate related issues concerning their applications.; We direct our research focus on graph-based, soft iteratively decodable codes, particularly those that are of high performance and low complexity. The work is composed of various pieces, but the main components are developed within the following two main themes. (1) The first is to design and analyze the proposed codes, namely product accumulate codes or PA codes, from the code theoretic perspective, which includes structural properties, decoding algorithms and efficiency, performance bounds and asymptotic thresholds. (2) The second is to investigate and evaluate PA codes as well as other state-of-the-art codes like turbo product codes and LDPC codes in a number of application scenarios, including wireless communications, optical fiber communications, digital data storage systems and packet data networks. The features we will address include performance bounds and thresholds, rate compatibility, joint differential detection and decoding, joint decoding and equalization, binary precoding, and thresholds of coded intersymbol interference channels.; The former is more coding theory centric and the latter is more application oriented. Through the study, we hope to shed insight into the understanding and practice of coding theory and techniques in a unified framework, and to reveal and bench-mark the potentials of some of the best-known codes in a variety of applications. |
