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Traditional channel coding with feedback constructs and transmits a codewordonly after all message bits are available at the transmitter. This paper joinsGuo & Kostina and Lalitha et. al. in developing approaches for causal (orprogressive) encoding, where the transmitter may begin transmitting codewordsymbols as soon as the first message bit arrives. Building on the work ofHorstein, Shayevitz and Feder, and Naghshvar et. al., this paper extends ourprevious computationally efficient systematic algorithm for traditionalposterior matching to produce a four-phase encoder that progressively encodesusing only the message bits causally available. Systematic codes work well withposterior matching on a channel with feedback, and they provide an immediatebenefit when causal encoding is employed instead of traditional encoding. Ouralgorithm captures additional gains in the interesting region where thetransmission rate mu is higher than the rate lambda at which message bitsbecome available. In this region, transmission of additional symbols beyondsystematic bits, before a traditional encoder would have begun transmission,further improves performance

Causal (Progressive) Encoding over BinarySymmetric Channels with Noiseless Feedback