Performance analysis of incremental redundancy type hybrid ARQ for finite-length packets in AWGN channel

We evaluate a hybrid automatic repeat request (HARQ) scheme adopting incremental redundancy (IR) type under a finite-length codeword condition in AWGN channels. In the IR-type HARQ scheme, a long codeword is divided into L blocks, so that L becomes the maximum number of HARQ rounds. Although a finite-length codeword has a transmission rate loss from the channel capacity, IR-type HARQ schemes can significantly reduce the loss due to an early-termination effect. We find the sub-optimal coding rate of a codeword for given parameters such as signal-to-noise ratio (SNR), error probability constraint, and L. In addition, we scale the gap between the channel capacity and the average transmission rate of the IR-type HARQ and show that the gap decreases in the order of 1/L when a specific condition is satisfied while the gap of the non-HARQ case decreases in the order of 1/√L.