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Physica Scripta

Secure multiterminal source coding with side information

Xiaomin Liu, Feiyu Chen, Zhengjun Xi

Published Oct 24, 2025• 0 citations
Publisher

Abstract

Abstract In this paper, we consider multiterminal source secure coding with quantum side information available to the receiver and the eavesdropper. We assume that the side information of the receiver is less noisy than that of the eavesdropper. First, we investigate the quantum Sgarro coding under security constraints and derive the bound for the achievable compression-equivocation region. Furthermore, we consider secure coding of correlated sources when two legitimate receivers have less noisy quantum side information and establish the corresponding achievable compression-equivocation region.

DOI
10.1088/1402-4896/ae1767

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Abstract In this paper, we consider multiterminal source secure coding with quantum side information available to the receiver and the eavesdropper. We assume that the side information of the receiver is less noisy than that of the eavesdropper. First, we investigate the quantum Sgarro coding under security constraints and derive the bound for the achievable compression-equivocation region. Furthermore, we consider secure coding of correlated sources when two legitimate receivers have less noisy quantum side information and establish the corresponding achievable compression-equivocation region.
The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.
In the secure cooperative source-coding problem that we consider, Encoder 1 and Decoder 1 observe, respectively, a pair of independent identically distributed (i.i.d.) correlated sources and wish to communicate the first source to Decoder 2 subject to a distortion constraint. Encoder 1 sends a message to both the decoders over a public nonsecure channel, and then Decoder 1-the helper-sends a message just to Decoder 2 over a secure channel. An eavesdropper, which has access to memoryless side-information that is correlated with the first source, intercepts the message sent by Encoder 1 and based on both wishes to minimize its uncertainty about the first source. The secrecy measure of the system is the equivocation of the first source at the eavesdropper. We determine the rates equivocation region for this problem assuming that conditioned on the side-information of Decoder 1 the eavesdropper's side-information is independent of the first source. To that end, we derive an inner and an outer bound that depend explicitly on the proportional rate that Encoder 1 spends in the cooperation process. Subsequently, we evaluate this region for the case of a doubly symmetric binary source and Hamming distortion.
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob, and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the conventional problems of secure source coding with side information at the decoders, and the wiretap channel. Inner and outer bounds on the rate-distortion-equivocation region for the case of arbitrary channels and side informations are derived. In some special cases of interest, it is shown that separation holds. By means of an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
This paper investigates the problem of source-channel coding for secure transmission with arbitrarily correlated side informations at both receivers. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the problems of secure source coding with (uncoded) side information at the decoders and the wiretap channel. A general outer bound on the rate-distortion-equivocation region, as well as an inner bound based on a pure digital scheme, is derived for arbitrary channels and side informations. In some special cases of interest, it is proved that this digital scheme is optimal and that separation holds. However, it is also shown through a simple counterexample with a binary source that a pure analog scheme can outperform the digital one while being optimal. According to these observations and assuming matched bandwidth, a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones is then presented. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. Through an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
This paper investigates the problem of source-channel coding for secure transmission of a Gaussian source over a Gaussian wiretap channel in presence of arbitrarily correlated side informations at both receivers. By means of an appropriate coding scheme (either hybrid digital/analog or pure digital), the optimal rate-distortion-equivocation region is characterized for most of the scenarios. These results provide the best achievable tradeoff between the requirement on the distortion level at the legitimate receiver and the equivocation rate at the eavesdropper.
In this paper, new inner and outer bounds on the achievable compression-equivocation rate region for generalized secure data compression with side information are given that do not match in general. In this setup, two senders, Alice and Charlie intend to transmit information to Bob via channels with limited capacity so that he can reliably reconstruct their observations. The eavesdropper, Eve, has access to one of the channels at each instant and is interested in the source of the same channel at the time. Bob and Eve also have their own observations which are correlated with Alice's and Charlie's observations. In this model, two equivocation and compression rates are defined with respect to the sources of Alice and Charlie. Furthermore, different special cases are discussed where the inner and outer bounds match. Our model covers the previously obtained results as well.