Maximum mutual information rate for the Uniformly Symmetric Variable Noise FSMC without channel state information

The orthodoxy in the time-varying channel is that, the mutual information (MI) rate of the Uniform Symmetric Variable Noise Finite State Markov Channel (USVN-FSMC) is maximized by the channel input of maximum entropy, i.e., independent and identically distributed (i.i.d.) and uniform. The optimal signal detection is performed by a decision-feedback decoder (DFD). However this decoder is not reliable; its state estimator often loses track of channel states. Only the error propagation is claimed as the reason. This paper first revisits the cause of the decoding unreliability. It is assumed that the channel input is known by the state estimator of the DFD (there is no error propagation). Simulations are designed to show that, even under this assumption, the channel state cannot be estimated reliably when the channel input approaches maximum entropy. Therefore, the inability to estimate the channel state, rather than error propagation, is the primary cause of the decoding unreliability. Simulation results also exhibit that the price of channel state estimation is a decrease in channel input entropy. This effect has not been included in the derivation of the MI rate in the existing literature. In the second part of the paper, a more accurate analysis of the MI rate of USVN-FSMCs is put forward. It is shown that, on one hand, channel state estimation increases the MI rate by enabling a more reliable information transfer. On the other hand, it requires redundancy in the channel input, which lowers the MI rate. An optimal tradeoff between these two opposite effects can be established, which leads to the maximum channel MI rate. This tradeoff does not occur for maximum-entropy channel inputs, neither does the maximum MI rate of the USVN-FSMC.