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IEEE International Symposium on Information Theory (ISIT)

Resolvability of the Multiple Access Channel with Two-Sided Cooperation

Noha Helal, Matthieu R. Bloch, Aria Nosratinia

Published Jun 1, 2020• 3 citations
Publisher

Abstract

We study the randomness required at the inputs of a multiple access channel in order to produce a desired, approximately i.i.d., output distribution, subject to cooperation in one of the following forms: (i) a common message, (ii) conferencing, (iii) feedback and (iv) generalized feedback. For the cases (i)-(iii), we characterize the channel resolvability via matching inner and outer bounds, and for generalized feedback we provide two inner bounds representing the role of decoding and randomness extraction, which can also be combined. One of the main contributions of this work is to show that resolvability rates of the multiple access channel are not improved with feedback, unlike the multiple access channel capacity which is improved by feedback.

DOI
10.1109/isit44484.2020.9174302

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We study the randomness required at the inputs of a multiple access channel in order to produce a desired, approximately i.i.d., output distribution, subject to cooperation in one of the following forms: (i) a common message, (ii) conferencing, (iii) feedback and (iv) generalized feedback. For the cases (i)-(iii), we characterize the channel resolvability via matching inner and outer bounds, and for generalized feedback we provide two inner bounds representing the role of decoding and randomness extraction, which can also be combined. One of the main contributions of this work is to show that resolvability rates of the multiple access channel are not improved with feedback, unlike the multiple access channel capacity which is improved by feedback.
We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.
We study the randomness needed for approximating the output distribution of a multiple-access channel, where the original input processes are independent of each other. The approximation is achieved by simulating (possibly alternative) input processes at each of the entries, where the sources of randomness available for the simulators are independent of each other, and the simulators do not cooperate. The resolvability region of a multiple-access channel is defined as the set of all random-bit rate pairs at which accurate output approximation is possible, where the simulation accuracy is measured by the variational distance between finite-dimensional output distributions. Inner and outer bounds on the resolvability region are derived, and close relations between the concepts of resolvability region and capacity region are demonstrated.
We investigate the effects of user cooperation on the secrecy of multiple access channels with generalized feedback (MAC-GF). We show that cooperation can increase the achievable secrecy region. We propose achievable schemes which use compress-and-forward (CAF) based transmission strategies. CAF based strategies allow users to increase their rates up to levels which are not decodable by the cooperating partners, consequently improving the secrecy of the users. We also provide outer bounds on the achievable equivocation rates. The outer bounds we derive depend only on the channel inputs and outputs, and hence, are easily computable. Finally, we specialize our results to a Gaussian MAC-GF, and present numerical results which demonstrate the beneficial effects of cooperation on secrecy.
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.
Communication networks have had a transformative impact on our society as they have revolutionized almost all aspects of human interaction. The explosive growth of data traffic has led to an increased demand on improving the reliability, efficiency and security aspects of the systems. In this paper, we focus on the multiple access channel, a communication model where several transmitters communicate to a common receiver (e.g., a cellular telephone network) in the presence of an external eavesdropper. The goal is to explore the competitive yet cooperative relationship between the transmitters in order to obtain an efficient communication under a certain reliability and security guarantee. Moreover, we take a special look into the inner and outer bounds on the secrecy capacity regions over the 2-transmitter DM-MAC with a degraded eavesdropper (assuming that both transmitters are cooperative). We notice that the inner and outer bounds differentiate themselves in the permissible sets of input distributions and thus not tight in general. This leaves the problem of secrecy capacity regions still open.
We consider the problem of shared randomness-assisted multiple access channel (MAC) simulation for product inputs and characterize the one-shot communication cost region via almost-matching inner and outer bounds in terms of the smooth max-information of the channel, featuring auxiliary random variables of bounded size. The achievability relies on a rejection-sampling algorithm to simulate an auxiliary channel between each sender and the decoder, and producing the final output based on the output of these intermediate channels. The converse follows via information-spectrum based arguments. To bound the cardinality of the auxiliary random variables, we employ the perturbation method from [Anantharamet al., IEEE Trans. Inf. Theory (2019)] in the one-shot setting. For the asymptotic setting and vanishing errors, our result expands to a tight single-letter rate characterization and consequently extends a special case of the simulation results of [Kurriet al., IEEE Trans. Inf. Theory (2022)] for fixed, independent and identically distributed (iid) product inputs to universal simulation for any product inputs. We broaden our discussion into the quantum realm by studying feedback simulation of quantum-to-classical (QC) MACs with product measurements [Atifet al., IEEE Trans. Inf. Theory (2022)]. For fixed product inputs and with shared randomness assistance, we give a quasi tight one-shot communication cost region with corresponding single-letter asymptotic iid expansion.