Joint design of block source codes and modulation signal sets

The problem of designing block source codes and modulation signal sets that are both energy and bandwidth constrained is considered. For the class of linear estimator-based decoders, necessary conditions for optimality for the encoder, decoder and modulation signal set are derived. An algorithm that iteratively solves these necessary conditions to converge to a locally optimum solution has been developed. By studying the performance of the previous class of digital communication systems in the limit of infinite encoding rates, it is demonstrated that the MSE of a bandwidth and energy constrained digital system is bounded from below by that of a block pulse amplitude modulation system. This bound is readily computable in terms of the eigenvalues of the source and channel covariance matrices. 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