Dynamic Programming for Sequential Deterministic Quantization of Discrete Memoryless Channels

In this article, under a general cost function C, we present dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for q-ary input discrete memoryless channel (DMC). The DP has complexity O(q (N-M) 2 M), where N and M are the alphabet sizes of DMC output output, respectively. Then, starting from quadrangle inequality, two techniques applied reduce method's complexity. One technique makes use Shor-Moran-Aggarwal-Wilber-Klawe (SMAWK) algorithm achieves M). other is much easier be implemented (N - )). We further derive sufficient condition which SDQ among all quantizers applicable. This generalizes results in literature binary-input DMC. Next, show that α-mutual information ( α-MI)-maximizing belongs category C. prove weaker than derived, aforementioned applicable design α-MI-maximizing quantizer. Finally, illustrate particular application our practical pulse-amplitude modulation systems.