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IEEE Transactions on Information Forensics and Security

Strong Secrecy of Arbitrarily Varying Multiple Access Channels

Yiqi Chen, Dan Nong He, Yuan Luo

Published Jan 1, 2021• 7 citations
Publisher

Abstract

This paper investigates the strong secrecy capacity of the arbitrarily varying multiple access channel (AVMAC). First, Csiszár's almost independent coloring lemma is generalized to establish an achievable secrecy rate region of the AVMAC with an eavesdropper, which includes existing results on both the arbitrarily varying wiretap channel and the multiple access wiretap channel. We then determine the capacity for a special case named semi-noiseless wiretap channel. In addition, a multi-letter outer bound is also presented. Finally, the results of this paper are further explained via a binary example with a numerical inner bound.

DOI
10.1109/tifs.2021.3087338

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arXiv:2306.14323•IEEE Transactions on Information Theory•Jan 29, 2025•1 citation
This paper investigates the strong secrecy capacity of the arbitrarily varying multiple access channel (AVMAC). First, Csiszár's almost independent coloring lemma is generalized to establish an achievable secrecy rate region of the AVMAC with an eavesdropper, which includes existing results on both the arbitrarily varying wiretap channel and the multiple access wiretap channel. We then determine the capacity for a special case named semi-noiseless wiretap channel. In addition, a multi-letter outer bound is also presented. Finally, the results of this paper are further explained via a binary example with a numerical inner bound.
The strong secrecy transmission problem of the arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. First, a stochastic-encoder code lower bound of the strong secrecy capacity is established by applying the type argument and Csiszár’s almost independent coloring lemma. Then, a superposition stochastic-encoder code lower bound of the secrecy capacity is provided. The superposition stochastic-encoder code lower bound can be larger than the ordinary stochastic-encoder code lower bound. Random code lower and upper bounds of the secrecy capacity of the AVWC with constraints are further provided. Based on these results, we further consider a special case of the model, namely severely less noisy AVWC, and give the stochastic-encoder code and random code capacities. It is proved that the stochastic-encoder code capacity of the AVWC with constraints is either equal to or strictly smaller than the corresponding random code capacity, which is consistent with the property of the ordinary AVC. Finally, some numerical examples are presented to better illustrate our capacity results. Compared to the soft covering lemma that requires the codewords to be generated i.i.d., our method has more relaxed requirements regarding codebooks. It is proved that the good codebooks for secure transmission can be generated by choosing codewords randomly from a given type set, which is critical when considering the AVWC with constraints.
We develop an outer bound for the secrecy capacity region of a class of multiple access wiretap channels (MAC-WT). In this class, which we call the weak eavesdropper class, each user's link to the legitimate receiver is stronger than its link to the eavesdropper. Our outer bound partially matches the achievable region in an n-letter form. In addition, a looser version of our outer bound provides close approximations to the capacity region of the Gaussian MAC-WT channel. In particular, we prove that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual rates for all weak eavesdropper Gaussian MAC-WT, and within 0.5 bits/channel use in all directions for certain weak eavesdropper Gaussian MAC-WT channels.
The strong secrecy transmission problem of arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. A stochastic code lower bound of the secrecy capacity is established by applying the type argument and Csiszár's almost independent coloring lemma, which includes the result of the ordinary AVWC as special case. Our codebook generation without the i.i.d. assumption of the soft covering lemma is to ensure the reliable communication over the AVWC with constraints. It is proved that the 0good codebooks for the strong secrecy transmission can be generated by choosing codewords randomly from a given type set, which is critical in this model.
We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.
The secrecy capacity problems over the general arbitrarily varying wiretap channel (AVWC), with respect to the maximal decoding error probability and strong secrecy criterion, are considered, where the channel state sequence may be known or unknown at the receiver. In the mean time, it is always assumed that the channel state sequence is known at the eavesdropper and unknown at the transmitter. Capacity results of both stochastic code (with random encoder and deterministic decoder) and random code (with random encoder and decoder) are discussed. This model includes the previous models of classic AVWC as special cases. Single-letter lower bounds on the secrecy capacities are given, which are proved to be the secrecy capacities when the main channel is less noisy than the wiretap channel. The coding scheme is based on Csiszar's almost independent coloring scheme and Ahlswede's elimination technique. Moreover, a new kind of typical sequence with respect to states is defined for this coding scheme. It is concluded that the secrecy capacity of stochastic code is identical to that of random code when the receiver knows the state sequence. Meanwhile, random code may achieve larger secrecy capacity when the state sequence is unknown by the receiver.
Strong secrecy communication over a discrete memoryless state-dependent multiple access channel (SD-MAC) with an external eavesdropper is investigated. The channel is governed by discrete memoryless and i.i.d. channel states, and the channel state information (CSI) is revealed to the encoders in a causal manner. The main results of this paper are inner and outer bounds of the capacity region, for which we investigate coding schemes incorporating wiretap coding and secret key agreements between the sender and the legitimate receiver. Two kinds of block Markov coding schemes are proposed. The first is a new coding scheme that uses backward decoding and the Wyner-Ziv coding, and the secret key is constructed from a lossy description of the CSI. The other is an extended version of an existing coding scheme for point-to-point wiretap channels with causal CSI. A numerical example shows that the achievable region given by the first coding scheme can be strictly larger than the second one. However, these two schemes do not outperform each other in general, and there exist some numerical examples in which each coding scheme achieves some rate pairs that cannot be achieved by another scheme. Our established inner bound reduces to some best-known results in the literature as special cases. We further investigate some capacity-achieving cases for state-dependent multiple access wiretap channels (SD-MAWCs) with degraded message sets. It turns out that the two coding schemes are both optimal in these cases.