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This dissertation presents a new class of irregular low-density parity-check (LDPC) codes of moderate length and high rate. The codes in this class admit low-complexity encoding and have lower error rate floors than other irregular LDPC code design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit error-rate of 10-9 are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates. Applications of these codes to magnetic data storage and wireless transmission channels are then studied. In the case of data storage, we assume an EPR4 partial response model with noise bursts which models media defects and thermal asperities. We show the utility of sending burst noise channel state information to both the partial response detector and the decoder. Doing so eliminates the error rate curve flattening seen by other researchers. The simulation results presented have demonstrated that LDPC codes are very effective against noise bursts and, in fact, are superior to Reed-Solomon codes in the regime simulated. We also have presented an algorithm for finding the maximum resolvable erasure-burst length, Lmax, for a given LDPC code. The simulation results make the possibility of an error control system based solely on an LDPC code very promising. For the wireless communication channel, we assume two types of Gilbert-Elliott channels and design LDPC codes for such channels. Under certain assumptions, this model leads us to what we call the burst-erasure channel with AWGN (BuEC-G), in which bits are received in Gaussian noise or as part of an erasure burst. To design codes for this channel, we take a "shortcut" and instead design codes for the burst-erasure channel (BuEC) in which a bit is received correctly or it is received as an erasure, with erasures occurring in bursts. We show that optimal BuEC code ensembles are equal to optimal binary erasure channel (BEC) code ensembles and we design optimal codes for these channels. The burst-erasure efficacy can also be measured by the maximum resolvable erasure-burst length Lmax. Finally, we present error-rate results which demonstrate the superiority of the designed codes on the BuEC-G over other codes that appear in the literature. |
