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IEEE Transactions on Information Forensics and Security

Polar Coding for the Multiple Access Wiretap Channel With Partial Rate-Limited Feedback via Rate-Splitting

Xingyu Chen, Huici Wu, Xiaofeng Tao, Jin Xu, Shixun Gong

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This paper investigates an explicit polar coding scheme for a two-user discrete memoryless multiple access wiretap channel with partial rate-limited feedback (MAC-WT-PLF). Feedback is exploited to increase channel-input correlation, inject dummy messages, and encrypt messages using a one-time pad. Existing MAC-WT polar coding schemes assume independent channel inputs, which cannot support the correlation requirement. Therefore, we propose an explicit polar mapping that leverages feedback to introduce correlation between the channel inputs. This mapping allows both the transmitter and the receiver to restructure the correlation in opposite decoding directions. The proposed scheme relies on source polarization, block Markov coding, superposition coding, lossy source coding, and ratesplitting, without making symmetry or degradation assumptions on the channel model. Rigorous information-theoretic asymptotic analysis establishes that the proposed scheme ensures both reliability and strong secrecy, and attains the entire achievable secrecy rate region given in prior work.

DOI
10.1109/tifs.2026.3687750

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This paper investigates an explicit polar coding scheme for a two-user discrete memoryless multiple access wiretap channel with partial rate-limited feedback (MAC-WT-PLF). Feedback is exploited to increase channel-input correlation, inject dummy messages, and encrypt messages using a one-time pad. Existing MAC-WT polar coding schemes assume independent channel inputs, which cannot support the correlation requirement. Therefore, we propose an explicit polar mapping that leverages feedback to introduce correlation between the channel inputs. This mapping allows both the transmitter and the receiver to restructure the correlation in opposite decoding directions. The proposed scheme relies on source polarization, block Markov coding, superposition coding, lossy source coding, and ratesplitting, without making symmetry or degradation assumptions on the channel model. Rigorous information-theoretic asymptotic analysis establishes that the proposed scheme ensures both reliability and strong secrecy, and attains the entire achievable secrecy rate region given in prior work.
This paper investigates the problem of secure transmission over a two-user discrete memoryless multiple-access wiretap channel with partial rate-limited feedback (MAC-WT-PLF). The receiver can causally and securely transmit feedback to one of the transmitters at a limited rate. Three achievable rate regions and one outer bound on the secrecy capacity are presented based on three proposed coding schemes and the Sato-type bounding approach. The proposed coding schemes show that the feedback can play multiple roles, i.e., encrypting part of messages, enlarging the size of the dummy message, and increasing the correlation between the channel inputs, to enhance the secrecy performance. Of particular interest is identifying the novel role of enlarging the size of the dummy message at one of the transmitters, which enables both transmitters to benefit from the feedback significantly. In addition, the proposed achievable rate regions and outer bound are computed for the Gaussian MAC-WT-PLF, and comparative numerical results are provided under different eavesdropping cases.
We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters. No degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with an explicit and low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting, which introduces two virtual transmitters, and cooperative jamming strategies implemented by these virtual transmitters. Specifically, our coding scheme combines point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on block Markov encoding to be able to deal with an arbitrary channel and strong secrecy. Consequently, our coding scheme is the combination of inter-dependent block Markov constructions. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.
We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters - no degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with a low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting and different cooperative jamming strategies. Specifically, our coding scheme combines several point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on a chaining construction to be able to deal with an arbitrary channel and strong secrecy. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.
It is commonly known that physical layer security is achieved with a trade-off in terms of the achievable rate. Hence, security constraints generate rate losses in wiretap channels. To mitigate such rate losses in multi-user channels, we propose a coding/decoding scheme for multi-user multiple access wiretap channel (MAC-WT), where previously transmitted messages are used as a secret key to enhance the secrecy rates of the transmitting users, until the usual Shannon capacity region of a multiple access channel (MAC) is achieved without the secrecy constraint. With this coding scheme, all messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal, we introduce secret key buffers at both the users and the legitimate receiver. Finally, we consider a fading MAC-WT and show that with this coding/decoding scheme, we can achieve the capacity region of a fading MAC channel (in the ergodic sense).
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked to the eavesdropper tends to zero.
This paper investigates the secrecy achievable region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted.