  This letter studies the power-limited throughput of a communication system
utilizing incremental redundancy (INR) hybrid automatic repeat request (HARQ).
We use some recent results on the achievable rates of finite-length codes to
analyze the system performance. With codewords of finite length, we derive
closed-form expressions for the outage probabilities of INR HARQ and study the
throughput in the cases with variable-length coding. Moreover, we evaluate the
effect of feedback delay on the throughput and derive sufficient conditions for
the usefulness of the HARQ protocols, in terms of power-limited throughput. The
results show that, for a large range of HARQ feedback delays, the throughput is
increased by finite-length coding INR HARQ, if the sub-codeword lengths are
properly adapted.
