The Iterative Decoding Of Modern Code

Error correction coding plays a crucial role in digital communication systems. Recently, more researchers have devoted to the study on powerful modern codes, such as Turbo and low-density parity check (LDPC) codes, due to their impressive performance close to Shannon limit. To differentiate the relative theory from the classical algebraic coding theory, they are called as modern error correction theory.The modern error correction codes share two characteristics: randomness and iterative decoding. Randomness at the encoder benefits the codeword weight spectrum, which approximates the weight spectrum of (conceptually) random codes. The iterative decoding asymptotically achieves the performance of maximum likelihood (ML) decoding, as well as maintaining acceptable decoding complexity even for long block-length codes. These two advantages not only assist practical implementation, but also agrees with the Shannon theorem.This work explores fundamental aspects of iterative decoding. Although iterative decoding promises the optimal ML decoding asymptotically, its non-linear property makes traditional analytical tools invalid. Therefore, many new theoretical tools have been proposed. This work investigates three approaches: stochastic analysis, non-linear analysis, and graph analysis.First, we introduce the stochastic analysis approach. Based on Gaussian assumption and symmetric condition, we propose a new ARQ application on MC-CDMA systems. Different from the traditional ARQ systems, this approach does not require re-transmitting all erroneous frames. Instead, only certain frames, with more errors than the given threshold, are re-transmitted. Hence, the efficiency of the entire system is greatly improved.Next, we briefly review the dynamic non-linear theorem in iterative decoding. Upon this, we extend and comprehensively illustrate various stages of iterative decoding system; in turn, greatly enrich the theorem of non-linear analysis in iterative decoding. We further propose a novel stopping criterion. Simulation results reveal that the new stopping criterion enhances system performance.Finally, enlightened by the graph theory, we propose another metric (CSS) to evaluate the performance of interleaver, which is one of the two dominant components in the design of turbo codes. The CSS metric not only quantizes and predicts the performance of interleavers, but can also be utilized as design criterion. The interleaver designed according to CSS has been demonstrated to present better performance comparing with many existing interleavers.