This dissertation presents four technical contributions in the theory and practice of low-density parity-check (LDPC) codes and orthogonal frequency division multiplexing (OFDM) systems withtransmission non-linearity and with interference due to high mobility.We first explore the universality of LDPC codes for the binary erasure channel (BEC), the AWGN channel, and the flat Rayleigh fading channel. Using excess mutual information as a performance measure, we demonstrate that an LDPC code designed on a singlechannel can be universally good across the three channels. Thus, a channel for which LDPC code design is simple may be used as a surrogate for channels that are more challenging.Due to fast channel variations, OFDM systems suffer from inter-carrier interference (ICI) in frequency-selective fast fading channels. We propose a novel iterative receiver design that achieves near-optimal performance while maintaining a complexity that grows only linearly with the number of OFDM carriers. Weprove that the matched filter bound for such a channel is also the maximum-likelihood sequence detection (MLSD) bound.Because of the presence of high peaks at OFDM modulator output, amplitude clipping due to amplifier saturation causes performance degradation. We show that existing analyses underestimate the capacity of OFDM systems with clipping, and we analyze thecapacity of clipped OFDM systems with AWGN and frequency-selective Rayleigh fading. We prove that for frequency-selective Rayleigh fading channels, under certain conditions, there exists an SNR threshold, above which the capacity of a clipped system is higherthan that of an unclipped system. We provide upper and lower bounds on the channel capacity and closed-form approximations of discrete-input capacities with and without clipping.We also derive tight MLSD lower bounds and propose near-optimal receivers for OFDM systems with clipping. We show that over frequency-selective Rayleigh fading channels, under certain conditions, a clipped system with MLSD can achieve better performance than an unclipped system. We show that the MLSD boundscan be achieved or closely approached by the proposed low complexity receivers in various channel types.

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