Andrew Thangaraj

We extend the broadcast channel with confidential messages to the situation where the receiver of the secret message also serves as a relay. We analyze the fundamental cooperation versus secrecy trade-offs for discrete memoryless channels and obtain the exact rate-equivocation region in this case. For the Gaussian channel, we consider various strategies leading to different levels of secrecy. Our study highlights the fundamental role of jamming as a means to increase secrecy rates, but also emphasizes the importance of carefully designed relaying strategies. ©2008 IEEE.

A code over GF(qm) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. In this work, a generalized version of the problem of self-orthogonality of the q-ary image of a qm-ary code has been considered. Given an inner product (more generally, a biadditive form), necessary and sufficient conditions have been derived for a code over a field extension and an expansion basis so that an image of that code is self-orthogonal. The conditions require that the original code be self-orthogonal with respect to several related biadditive forms whenever certain power sums of the dual basis elements do not vanish. The conditions are particularly simple to state and apply for cyclic codes. As a possible application, new quantum error-correcting codes have been constructed with larger minimum distance than previously known. ©2007 IEEE.

In this work, we derive an algebraic formulation for the scalar linear network coding problem as an alternative to the one presented by Koetter et al in [1]. Using an equivalence between network information flow and group-valued circulations, we derive a system of polynomial equations that algebraically represents the scalar linear network coding problem. Surprisingly, this system of polynomials has a maximum degree of 2. We illustrate our formulation and its advantages through example networks drawn from the literature. © 2008 IEEE.

Soft-decision decoding of algebraic codes has been an area of active research interest for a long time. In this paper, we present sub-optimal, soft decoders for extended binary BCH codes and certain subcodes of extended RS codes. Our proposed decoders consist of a soft-information processing block followed by a traditional, hard-decision, bounded-distance decoder for the underlying BCH or RS codes. The soft-processor in both cases consists of SISO decoders for extended Hamming codes, which can be implemented with low complexity. The coding gains obtained are comparable with other soft decoders proposed in the literature.

It is well-known that a Gaussian source distribution is required for maximum information transfer across a Gaussian channel. In a coded modulation system an equiprobable symbol constellation loses at most 1.53 dB when compared to a Gaussian source. To bridge this shaping gap, a code can be used to make the source distribution more Gaussian over an expanded constellation that results in lower average transmitted energy. Trellis shaping uses convolutional codes and the Viterbi algorithm for minimizing the transmitted energy. In this work, we propose trellis shaping using low-density parity-check codes as the shaping codes. We show that the 2-state min-sum algorithm over the Tanner graph can be used to efficiently implement the energy minimization. This is a more than 4-fold decrease in complexity over 4-state convolutional code-based trellis shaping. Using one of our simple shaping codes, we have observed a shaping gain of up to 0.65 dB (with CER = 1.26; PAPR = 3.86) (as compared with CER=1.41 and PAPR=3.3 for convolutional-code based trellis shaping with similar shaping gain). This encouraging result indicates that more complex LDPC-based approaches will do even better. We also present simulation results to show that constellation shaping provides similar gains over wireless channels under slow fading conditions. ©2007 IEEE.

We investigate the use of capacity and near-capacity achieving LPDC codes on the wire tap channel, where the dual conditions of reliable communications and security are required. We show that good codes for conventional channels (like BSC and BEC) also have interesting and useful security properties. In this paper we show the connection between the decoding threshold of the code and its security against eavesdropping. We also give practical code constructions for some special cases of the wire tap channel and show that security (in the Shannon sense) is a function of the decoding threshold. Some of these constructions achieve the secrecy capacity as denned by Wyner. These codes provide secure communications without conventional key distribution and provide a physical-layer approach for either secure communications or key distribution.

We propose a new information reconciliation method which allows two parties sharing continuous random variables to agree on a common bit string. We show that existing coded modulation techniques can be adapted for reconciliation and give an explicit code construction based on LDPC codes in the case of Gaussian variables. Simulations show that our method achieves higher efficiency than previously reported results. © 2006 IEEE.

In this paper we consider encoder and decoder design for codes achieving perfect secrecy on the wiretap channel. We consider the special case of a noiseless main channel and binary erasure channel (BEC) as the wiretapper's channel and show that it is possible to construct linear-time decodable secrecy codes based on LDPC codes that achieve perfect secrecy.