On The Reliability Function of Discrete Memoryless Multiple-Access Channel with Feedback

We derive a lower and upper bound on the reliability function of discrete memoryless multiple-access channel (MAC) with noiseless feedback and variable-length codes (VLCs). The bounds are similar to the one for point-to-point channels, increasing linearly with respect to an appropriate distance between the rate pair and the capacity boundary. For the lower bound on the error exponent, we adapt Yamamoto and Itoh’s coding scheme consisting of a data and a confirmation stage. In the data stage we use arbitrary feedback capacity-achieving codes. In the confirmation stage, each transmitter sends one bit of information to the receiver using a pair of codebooks of size two, one for each transmitter. The codewords at this stage are selected randomly according to an appropriately optimized joint probability distribution. For the upper bound on the error exponent, we adopt the proof techniques of Burnashev for the reliability function of the point-to-point case. The upper bound is derived by studying the rate of decrease of appropriate message entropies.