Low-precision quantizer design for communication problems

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In this work, the design of low-precision quantizers for two selected problems in communications is addressed: the multiple-access relay channel with compression of the received signals at the relay, and the point-to-point link with intersymbol-interference, additive noise, and analog-to-digital conversion at the receiver. For the multiple-access relay channel, scalar and two-dimensional quantizers are designed for log-likelihood ratios at the relay yielding a low complexity scheme. The sum-rate optimal allocation of compression rates using a compress-and-forward strategy is also considered. The low-precision analog-to-digital converter design problem for intersymbol-interference channels is studied next, where the focus is on maximizing the information rate over such channels. The smallest possible size of the analog-to-digital converter alphabet yielding maximal information rate is derived for noiseless channels as a function of the transmit alphabet size, and scalar and two-dimensional converters are designed for noisy channels. Finally, the analog-to-digital converter design problem is complemented by studying channel estimation using a single-bit adaptively dithered quantizer. Lower bounds on the mean squared error are derived, and dither and estimation schemes are proposed that are shown to closely approach the lower bounds.