Secure Multiplex Coding with a Common Message

We determine the capacity region of the secure multiplex coding with a common message, and evaluate the mutual information and the equivocation rate of a collection of secret messages to the second receiver (eavesdropper), which were not evaluated by Yamamoto et al.Comment: 5 pages, no figure, IEEEtran.sty, final version to appear in Proc. ISIT 201

Secure Multiplex Coding Over Interference Channel with Confidential Messages

In this paper, inner and outer bounds on the capacity region of two-user interference channels with two confidential messages have been proposed. By adding secure multiplex coding to the error correction method in [15] which achieves the best achievable capacity region for interference channel up to now, we have shown that the improved secure capacity region compared with [2] now is the whole Han-Kobayashi region. In addition, this construction not only removes the rate loss incurred by adding dummy messages to achieve security, but also change the original weak security condition in [2] to strong security. Then the equivocation rate for a collection of secret messages has also been evaluated, when the length of the message is finite or the information rate is high, our result provides a good approximation for bounding the worst case equivocation rate. Our results can be readily extended to the Gaussian interference channel with little efforts.Comment: 10 pages, 6 figure

Coding and Signal Processing for Secure Wireless Communication

Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel

Design and Analysis of Communication Schemes via Polar Coding

Polar codes, introduced by Arikan in 2009, gave the first solution to the problem of designing explicit coding schemes that attain Shannon capacity of several basic models of communication channels. This discovery made it possible to attain theoretical limits of communication in a number of other problems of data compression and multi-user communication as well as provided new perspectives on extremal configurations of some discrete-time random walks. This thesis is devoted to the design of communication protocols for several basic information-theoretic problems as well to the problem of efficient construction of polar codes. In the first part we consider the problem of optimizing the amount of data transmit- ted between two terminals performing interactive computation of a function. Information- theoretic limits for one model of interactive computation were found in recent literature. We consider the distributed source coding problem that arises in the analysis of this model, designing a polar coding scheme that serves the basis for the distributed computation. As a result, it becomes possible to attain the smallest possible rate of data exchange between the terminals using an explicit protocol of encoding and data exchange that supports reli- able computation of the function by both parties. We also extend our considerations to a multi-terminal variation of this problem. Secondly, we turn to the problem of communication between two parties over a link observed by an adversary, known as the “wiretap channel.” Explicit capacity-achieving schemes for various models of the wiretap channel have received significant attention in recent literature. In this work, we address the general model of the channel, removing the constraints on the channels adopted in the earlier works. We show that secrecy capacity of the wiretap channel under a “strong secrecy constraint” can be achieved using an ex- plicit scheme based on polar codes. We also extend our construction to the case of the broadcast channel with confidential messages due to Csiszar and Korner, achieving the entire capacity region of this communication model. In the last part of the thesis we consider the problem of efficient construction of polar codes. While Arıkan’s scheme is explicit, his original proposal suffers from high construction complexity which grows exponentially with the number of evolution steps. An approximation procedure for binary-input channels was proposed and analyzed in the literature. Here we propose and study a construction algorithm for polar codes with arbitrarily-sized input alphabets. We establish a complexity estimate of the algorithm and derive an estimate of the approximation error that ensues from its use. The approximation error reduces the gap to the recently established lower bound for this type of algorithms. The validity of the proposed algorithm is supported by experimental results