Coding and Transmission Strategies for Secrecy

Abstract: In this thesis we consider several problems relating to information theoretic security. The wiretap channel is the simplest information theoretic setting which takes security into account, and in the first chapters of the thesis we design some practical coding schemes for this channel model.First we consider the design of two edge type low density parity check (LDPC) codes for the binary erasure wiretap channel (BEC-WT). For the scenario when the main channel is error free and the wiretapper's channel is a binary erasure channel (BEC) we find secrecy capacity achieving code sequences based on standard LDPC code sequences for the BEC. However, this construction does not work when there are also erasures on the main channel. For this case we develop a method based on linear programming to optimize two edge type degree distributions. Using this method we find code ensembles that perform close to the secrecy capacity of the BEC-WT. We generalize a method of Méasson, Montanari, and Urbanke in order to compute the conditional entropy of the message at the wiretapper. We apply this method to relatively simple ensembles and find very good secrecy performance.We then show that Arikan's polar codes can be used to achieve the whole capacity-equivocation region of for any degraded symmetric binary input wiretap channel. We also design capacity achieving polar codes for the decode-and-forward scheme for the physically degraded relay channel, and for the bidirectional broadcast channel with common and confidential messages.In the subsequent chapter we consider a Gaussian system model. We show that sparse regression codes (SPARCS) as introduced by Joseph and Barron achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel, and can be used to implement the decode-and-forward scheme for the Gaussian relay channel. We also consider secret key agreement using correlated Gaussian random variables and a rate-limited public channel. We show that SPARCs attain the capacity region also for this problem.Finally we consider secret key agreement over reciprocal fading channels. We first consider a multiple-antenna setup in the high signal-to-noise-ratio (SNR) regime and propose a scheme based on training and randomness sharing. We then consider a single antenna setup in the low SNR regime, where one of the terminals is only allowed to transmit pilot signals. We propose a bursty transmission scheme based on training and opportunistic transmission using a wiretap channel code, and show that this scheme is optimal.