Finite-blocklength analysis of the ARQ-protocol throughput over the Gaussian collision channel

We present a finite-blocklength analysis of the throughput and the average delay achievable in a wireless system where i) several uncoordinated users transmit short coded packets, ii) interference is treated as noise, and iii) 1-bit feedback from the intended receivers enables the use of a simple automatic repeat request (ARQ) protocol. Our analysis exploits the recent results on the characterization of the maximum coding rate at finite blocklength and finite block-error probability by Polyanskiy, Poor, and Verdú (2010), and by Yang et al. (2013). For a given number of information bits, we determine the coded-packet size that maximize the per-user throughput and minimize the average delay. Our numerical results indicate that, when optimal codes are used, very short coded packets (of length between 50 to 100 channel uses) yield significantly lower average delay at an almost negligible throughput loss, compared to longer coded packets.