Causal (Progressive) Encoding over Binary Symmetric Channels with Noiseless Feedback

Traditional communication systems transmit a code-word only after all message bits are available at the transmitter. This paper joins Guo & Kostina and Lalitha et al. in developing approaches for causal encoding, where the transmitter may begin transmitting codeword symbols as soon as the first message bit arrives. Building on the posterior matching encoders of Horstein, Shayevitz & Feder, and Naghshvar et al., this paper extends our computationally efficient systematic encoder to progressively encode using only the message bits that are 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 source rate
$\lambda$
at which message bits become available. In this region, we improve performance further through the transmission of additional, non-systematic symbols before a traditional encoder would have even begun transmission.