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arXiv:2306.14323 · IEEE Transactions on Information Theory

On Strong Secrecy for Multiple Access Channels With States and Causal CSI

Yiqi Chen, Tobias J. Oechtering, Mikael Skoglund, Yuan Luo

Published Jan 29, 2025• 1 citation
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Abstract

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.

DOI
10.1109/tit.2025.3536017

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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.
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. An inner bound of the capacity is provided. To establish the inner bound, we investigate coding schemes incorporating wiretap coding and secret key agreement between the sender and the legitimate receiver. Two kinds of block Markov coding schemes are studied. The first one uses backward decoding and Wyner-Ziv coding and the secret key is constructed from a lossy reproduction of the CSI. The other one is an extended version of the existing coding scheme for point-to-point wiretap channels with causal CSI. 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.
In this paper, the problem of secret key agreement in state-dependent multiple access channels with an eavesdropper is studied. For this model, the channel state information is non-causally available at the transmitters; furthermore, a legitimate receiver observes a degraded version of the channel state information. The transmitters can partially cooperate with each other using a conferencing link with a limited rate. In addition, a backward public channel is assumed between the terminals. The problem of secret key sharing consists of two rounds. In the first round, the transmitters wish to share a common key with the legitimate receiver. Lower and upper bounds on the common key capacity are established. In a special case, the capacity of the common key is obtained. In the second round, the legitimate receiver agrees on two independent private keys with the corresponding transmitters using the public channel. Inner and outer bounds on the private key capacity region are characterized. In a special case, the inner bound coincides with the outer bound. We provide some examples to illustrate our results.
This paper studies the impact of partial encoder cooperation on the secrecy of the multiple access channel (MAC) with an external eavesdropper. In particular, two encoders, connected by two communication links with finite capacities, wish to send secret messages to the common intended decoder in the presence of a passive eavesdropper. The inner and outer bounds on the secrecy capacity are derived for the discrete memoryless channel. The derived inner bound rate region is achievable by combining Willems's coding for the MAC with partially cooperating encoders and Wyner's random binning for the wiretap channel. Then, both the inner and outer bounds are extended to the Gaussian case and the corresponding rate regions are established. Several simple achievable transmission schemes are proposed for the Gaussian channel and the numerical results show that the partial encoder cooperation can increase the achievable rate regions.
In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC-CM, we derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, we illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the “iterative” forward-backward coding scheme, combining wiretap channel coding and secret-key-agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).
We investigate the secrecy capacity region of 2-receiver, 1-eavesdropper Broadcast Channel (BC) with two causal states and conferencing decoders. The encoder sends two messages, one of them for both legitimate receivers and the other one for the first legitimate receiver. It keeps these messages secret from the eavesdropper. Each state is causally available at the corresponding receiver, while both states are known causally at the encoder. Each receiver wishes to send the state which is not available at the other receiver, through a noiseless link with limited capacity. We find an inner bound on the secrecy capacity region of this channel. The achievability scheme employs block Markov coding and Shannon strategy for channels with state. In each block, we make use of the states to generate two keys which will be used in the next block. The idea is to utilize the cooperation of both receivers to recover both keys at each receiver while ensuring secrecy. We also establish an outer bound on the secrecy capacity region of the 2-rec, 1-eav. BC with Causal Channel State Information (CCSI) and conferencing. We prove that the proposed bounds coincide for a special case.