Quantization effect on second moment of log-likelihood ratio and its application to decentralized sequential detection

It is well known that quantization cannot increase the Kullback-Leibler divergence which can be thought of as the expected value or first moment of the log-likelihood ratio. In this paper, we investigate the quantization effects on the second moment of the log-likelihood ratio. It is shown that quantization may result in an increase in the case of the second moment, but the increase is bounded above by 2/e. The result is then applied to decentralized sequential detection problems to provide a simpler sufficient condition for asymptotic optimality theory, and the technique is also extended to investigate the quantization effects on other higher-order moments of the log-likelihood ratio and provide lower bounds on higher-order moments.