One-Shot Multiple Access Channel Simulation

IEEE International Symposium on Information Theory (ISIT), pp. 2981–2986

Abstract

We consider the problem of simulating a two-sender multiple access channel (MAC) for fixed product inputs, where each sender transmits a message to the decoder over a rate-limited noiseless link based on its input and unlimited randomness shared with the decoder. As our main contribution, we characterize the one-shot communication cost region via almost-matching inner and outer bounds phrased in terms of the smooth max-information of the channel. The achievability relies on a rejection-sampling algorithm to simulate a quantization channel between each sender and decoder, and producing the final output based on the output of these intermediate channels. The converse follows via information-spectrum based arguments relating operational quantities to information measures. Our one-shot results recover the single-letter asymptotic rate region for MAC simulation with fixed, independent and identically distributed product inputs, that was obtained in [Kurri et al., IEEE Transactions on Information Theory 68, 7575 (2022)]. We extend our result to quantum-to-classical channels with a separable decomposition [Atif et al., IEEE Transactions on Information Theory 68, 1085 (2022)], for which we obtain a similar characterization.

Authors 3

1. Aditya Nema Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany

2. Sreejith Sreekumar Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany

3. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany