Quantization of Fano metrics using relative entropy in modeling channels with memory

In fading channels that exhibit memory, errors tend to occur in blocks. Knowledge of the channel condition of the previous block can be used to predict the future channel condition and improve the performance of the channel decoding system. Channels with memory can be approximated by finite-state Markov models. Once the number of channel states is fixed, the channel observations used to model the channel must be quantized into one of the given states. It has been shown that accurate channel models can be obtained by employing a quantization scheme that is optimized based on an objective function specific to the problem under consideration. In this paper, we seek to accurately model the flat fading channels in a Fano decoding system. We introduce the relative entropy in quantizing channel observations such as the Fano metrics. Simulations show that the proposed quantization scheme can allow some statistics related to channel states to be separated maximally, leading to improved estimation and prediction of the fading channels with memory.