Joint Design of Block Source Codes and Modulation Signal Sets
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We consider the problem of designing a bandwidth-efficient, power-limited digital communication system for transmitting information from a source with known statistics over a noisy waveform channel. Each output vector of the source is encoded by a block encoder to one of a finite number of signals in a modulation signal set. The received waveform is processed in the receiver by an estimation-based decoder. The goal is to design an encoder, decoder and modulation signal set so as to minimize the mean squared-error (MSE) between the source vector and its estimate in the receiver. For highly noisy gaussian channels we justify restricting the estimator to the class of linear estimators. With this restriction, we derive necessary conditions for optimality of the encoder, decoder and the signal set and develop a convergent algorithm for solving these necessary conditions. We prove that the MSE of the digital system designed here is bounded from below by the MSE of an analog modulation system. Performance results for the digital system and signal constellation designs are presented for first- order Gauss-Markov sources and a white Gaussian channel. Comparisons are made against a standard vector quantizer (VQ)- based system, the bounding analog modulation system and the optimum performance theoretically attainable. The results indicate that for a correlated source, a sufficiently noisy channel and specific source block sizes and bandwidths, the digital system performance coincides with the optimum performance theoretically attainable. Further, significant performance improvements over the standard VQ-based system are demonstrated when the channel is noisy. Situations in which the linearity assumption results in poor performance are also identified.