We design and analyze LDPC codes for magnetic disk drives, wireless modems, and packet transmission on the internet in this dissertation. A new method of constructing rate-compatible LDPC codes is proposed for large file broadcast on the Internet and a family of variable-length rate-compatible LDPC codes is designed with very low error-rate floors. We study the concatenated zigzag (CZ) code and the turbo product-code with single parity-check component code (TPC/SPC) for EPR4 channel. Simulations show a coding gain of about 4 dB over uncoded EPR4 by the two codes. Collaborating with Seagate Technologies, we made greater than 100Gb/in2 recordings using a TPC/SPC code. A coding gain comparable to the simulations was observed. We examine the TPC/SPC-coded EPR4 channel with soft-output Viterbi Algorithm (SOVA) and show that it is SOVA's optimistic reliability outputs that result in SOVA detector's performance degradation relative to the BCJR detector. We propose a simple remedy and demonstrate that the modified SOVA-TPC/SPC system gives about the same performance as the BCJR-TPC/SPC system. Using a similar methodology, we demonstrate the min-sum algorithm for LDPC code also provides optimistic reliability values. Based on the Gaussian approximation and EXIT chart, we develop a design technique for LDPC-coded higher-order modulation systems on an AWGN channel and present an example of a 2 bits/symbol LDPC-coded 8PSK scheme operating about 0.6 dB from the capacity at a BER of 10-6. We also propose a reliability-based mapping strategy. Compared to conventional strategies, this strategy gives a 0.15 dB-0.2 dB performance improvement without added complexity. The LDPC-coded OFDM system is analyzed based on a mutual information metric. We demonstrate that the mutual information between the transmitted binary sequence and the soft input to LDPC decoder is a precise and robust measure for characterizing the performance of the LDPC-coded system. Given this, we formulate an adaptive bit-loading and power-allocation problem, and design adaptive mutual information-based algorithms. Simulations show that those algorithms ensure the system robust performance against channel fluctuations. It is also shown that, with those algorithms, the system only suffers little performance loss if coding rate adaptation is not used.
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