Andrew Thangaraj

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.

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.

We show that duals of certain low-density paritycheck (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length n and girth ≥ 2k, for some k ≥ 2. We show that if the minimum left degree of the ensemble is lmin, the expected probability of block error is O(1/n[lmink/2]-k) when the erasure probability ε < εef, where εef depends on the degree distribution of the ensemble. As long as lmin > 2 and k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1-εef. © 2010 IEEE.

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability ε , decays as O(exp (-c 1nc2)) with the block-length n for positive constants c1 and c2 , as long as ε is less than the erasure threshold εth of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than 1-εth. © 2011 IEEE.

This paper Investigates a practical secret key agreement protocol over the Gaussian wire-tap channel. The protocol is based on an efficient information reconciliation method which allows two parties having access to correlated continuous random variables to agree on a common bit string. We describe an explicit reconciliation method based on LDPC codes optimized with EXIT charts and density evolution. When used in conjunction with existing privacy amplication techniques our method allows secret key agreement over the Gaussian wire-tap channel close to the secrecy capacity. © 2006 IEEE.