Certificate of Originality

Low-density parity-check (LDPC) codes can be applied to many different types of communication systems such as video broadcasting and satellite communications. However, the performance of the codes in practice may deviate a lot from the theoretical limits, achievable only by codes with infinite length. In this thesis, we will conduct a detailed investigation on the performance of short-length LDPC codes over additive white Gaussian noise (AWGN) channels. First, we look into the rich dynamical behavior occurring at the LDPC decoders when the LDPC code has a finite length. We will report the various types of bifurcation phenomena as the signal-to-noise ratio (SNR) increases. By linearizing the iterative equations used for decoding the signals, we are able to evaluate the eigenvalues corresponding to the fixed points. Based on the eigenvalues, we can further characterize the properties of the fixed points. In addition, we make use of a simple feedback technique in an attempt to improving the convergence rate of the decoder at the waterfall (medium-SNR) region. Then, we attempt to “optimize” the distributions of the variable-node degrees and check-node degrees such that lower error rates can be produced. Although some “optimized” variable-node and check-node degree distributions have already been reported in the literature, they are found based on the assumption that the LDPC codes having an infinite length. Therefore, the error performance of a finite-length LDPC code obeying such degree distributions may not be “optimized” and there are possibilities that codes following other degree distributions may produce better performance in terms of block/bit error rates (BLERs/BERs). Since the LDPC decoders rely on passing messages iteratively between the set of variable nodes and the set of check nodes, decreasing the short average path length (APL) will no doubt accelerate the exchange of messages among the variable nodes, thereby reducing