Causal (Progressive) Encoding over BinarySymmetric Channels with Noiseless Feedback

TL;DR

This paper develops a causal encoding scheme for binary symmetric channels with noiseless feedback, enabling early transmission of message bits and improving communication efficiency over traditional methods.

Contribution

It extends previous posterior matching algorithms to a four-phase encoder that causally encodes message bits as they arrive, enhancing performance in high-rate regions.

Findings

Progressive encoding improves transmission efficiency.

Systematic codes with posterior matching outperform traditional encoding.

Additional symbol transmission benefits high-rate scenarios.

Abstract

Traditional channel coding with feedback constructs and transmits a codeword only after all message bits are available at the transmitter. This paper joins Guo & Kostina and Lalitha et. al. in developing approaches for causal (or progressive) encoding, where the transmitter may begin transmitting codeword symbols as soon as the first message bit arrives. Building on the work of Horstein, Shayevitz and Feder, and Naghshvar et. al., this paper extends our previous computationally efficient systematic algorithm for traditional posterior matching to produce a four-phase encoder that progressively encodes using only the message bits causally available. Systematic codes work well with posterior matching on a channel with feedback, and they provide an immediate benefit when causal encoding is employed instead of traditional encoding. Our algorithm captures additional gains in the interesting region where the transmission rate mu is higher than the rate lambda at which message bits become available. In this region, transmission of additional symbols beyond systematic bits, before a traditional encoder would have begun transmission, further improves performance