RATE-DISTORTION PERFORMANCE OF OPTIMUM ENTROPY-CONSTRAINED QUANTIZERS

The problem of optimum entropy-constrained zero-memory quantizer design for memoryless sources is studied. Algorithmic methods for obtaining these quantizers are developed and numerical results illustrating the rate-distortion performance of the optimal quantizer for a wide class of memoryless sources are obtained. This study is extended to the more complex and useful case of predictive quantization for sources with memory. In this case, the rate-distortion performance results of optimal entropy-constrained predictive coding schemes are obtained for stationary first-order Gauss-Markov and Laplace-Markov sources. Furthermore, asymptotic results determining the performance of the predictive quantizer at high rates are developed.

As a related issue, the buffer overflow/underflow problem that arises in transmitting variable-length codes over a synchronous channel is investigated. Asymptotically tight upper and lower bounds on the average terminal time are developed. These results indicate that to reduce the overflow/underflow problem to within tolerable limits, inordinately large buffers are required. To alleviate this difficulty, an adaptive buffer-instrumented scheme for variable-length coding of entropy-constrained quantizers is developed in which the quantization parameters are controlled according to the state of the buffer. It is shown, through simulations, that the overflow/underflow problem is practically eliminated at the cost of negligible increase in distortion.

Finally, the mismatch issue in zero-memory quantization is addressed and the mismatch loss is calculated in a rate-distortion theorectic sense for several examples. Furthermore, block transform image coding is considered as a realistic example where the mismatch issue arises, and the potential advantages of using an adaptive quantization scheme are discussed.