Vinod M. Prabhakaran

On compressing encrypted data

When it is desired to transmit redundant data over an insecure and bandwidth-constrained channel, it is customary to first compress the data and then encrypt it. In this paper, we investigate the novelty of reversing the order of these steps, i.e., first encrypting and then compressing, without compromising either the compression efficiency or the information-theoretic security. Although counter-intuitive, we show surprisingly that, through the use of coding with side information principles, this reversal of order is indeed possible in some settings of interest without loss of either optimal coding efficiency or perfect secrecy. We show that in certain scenarios our scheme requires no more randomness in the encryption key than the conventional system where compression precedes encryption. In addition to proving the theoretical feasibility of this reversal of operations, we also describe a system which implements compression of encrypted data.

Decentralized erasure codes for distributed networked storage

In this correspondence, we consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We want a data collector, who can appear anywhere in the network, to query any k storage nodes and be able to retrieve the data. We introduce decentralized erasure codes, which are linear codes with a specific randomized structure inspired by network coding on random bipartite graphs. We show that decentralized erasure codes are optimally sparse, and lead to reduced communication, storage and computation cost over random linear coding.

Interference Channels With Destination Cooperation

Interference is a fundamental feature of the wireless channel. To better understand the role of cooperation in interference management, the two-user Gaussian interference channel where the destination nodes can cooperate by virtue of being able to both transmit and receive is studied. The sum capacity of this channel is characterized up to a constant number of bits. The coding scheme employed builds up on the superposition scheme of Han and Kobayashi for two-user interference channels without cooperation. New upperbounds to the sum capacity are also derived.

Interference Channels With Source Cooperation

In this paper, the role of cooperation in managing interference-a fundamental feature of the wireless channel-is investigated by studying the two-user Gaussian interference channel where the source nodes can both transmit and receive in full duplex. The sum capacity of this channel is obtained within a gap of a constant number of bits. The coding scheme used builds up on the superposition scheme of Han and Kobayashi for the two-user interference channel without cooperation. New upperbounds on the sum capacity are also derived. The same coding scheme is shown to obtain the sum capacity of the symmetric two-user Gaussian interference channel with noiseless feedback within a constant gap.

Distributed Fountain Codes for Networked Storage

We investigate the problem of constructing fountain codes for distributed storage in sensor networks. Specifically, we assume that there are n storage nodes with limited memory and k < n data nodes generating the data by sensing the environment. We want a data collector who can appear anywhere in the network, to query any k + epsi storage nodes and be able to retrieve almost all the data packets. We demonstrate how it is possible to solve this problem by using a specific kind of fountain code that requires only linear communication and decoding complexity. Further, for a grid topology, we propose a randomized algorithm that constructs the fountain code over a network using only geographical knowledge and local decisions. A key step in the analysis of our algorithm is a novel result concerning random walks on finite grids with traps

Towards a theory for video coding using distributed compression principles

This paper presents an information-theoretic study of video codecs that are based on the principle of source coding with side information at the decoder. In contrast to the classical Wyner-Ziv side-information source coding problem (1976), in this work we address the situation where the source and side-information are connected through a state of nature that is unknown to both the encoder and the decoder. We dub this framework as source encoding with side-information under ambiguous state of nature (SEASON). Our objective is to compare the achievable rate-distortion (R/D) performance of conventional video codecs designed under the motion-compensated predictive coding (MCPC) framework and video codecs designed under the SEASON framework. Our analysis shows that under appropriate motion models and for Gaussian displaced frame difference (DFD) statistics, the R/D performance of a classical MCPC-based video codec is matched by that of our proposed SEASON-based video codec, with the hitter being characterized by the novel concept of moving the motion compensation task from the encoder to the decoder.

The secrecy capacity of a class of parallel Gaussian compound wiretap channels

The compound wiretap channel provides a general framework for studying secrecy communication under channel uncertainty. Characterizing the secrecy capacity of nondegraded compound wiretap channels is a challenging problem in information theory. This paper considers the class of parallel Gaussian compound wiretap channels with only one possible channel realization for the legitimate receiver and characterizes the secrecy capacity. (Such parallel Gaussian compound wiretap channels are generally nondegraded.) Moreover, it is shown that the proposed coding scheme strictly outperforms the best known single-letter scheme with Gaussian codebooks.

Hybrid Digital-Analog Codes for Source-Channel Broadcast of Gaussian Sources Over Gaussian Channels

The problem of broadcasting a parallel Gaussian source over an additive white Gaussian noise broadcast channel under the mean-squared error distortion criterion is studied. A hybrid digital-analog coding strategy which combines source coding with side information, channel coding with side information, layered source coding, and superposition broadcast channel coding is presented. When specialized to the open problem of broadcasting a white Gaussian source over an additive white Gaussian noise broadcast channel with bandwidth mismatch, which has been the subject of several previous investigations, this coding scheme strictly improves on the state of the art.

Secrecy via sources and channels — A secret key - Secret message rate tradeoff region

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available - correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve. No other resource, in particular, no other channel is available. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution based on a separation architecture and prove its optimality under three settings: when Eves source and channel are degraded versions of Bobs, and either Bobs source or channel is by itself useless in generating a secret key.

Critical database size for effective caching

Replicating or caching popular content in memories distributed across the network is a technique to reduce peak network loads. Conventionally, the performance gain of caching was thought to result from making part of the requested data available closer to end users. Recently, it has been shown that by using a carefully designed technique to store the contents in the cache and coding across data streams a much more significant gain can be achieved in reducing the network load. Inner and outer bounds on the network load v/s cache memory tradeoff were obtained in [1]. We give an improved outer bound on the network load v/s cache memory tradeoff. We also address the question of to what extent caching is effective in reducing the server load when the number of files becomes large as compared to the number of users. We show that the effectiveness of caching become small when the number of files becomes comparable to the square of the number of users.