  As sensing and instrumentation play an increasingly important role in systems
controlled over wired and wireless networks, the need to better understand
delay-sensitive communication becomes a prime issue. Along these lines, this
article studies the operation of data links that employ incremental redundancy
as a practical means to protect information from the effects of unreliable
channels. Specifically, this work extends a powerful methodology termed
sequential differential optimization to choose near-optimal block sizes for
hybrid ARQ over erasure channels. In doing so, an interesting connection
between random coding and well-known constants in number theory is established.
Furthermore, results show that the impact of the coding strategy adopted and
the propensity of the channel to erase symbols naturally decouple when
analyzing throughput. Overall, block size selection is motivated by normal
approximations on the probability of decoding success at every stage of the
incremental transmission process. This novel perspective, which rigorously
bridges hybrid ARQ and coding, offers a pragmatic means to select code rates
and blocklengths for incremental redundancy.
