Quantization Systems for Hidden Markov Sources
Goblirsch, David M.
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We consider the problem of transmitting data from a continuous- amplitude, discrete-time source over a bandlimited waveform channel using a block-structured digital communication system. Our objective is to design the source encoder-decoder pair, the channel encoder-decoder pair and the modulator-demodulator pair so as to minimize a squared-error distortion measure between the source sequence and its replica in the receiver, subject to constraints on the transmitted signal power and bandwidth. We formulate the problem in a general sense and derive necessary conditions for optimality for the design variables, namely, the encoder map, the decoder map and the modulation signal set. We then consider two systems for which the necessary conditions for optimality hold. The receiver of the first system consists of an unquantized soft-decision demodulator followed by a linear estimator-based decoder. We solve the necessary conditions for optimality using an iterative solution technique. We then study the performance of this class of systems as the encoding rate increases, for a fixed bandwidth. Performance comparisons are made against a reference system as well as bounds from information theory. Significant improvements over the reference system are demonstrated and the performance is shown to coincide with an information-theoretic bound in two cases. The receiver of the second system consists of a quantized demodulator followed by an optimum decoder. For a fixed signal set, the optimal encoder and decoder conditions are solved using an iterative solution technique. Performance comparisons are made against the linear estimator-based system, the reference system and bounds from information theory. We then study the quantized demodulator- based system as the encoding rate becomes large, for a fixed bandwidth. We demonstrate that this system converges to a linear analog modulation system in some cases and to a nonlinear analog modulation system in others. Finally, we study the performance of the two systems to channel mismatch. We demonstrate that both of these systems are more robust to channel mismatch than the reference system.