arXiv subjects

Vinod Prabhakaran

Publications and source records attributed to Vinod Prabhakaran.

9 recordsLinked to original sources

arXiv2020

On the Capacity Enlargement of Gaussian Broadcast Channels with Passive Noisy Feedback

It is well known that the capacity region of an average transmit power constrained Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers is enlarged by the presence of causal noiseless feedback. Capacity region enlargement is also known to be possible by using only passive noisy feedback, when the GBC has identical noise variances at the receivers. The last fact remains true even when the feedback noise variance is very high, and available only from one of the receivers. While such capacity enlargements are feasible for several other feedback models in the Gaussian BC setting, it is also known that feedback does not change the capacity region for physically degraded broadcast channels. In this paper, we consider a two user GBC with independent noise realizations at the receivers, where the feedback links from the receivers are corrupted by independent additive Gaussian noise processes. We investigate the set of four noise variances, two forward and two feedback, for which no capacity enlargement is possible. A sharp characterization of this region is derived, i.e., any quadruple outside the presented region will lead to a capacity enlargement, whereas quadruples inside will leave the capacity region unchanged. Our results lead to the conclusion that when the forward noise variances are different, too noisy a feedback from one of the receivers alone is not always beneficial for enlarging the capacity region, be it from the stronger user or the weaker one, in sharp contrast to the case of equal forward noise variances.

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arXiv2017

Private Coded Caching

Recent work by Maddah-Ali and Niesen introduced coded caching which demonstrated the benefits of joint design of storage and transmission policies in content delivery networks. They studied a setup where a server communicates with a set of users, each equipped with a local cache, over a shared error-free link and proposed an order-optimal caching and delivery scheme. In this paper, we introduce the problem of secretive coded caching where we impose the additional constraint that a user should not be able to learn anything, from either the content stored in its cache or the server transmissions, about a file it did not request. We propose a feasible scheme for this setting and demonstrate its order-optimality with respect to information-theoretic lower bounds.

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arXiv2017

Plausible Deniability over Broadcast Channels

In this paper, we introduce the notion of Plausible Deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party have enough freedom to produce a fake output that is likely plausible given the eavesdropper's observation. We examine three variants of this problem -- Message Deniability, Transmitter Deniability, and Receiver Deniability. In the first setting, the message sender is summoned to produce the sent message. Similarly, in the second and third settings, the transmitter and the receiver are required to produce the transmitted codeword, and the received vector respectively. For each of these settings, we examine the maximum communication rate that allows a given minimum rate of plausible fake outputs. For the Message and Transmitter Deniability problems, we fully characterise the capacity region for general broadcast channels, while for the Receiver Deniability problem, we give an achievable rate region for physically degraded broadcast channels.

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arXiv2016

Lower Bounds for Interactive Function Computation via Wyner Common Information

The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus is on coming up with lower bounds on this. The information cost of a protocol is the amount of information the protocol reveals to Alice and Bob about each others inputs, and the information complexity of a function is the infimum of information costs over all valid protocols. For the amortized case, it is known that the optimal rate for the computation is equal to the information complexity. Exactly computing this information complexity is not straight forward however. In this work we lower bound information complexity for independent inputs in terms of the Wyner common information of a certain pair of random variables. We show a structural property for the optimal auxiliary random variable of Wyner common information and exploit this to exactly compute the Wyner common information in certain cases. The lower bound obtained through this technique is shown to be tight for a non-trivial example - equality (EQ) for the ternary alphabet. We also give an example to show that the lower bound may, in general, not be tight.

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arXiv2016

Capacity Results for Multicasting Nested Message Sets over Combination Networks

The problem of multicasting two nested messages is studied over a class of networks known as combination networks. A source multicasts two messages, a common and a private message, to several receivers. A subset of the receivers (called the public receivers) only demand the common message and the rest of the receivers (called the private receivers) demand both the common and the private message. Three encoding schemes are discussed that employ linear superposition coding and their optimality is proved in special cases. The standard linear superposition scheme is shown to be optimal for networks with two public receivers and any number of private receivers. When the number of public receivers increases, this scheme stops being optimal. Two improvements are discussed: one using pre-encoding at the source, and one using a block Markov encoding scheme. The rate-regions that are achieved by the two schemes are characterized in terms of feasibility problems. Both inner-bounds are shown to be the capacity region for networks with three (or fewer) public and any number of private receivers. Although the inner bounds are not comparable in general, it is shown through an example that the region achieved by the block Markov encoding scheme may strictly include the region achieved by the pre-encoding/linear superposition scheme. Optimality results are founded on the general framework of Balister and Bollobás (2012) for sub-modularity of the entropy function. An equivalent graphical representation is introduced and a lemma is proved that might be of independent interest. Motivated by the connections between combination networks and broadcast channels, a new block Markov encoding scheme is proposed for broadcast channels with two nested messages. The rate-region that is obtained includes the previously known rate-regions. It remains open whether this inclusion is strict.

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arXiv2014

Interference Channels with Half-Duplex Source Cooperation

The performance gain by allowing half-duplex source cooperation is studied for Gaussian interference channels. The source cooperation is {\em in-band}, meaning that each source can listen to the other source's transmission, but there is no independent (or orthogonal) channel between the sources. The half-duplex constraint supposes that at each time instant the sources can either transmit or listen, but not do both. Our main result is a characterization of the sum capacity when the cooperation is bidirectional and the channel gains are symmetric. With unidirectional cooperation, we essentially have a cognitive radio channel. By requiring the primary to achieve a rate close to its link capacity, the best possible rate for the secondary is characterized within a constant. Novel inner and outer bounds are derived as part of these characterizations.

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arXiv2013

Using Feedback for Secrecy over Graphs

We study the problem of secure message multicasting over graphs in the presence of a passive (node) adversary who tries to eavesdrop in the network. We show that use of feedback, facilitated through the existence of cycles or undirected edges, enables higher rates than possible in directed acyclic graphs of the same mincut. We demonstrate this using code constructions for canonical combination networks (CCNs). We also provide general outer bounds as well as schemes for node adversaries over CCNs.

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arXiv2010

Assisted Common Information with Applications to Secure Two-Party Computation

Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party's output than what its own output reveals. To aid in this, they have available a set up - correlated random variables whose distribution is different from the desired distribution - as well as unlimited noiseless communication. In this paper we present an upperbound on how efficiently a given set up can be used to produce samples from a desired distribution. The key tool we develop is a generalization of the concept of common information of two dependent random variables [Gacs-Korner, 1973]. Our generalization - a three-dimensional region - remedies some of the limitations of the original definition which captured only a limited form of dependence. It also includes as a special case Wyner's common information [Wyner, 1975]. To derive the cryptographic bounds, we rely on a monotonicity property of this region: the region of the "views" of Alice and Bob engaged in any protocol can only monotonically expand and not shrink. Thus, by comparing the regions for the target random variables and the given random variables, we obtain our upperbound.

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arXiv2006

Decentralized Erasure Codes for Distributed Networked Storage

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.

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