TY - JOUR
T1 - Joint Design of Block Source Codes and Modulation Signal Sets
AU - Vaishampayan, Vinay A.
AU - Farvardin, Nariman
PY - 1992/7
Y1 - 1992/7
N2 - The problem of designing a bandwidth-efficient, average-power-limited digital communication system for transmitting information from a source with known statistics over a noisy waveform channel is considered. 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 to minimize the mean squared error (mse) between the source vector and its estimate in the receiver. For a linear decoder, 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 band-widths, 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.
AB - The problem of designing a bandwidth-efficient, average-power-limited digital communication system for transmitting information from a source with known statistics over a noisy waveform channel is considered. 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 to minimize the mean squared error (mse) between the source vector and its estimate in the receiver. For a linear decoder, 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 band-widths, 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.
KW - Combined source-channel coding
KW - quantization
KW - signal design
KW - vector
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U2 - 10.1109/18.144704
DO - 10.1109/18.144704
M3 - Article
AN - SCOPUS:0001446290
SN - 0018-9448
VL - 38
SP - 1230
EP - 1248
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -