Near-Optimal Nonbinary Index Assignment for Equiprobable Uniform Quantizers and M-PSK Transmission

Abstract

In conventional communication systems, quantized source symbols are represented by distinct binary labels, which are then mapped to bandwidth-efficient modulation symbols (such as M-PSK) for transmission. Assigning quantization levels to binary labels is known as the binary index assignment (IA) and has been well studied under the assumption that binary indices are transmitted over the binary symmetric channel. It is well-known that the natural binary code gives the optimal binary IA for uniform quantizers with uniform sources. Alternatively, we can also assign quantization levels to M-ary labels to fit the M-ary transmission. This M-ary IA approach generalizes and could outperform the binary IA, and has potential applications in power-efficient transmission such as wireless sensor networks. Although there exist some significant progresses in the study of finding the optimal M-ary IA, the problem is still open. In this paper, we investigate the M-ary IA problem for equiprobable uniform scalar quantizers and M-PSK transmission. We derive a lower bound on the channel mean-squared distortion (MSD) among all possible M-ary IAs and construct a solution which is optimal for M = 3, 4. For M ≥ 5, the solution becomes near-optimal, and its MSD performance approaches the lower bound to within a small gap. In addition, under some wireless sensor network scenarios with 64-level quantization and 8-PSK, we demonstrate that the percentage energy saving of the proposed nonbinary IA solution could be up to 45% relative to the optimal binary IA approach.