arXiv subjects

Chandra R Murthy

Publications and source records attributed to Chandra R Murthy.

5 recordsLinked to original sources

arXiv2020

Sample-Measurement Tradeoff in Support Recovery under a Subgaussian Prior

Data samples from $\mathbb{R}^{d}$ with a common support of size $k$ are accessed through $m$ random linear projections (measurements) per sample. It is well-known that roughly $k$ measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do $k$ overall measurements still suffice when only $m$ measurements per sample are allowed, with $m<k$? We answer this question in the negative by considering a generative model setting with independent samples drawn from a subgaussian prior. We show that $n=Θ((k^2/m^2)\cdot\log k(d-k))$ samples are necessary and sufficient to recover the support exactly. In turn, this shows that when $m<k$, $k$ overall measurements are insufficient for support recovery; instead we need about $m$ measurements each from $k^{2}/m^2$ samples, i.e., $k^{2}/m$ overall measurements are necessary.

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arXiv2018

Energy Harvesting Communications Using Dual Alternating Batteries

Practical energy harvesting (EH) based communication systems typically use a battery to temporarily store the harvested energy prior to its use for communication. The batteries can be damaged when they are repeatedly charged (discharged) after being partially discharged (charged), overcharged or deeply discharged. This motivates the cycle constraint which says that a battery must be charged (discharged) only after it is sufficiently discharged (charged). We also assume Bernoulli energy arrivals, and a half-duplex constraint due to which the batteries are not charged and discharged simultaneously. In this context, we study EH communication systems with: (a) a single-battery with capacity 2B units and (b) dual-batteries, each having capacity of B units. The aim is to obtain the best possible long-term average throughputs and throughput regions in point-to-point (P2P) channels and multiple access channels (MAC), respectively. For the P2P channel, we obtain an analytical optimal solution in the single-battery case, and propose optimal and sub-optimal power allocation policies for the dual-battery case. We extend these policies to obtain achievable throughput regions in MACs by jointly allocating rates and powers. From numerical simulations, we find that the optimal throughput in the dual-battery case is significantly higher than that in the single-battery case, although the total storage capacity in both cases is 2B units. Further, in the proposed policies, the largest throughput region in the single-battery case is contained within that of the dual-battery case.

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arXiv2018

On the Restricted Isometry of the Columnwise Khatri-Rao Product

The columnwise Khatri-Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often contingent on proving the restricted isometry property (RIP) of a certain system matrix expressible as a Khatri-Rao product of two matrices. In this work, we analyze the RIP of a generic columnwise Khatri-Rao product matrix by deriving two upper bounds for its $k^{\text{th}}$ order Restricted Isometry Constant ($k$-RIC) for different values of $k$. The first RIC bound is computed in terms of the individual RICs of the input matrices participating in the Khatri-Rao product. The second RIC bound is probabilistic, and is specified in terms of the input matrix dimensions. We show that the Khatri-Rao product of a pair of $m \times n$ sized random matrices comprising independent and identically distributed subgaussian entries satisfies $k$-RIP with arbitrarily high probability, provided $m$ exceeds $O(k \log n)$. Our RIC bounds confirm that the Khatri-Rao product exhibits stronger restricted isometry compared to its constituent matrices for the same RIP order. The proposed RIC bounds are potentially useful in the sample complexity analysis of several sparse recovery problems.

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arXiv2011

Two Classes of Broadcast Channels With Side-Information: Capacity Outer Bounds

In this paper, we derive outer bounds on the capacity region of two classes of the general two-user discrete memoryless broadcast channels with side-information at the transmitter. The first class comprises the classical broadcast channel where a sender transmits two independent messages to two receivers. A constraint that each message must be kept confidential from the unintended receiver constitutes the second class. For both classes, the conditional distribution characterizing the channel depends on a state process and the encoder has side-information provided to it in a noncausal manner. For the first class of channels, an outer bound is derived employing techniques used to prove the converse theorem for the Gel'fand-Pinsker's channel with random parameters; the bounds are tight for individual rate constraints, but can be improved upon for the sum rate. The technique for deriving outer bounds for the second class of channels hinges on the confidentiality requirements; we also derive a genie-aided outer bound, where a hypothetical genie gives the unintended message to a receiver which treats it as side-information during equivocation computation. For both classes of channels, Csiszár's sum identity plays a central role in establishing the capacity outer bounds.

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arXiv2011

Secure Broadcasting With Side-Information

In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.

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