Andrew Thangaraj

Physical layer security protocols exploit inviolable physical laws at the signal level for providing guarantees on secrecy of communications. These protocols invariably involve randomized encoding at the transmitter, for which an ideal random number generator is typically assumed in the literature. In this work, we study the impact of using weak Pseudo Random Number Generators (PRNGs) in physical layer security protocols for coding and forward key distribution over Binary Symmetric and Gaussian wiretap channels. In the case of wiretap channel coding, we study fast correlation attacks that aim to retrieve the initial seed used in the PRNGs. Our results show that randomized coset encoding, which forms an important part of wiretap channel coding, provides useful robustness against fast correlation attacks. In the case of single-round or forward key distribution over a Gaussian wiretap channel, the bits from a PRNG are nonlinearly transformed to generate Gaussian-distributed pseudo random numbers at the transmitter. In such cases, we design modified versions of the fast correlation attacks accounting for the effects of the nonlinear transformation and soft input. We observe that, even for moderately high memory, the success probability of the modified fast correlation attacks become the same as that of a random guess in many cases. © 2014 IEEE.

Codes defined on graphs and their properties have been subjects of intense recent research. In this work, we are concerned with codes that have planar Tanner graphs. When the Tanner graph is planar, message-passing decoders can be efficiently implemented on chips without any issues of wiring. Also, recent work has shown the existence of optimal decoders for certain planar graphical models. The main contribution of this paper is an explicit upper bound on minimum distance d of codes that have planar Tanner graphs as a function of the code rate R for R ≥ 5/8. The bound is given by As a result, high-rate codes with planar Tanner graphs will result in poor block-error rate performance, because of the constant upper bound on minimum distance. © 2012 AIMS.

Binary-input memoryless channels with a run length constrained input are considered. Upper bounds to the capacity of such noisy run length constrained channels are derived using the dual capacity method with Markov test distributions satisfying the Karush-Kuhn-Tucker conditions for the capacity-Achieving output distribution. Simplified algebraic characterizations of the bounds are presented for the binary erasure channel and the binary symmetric channel. These upper bounds are very close to achievable rates, and improve upon previously known feedback-based bounds for a large range of channel parameters. For the binary-input additive white Gaussian noise channel, the upper bound is simplified to a small-scale numerical optimization problem. These results provide some of the simplest upper bounds for an open capacity problem that has theoretical and practical relevance.

It was well known from Shannon's days that characteristics of the physical channel like attenuation, fading and noise can impair reliable communication. But it was more recently that the beneficial side effects of channel characteristics in ensuring secret communication started getting attention. Studies have been made to quantify the amount of secrecy that can be reaped by combining channel coding with security protocols. The Wiretap channel proposed by Wyner is arguably one of the oldest models of physical layer security protocols. In this paper, we present a brief tutorial introduction to the Wiretap channel, followed by an application of the physical layer model to a class of Key Distribution protocols. We present results from an implementation of key distribution protocols using Software Defined Radio tools along with physical RF hardware peripherals. We believe this approach is much more tangible and informative than computer based simulation studies. © 2013, DESIDOC.

With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy. © 2007 IEEE.

In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its demand to obtain polynomial equations. In this paper, we propose a method to derive the polynomial equations using source-to-sink path gains as the variables. In the path gain formulation, we show that linear and quadratic equations suffice; therefore, network coding becomes equivalent to a system of polynomial equations of maximum degree 2. We present algorithms for generating the equations in the path gains and for converting path gain solutions to edge-to-edge gain solutions. Because of the low degree, simplification is readily possible for the system of equations obtained using path gains. Using small-sized network coding problems, we show that the path gain approach results in simpler equations and determines solvability of the problem in certain cases. On a larger network (with 87 nodes and 161 edges), we show how the path gain approach continues to provide deterministic solutions to some network coding problems. © 2010 IEEE.

We consider a large class of bidirectional relaying scenarios with physical layer network coding, and analytically characterize the relay's error performance in decoding the network-coded combination at high signal-to-noise ratio (SNR). Our analysis applies to scenarios with 1) binary or higher order real/complex modulation, 2) real or complex channel coefficients, and 3) linear or non-linear network maps for network coding at the relay. We consider block fading and allow the relay to choose from a set of network maps based on the channel coefficients of the source to relay links in every block. We derive expressions for pairwise error probability and approximate expected overall error probability. We also derive lower bounds for these error probabilities. We validate these expressions using simulations and show that our approximations are tight in the high SNR regime.

The renewed interest for physical-layer security techniques has put forward a new role for error-control codes. In addition to ensuring reliability, carefully designed codes have been shown to provide a level of information-theoretic secrecy, by which the amount of information leaked to an adversary may be controlled. The ability to achieve information-theoretic secrecy relies on the study of alternative coding mechanisms, such as channel resolvability and privacy amplification, in which error-control codes are exploited as a means to shape the distribution of stochastic processes. This use of error-control codes, which goes much beyond that of correcting errors, creates numerous new design challenges. The objective of this paper is threefold. First, the paper aims at providing system engineers with explicit tools to build simple secrecy codes in order to stimulate interest and foster their integration in communication system prototypes. Second, it aims at providing coding and information theorists with a synthetic overview of the theoretical concepts and techniques for secrecy. Finally, it aims at highlighting the open challenges and opportunities faced for the integration of these codes in practical systems.

The capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases. In this paper, we consider single-tap binary-input Gaussian channels with inter-symbol interference (ISI). The dual capacity method is used to obtain upper bounds using Markov test distributions. The bound, expressed as a single-letter optimization problem, is solved numerically. For higher memory, the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem. Bounds were obtained for the important case of the dicode channel, and these are better than the previously known upper bounds and are close to achievable rates over a wide range of SNRs.

We study the use of Low-Density Parity-Check (LDPC) codes for two-phase, network-coded bidirectional relaying with higher-order modulation. In the multiple-access phase, the sum of transmitted symbols scaled by the channel gains is the received relay constellation, which is network-mapped (clustered) to a transmit constellation for the ensuing broadcast phase. This operation at the relay is termed Clustered-Scaled-Sum (CSS) decoding. We propose a CSS coding scheme for bidirectional relaying using a single LDPC code over a ring with higher-order PAM or QAM alphabets. We design a message-passing decoder for CSS decoding with trade-offs possible between complexity and performance. We suggest a method for completing a Constrained Partially-filled Latin Square (CPLS) to a latin square, which is used in the construction of network maps at the relay for any channel fading state. The performance of the CSS coding scheme with LDPC codes over rings is shown to be very close to information-theoretic outer bounds.