Performance of M-ary feedback communication systems

An analytical evaluation of the performance of M-ary feedback communication systems with MAP strategy is presented. An approximate lower performance bound is found, using the Cauchy inequality and then using the Jensen inequality. The bounds are compared and are found to coincide, yielding an estimate of the system performance. The mean path approximation tends to underestimate the system average transmission time. It is shown that the difference between the theoretical results and the computer simulation data is rather small: approximately 1 dB in terms of average transmission time. It is also shown that feedback systems are better than one-way systems in terms of the SNR required to achieve a prescribed error probability.