Modulation and coding for the Gaussian collision channel

Abstract

Abstract-We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed.More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. Outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided.Index Terms-Coding and modulation, frequency-hopped communications, information outage probability, multiple-access collision channel.

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

“…In this preliminary investigation, we shall focus on a simple system model, namely, a wireless communication system where several uncoordinated users transmit short coded packets using frequency hopping and a simple automatic repeat request (ARQ) protocol. This setup, which is closely related to the one known in the literature as slotted Gaussian collision channel with feedback [11], [12], is particularly relevant for machinetype communication systems involving a very large number of devices. We consider both the case when the channel among each users is impaired by additive Gaussian noise only, and the quasi-static fading case, where the fading gains are random but stay constant over the duration of each packet.…”