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IEEE International Symposium on Information Theory (ISIT)

New models for interference and broadcast channels with confidential messages

Mohamed Nafea, Aylin Yener

Published Jun 1, 2017• 7 citations
Publisher

Abstract

A new model for the interference channel with confidential messages (IC-CM) is introduced, where each receiver, besides his noisy observations, is provided with a fixed-length subset, of his choosing, of noiseless observations for the transmitted codewords of both users, making confidential communication more challenging than the previous such model. In addition, in the same spirit, a broadcast channel with confidential messages (BC-CM), where the receivers noiselessly tap into subsets of their choice of the transmitted codeword, is considered. Achievable strong secrecy rate regions for both models are derived. In both models, the size of the subset quantifies a secure rate trade-off between the two receivers. The case of the new BC-CM model with one receiver's noisy observations are degraded with respect to the other receiver, and only the degraded receiver is provided with the subset of noiseless observations, is highlighted. In this case, the receiver with the degraded noisy observations has a positive rate after a certain threshold of his noiseless observations, i.e., with the aid of these symbols.

DOI
10.1109/isit.2017.8006841

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A new model for the interference channel with confidential messages (IC-CM) is introduced, where each receiver, besides his noisy observations, is provided with a fixed-length subset, of his choosing, of noiseless observations for the transmitted codewords of both users, making confidential communication more challenging than the previous such model. In addition, in the same spirit, a broadcast channel with confidential messages (BC-CM), where the receivers noiselessly tap into subsets of their choice of the transmitted codeword, is considered. Achievable strong secrecy rate regions for both models are derived. In both models, the size of the subset quantifies a secure rate trade-off between the two receivers. The case of the new BC-CM model with one receiver's noisy observations are degraded with respect to the other receiver, and only the degraded receiver is provided with the subset of noiseless observations, is highlighted. In this case, the receiver with the degraded noisy observations has a positive rate after a certain threshold of his noiseless observations, i.e., with the aid of these symbols.
The model for a broadcast channel with confidential messages (BC-CM) plays an important role in the physical layer security of modern communication systems. In recent years, it has been shown that a noiseless feedback channel from the legitimate receiver to the transmitter increases the secrecy capacity region of the BC-CM. However, at present, the feedback coding scheme for the BC-CM only focuses on producing secret keys via noiseless feedback, and other usages of the feedback need to be further explored. In this paper, we propose a new feedback coding scheme for the BC-CM. The noiseless feedback in this new scheme is not only used to produce secret keys for the legitimate receiver and the transmitter but is also used to generate update information that allows both receivers (the legitimate receiver and the wiretapper) to improve their channel outputs. From a binary example, we show that this full utilization of noiseless feedback helps to increase the secrecy level of the previous feedback scheme for the BC-CM.
A new broadcast wiretap channel (B-WTC) with a wiretapper who noiselessly taps into a fixed-length subset of the transmitted symbols of her choice, and observes the remainder through a noisy channel, is studied. An achievable strong secrecy rate region which extends Marton's inner bound to the proposed setting, is derived. Strong secrecy capacity regions for two classes of the new B-WTC, namely the new B-WTC with deterministic receivers, and the new B-WTC with degraded receivers and more noisy wiretapper, are identified. These results extend the recently proposed new wiretap channel model to the broadcast setting.
The broadcast channel (BC) with one confidential message and where the decoders cooperate via a one-sided link is considered. A pair of messages is transmitted, one message for each user. The message to the cooperative user is confidential and is kept secret from the cooperation-aided user. The secrecy level is measured by the equivocation rate. An inner bound on the secrecy-capacity region of the BC is derived. The inner bound is achieved by double-binning the codebook of the secret message. The inner bound is tight for the semi-deterministic (SD) and physically degraded (PD) cases. The secrecy results are compared to those of the corresponding BCs without a secrecy constraint. A cooperative Blackwell channel example illustrates the impact of secrecy on the rate regions.
In this paper, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with noncausal side information, and Csiszár and Körner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity-equivocation region composed of all achievable rates-equivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy.
A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semideterministic and physically degraded BCs, and the results are compared with those of the corresponding BCs without a secrecy constraint. Black well and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.
The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner's random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper; or the K-receiver BC without a wiretapper.