Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints

In this paper, we present two low complexity algorithms that achieve capacity for the noiseless (d,k) constrained channel when k=2d+1, or when k-d+1 is not prime. The first algorithm, called symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. [1]. In addition to achieving capacity for (d,2d+1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving, and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf [2]. This method uses fewer than k-d biased bit streams to achieve capacity for (d,k) constraints with k-d+1 not prime. In particular, the encoder for (d,d+2^m-1) constraints, 1\le m<\infty, requires only m biased bit streams.Comment: 16 pages, submitted to the IEEE Transactions on Information Theor

Capacity Analysis for Continuous Alphabet Channels with Side Information, Part I: A General Framework

Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite alphabet channels. However, the results are not easily generalizable to the case of continuous alphabet channels due to analytic difficulties inherent with continuous alphabets. In the first part of this two-part paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. For this purpose, we establish novel necessary and sufficient conditions for weak* continuity and strict concavity of the mutual information. These conditions are used in investigating the existence and uniqueness of the capacity-achieving measures. Furthermore, we derive necessary and sufficient conditions that characterize the capacity value and the capacity-achieving measure for continuous alphabet channels with side information at the receiver.Comment: Submitted to IEEE Trans. Inform. Theor

Physical-Layer Security: Combining Error Control Coding and Cryptography

In this paper we consider tandem error control coding and cryptography in the setting of the {\em wiretap channel} due to Wyner. In a typical communications system a cryptographic application is run at a layer above the physical layer and assumes the channel is error free. However, in any real application the channels for friendly users and passive eavesdroppers are not error free and Wyner's wiretap model addresses this scenario. Using this model, we show the security of a common cryptographic primitive, i.e. a keystream generator based on linear feedback shift registers (LFSR), can be strengthened by exploiting properties of the physical layer. A passive eavesdropper can be made to experience greater difficulty in cracking an LFSR-based cryptographic system insomuch that the computational complexity of discovering the secret key increases by orders of magnitude, or is altogether infeasible. This result is shown for two fast correlation attacks originally presented by Meier and Staffelbach, in the context of channel errors due to the wiretap channel model.Comment: 12 pages, 5 figures. Submitted and accepted to the International Conference on Communications (ICC) 2009. v2: equivalent to the version that will be published in the conference proceedings. Has some altered notation from version 1 as well as slight changes in the wording to make the paper more readable and easier to understan