Abstract-Posterior matching (PM) is a sequential horizonfree feedback communication scheme introduced by the authors, who also provided a rather involved optimality proof, showing that it achieves capacity for a large class of memoryless channels. Naghshvar et al. considered a non-sequential variation of PM with a fixed number of messages and a random decision-time, and gave a simpler proof establishing its optimality via a novel extrinsic Jensen-Shannon divergence argument. Another simpler optimality proof was given by Li and El Gamal, who considered a fixed-rate fixed block-length variation of PM with an additional randomization. Both these works also provided error exponent bounds. However, their simpler achievability proofs apply only to discrete memoryless channels, and are restricted to a nonsequential setup with a fixed number of messages. In this paper, we provide a short and transparent proof for the optimality of the fully sequential randomized horizon-free PM scheme over general memoryless channels. Borrowing the key randomization idea of Li and El Gamal, our proof is based on analyzing the random walk behavior of the shrinking posterior intervals induced by a reversed iterated function system decoder.
Also, Shayevitz and Feder REF examined a randomized variant of the original PM scheme with a random dither and were able to provide a much simpler proof of optimality over general memoryless channels when W ∈ (0, 1).
A Simple Proof for the Optimality of Randomized Posterior Matching
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics