Andrew Thangaraj

Reed-Muller (RM) codes, a classical family of codes known for their elegant algebraic structure, have recently been shown to achieve capacity under maximum-likelihood (ML) decoding on the binary erasure channel and this has rekindled interest in their efficient decoding. We consider the code family RM(m-3,m) and develop a new ML decoder, for transmission over the binary symmetric channel, that exploits their large symmetry group. The new decoder has lower complexity than an earlier method introduced by Seroussi and Lempel in 1983.

Coded caching is a technique where we utilize multi-casting opportunities to reduce rate in cached networks. One limitation of coded caching schemes is that they reveal the demands of all users to their peers. In this work, we consider coded caching schemes that assure privacy for user demands with a particular focus on reducing subpacketization. For the 2-user, 2-file case, we present a new linear demand-private scheme with the lowest possible subpacketization. This is done by presenting the scheme explicitly and proving impossibility results under lower subpacketization. When only partial privacy is required, we show that subpacketization can be significantly reduced when there are a large number of files.

Classifiers based on Deep Neural Networks (DNNs) are vulnerable to adversarial attacks. To protect DNNs from adversarial attacks, recent research suggests the use of a diverse ensemble of models and combining their outputs. While this provides defence under adversarial input, the total number of parameters in the ensemble is significantly higher when compared to a single network. In this work, we propose a new method for designing and training model ensembles that provides equivalent protection with much fewer parameters. The main idea is to partition the classes into groups and train a shared part in every neural network of the ensemble to separate the classes but cluster groups together by using a carefully designed loss function. The rest of the neural network is trained to classify smaller sets of training classes containing one class from each group. The training classes are varied for different models to achieve diversity. Evaluations with the MNIST and CIFAR10 data sets confirm the effectiveness of our approach when compared with other existing approaches.

Estimation of missing mass or the total probability of unseen letters in a random sample is an important problem with several applications. The Good-Turing (GT) estimator is one of the most popular estimators for missing mass. The bias of the GT estimator is known to fall inversely with the number of samples when they are independent and identically distributed. When the samples form a Markov chain, very little is known about the convergence of the GT estimator even though it is widely used for smoothing in language models that are mostly Markovian. In this work, we initiate and make progress towards characterizing bias of the GT estimator for missing mass in Markov chains. We develop a useful 'multi-letter' characterization of the bias, which leads to sufficient conditions on the transition probability matrix for convergence of the bias of the GT estimator to zero.

Coded caching is a technique where multicasting and coding opportunities are utilized to achieve better rate-memory tradeoff in cached networks. A crucial parameter in coded caching is subpacketization, which is the number of parts a file is to be split into for coding purposes. The Maddah-Ali-Niesen scheme has order-optimal rate, but the subpacketization is exponential in the number of users for certain memory regimes. In contrast, coded caching schemes designed using placement delivery arrays (PDAs) can have linear subpacketization with a penalty in rate. In this work, we propose several constructions of efficient PDAs through lifting, where a base PDA is expanded by replacing each entry by another PDA. By proposing and using the notion of Blackburn-compatibility of PDAs, we provide multiple lifting constructions with increasing coding gains. We compare the constructed coded caching schemes with other existing schemes for moderately high number of users and show that the proposed constructions are versatile and achieve a good rate-memory tradeoff at low subpacketizations.

Motivated by the classical synchronization problem and emerging applications in bioinformatics, we study noisy deletion channels in a regime of practical interest: short code length, low decoding complexity and low SNR. Our work is inspired by an important insight from information theory and Markov chains: appropriately parametrized Markov codewords can correct deletions and errors (due to noise) simultaneously. We extend this idea to practice by developing a low complexity decoder for short Markov codes, which displays competitive performance in simulations at low SNRs. Our decoder design combines the sequence prediction capability of recurrent neural networks with the assured performance of maximum a posteriori (MAP) decoders like the BCJR decoder.

Distribution estimation under error-prone or non-ideal sampling modelled as "sticky"channels have been studied recently motivated by applications such as DNA computing. Missing mass, the sum of probabilities of missing letters, is an important quantity that plays a crucial role in distribution estimation, particularly in the large alphabet regime. In this work, we consider the problem of estimation of missing mass, which has been well-studied under independent and identically distributed (i.i.d) sampling, in the case when sampling is "sticky". Precisely, we consider the scenario where each sample from an unknown distribution gets repeated a geometrically-distributed number of times. We characterise the minimax rate of Mean Squared Error (MSE) of estimating missing mass from such sticky sampling channels. An upper bound on the minimax rate is obtained by bounding the risk of a modified Good-Turing estimator. We derive a matching lower bound on the minimax rate by extending the Le Cam method.