Linear feedback communication systems with Markov sources: optimal system design and performance evaluation

The optimal analog discrete-time feedback communication system is designed for the transmission of a Markov process, such as that generated by a combined source/channel encoder. The forward channel is affected by an additive white Gaussian noise, while the feedback channel is causal and noiseless; no repetition of the transmitted sample is assumed. On the basis of the minimum mean square error (MMSE) criterion, the optimal transmitter and receiver are derived under the constraint of a maximum power level for the transmission over the forward channel. The resulting optimized system is adaptive and fully exploits the available power, thus maximizing the information rate transferred by the system itself. For comparison purposes, the optimal MMSE communication system without feedback link is also designed. The MSE performance of both systems, with and without feedback link, is evaluated by means of closed-form expressions and their convergence rate to the steady state is also computed. Using the feedback link gives significant performance improvements when the input-encoded process is moderately or highly correlated; in this case, the advantages offered by the combined source-channel coding techniques are fully exploited by the proposed optimized feedback communication systems