arXiv subjects

Mehul Motani

Publications and source records attributed to Mehul Motani.

At least 55 records · Page 3Linked to original sources

arXiv2017

Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources

Motivated by streaming multi-view video coding and wireless sensor networks, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converge, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse square root of the blocklength $n$, while the error probability decays subexponentially fast in $n$. Our main result focuses on directions of approaches to corner points of the Slepian-Wolf region. It states that for each correlated source and all corner points, there exists a non-empty subset of directions of approaches such that the moderate deviations constant (the constant of proportionality for the subexponential decay of the error probability) is enhanced (over the non-streaming case) by at least a factor of $T$, the block delay of decoding source block pairs. We specialize our main result to the setting of streaming lossless source coding and generalize this result to the setting where we have different delay requirements for each of the two source blocks. The proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information-theoretic streaming literature. We adapt the so-called truncated memory encoding idea from Draper and Khisti (2011) and Lee, Tan, and Khisti (2016) to ensure that the effect of error accumulation is nullified in the limit of large blocklengths. We also adapt the use of the so-called minimum weighted empirical suffix entropy decoder which was used by Draper, Chang, and Sahai (2014) to derive achievable error exponents for symbolwise streaming Slepian-Wolf coding.

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arXiv2017

Non-Asymptotic Converse Bounds and Refined Asymptotics for Two Lossy Source Coding Problems

In this paper, we revisit two multi-terminal lossy source coding problems: the lossy source coding problem with side information available at the encoder and one of the two decoders, which we term as the Kaspi problem (Kaspi, 1994), and the multiple description coding problem with one semi-deterministic distortion measure, which we refer to as the Fu-Yeung problem (Fu and Yeung, 2002). For the Kaspi problem, we first present the properties of optimal test channels. Subsequently, we generalize the notion of the distortion-tilted information density for the lossy source coding problem to the Kaspi problem and prove a non-asymptotic converse bound using the properties of optimal test channels and the well-defined distortion-tilted information density. Finally, for discrete memoryless sources, we derive refined asymptotics which includes the second-order, large and moderate deviations asymptotics. In the converse proof of second-order asymptotics, we apply the Berry-Esseen theorem to the derived non-asymptotic converse bound. The achievability proof follows by first proving a type-covering lemma tailored to the Kaspi problem, then properly Taylor expanding the well-defined distortion-tilted information densities and finally applying the Berry-Esseen theorem. We then generalize the methods used in the Kaspi problem to the Fu-Yeung problem. As a result, we obtain the properties of optimal test channels for the minimum sum-rate function, a non-asymptotic converse bound and refined asymptotics for discrete memoryless sources. Since the successive refinement problem is a special case of the Fu-Yeung problem, as a by-product, we obtain a non-asymptotic converse bound for the successive refinement problem, which is a strict generalization of the non-asymptotic converse bound for successively refinable sources (Zhou, Tan and Motani, 2017).

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arXiv2017

Performance of Energy Harvesting Receivers with Power Optimization

The difficulty of modeling energy consumption in communication systems leads to challenges in energy harvesting (EH) systems, in which nodes scavenge energy from their environment. An EH receiver must harvest enough energy for demodulating and decoding. The energy required depends upon factors, like code rate and signal-to-noise ratio, which can be adjusted dynamically. We consider a receiver which harvests energy from ambient sources and the transmitter, meaning the received signal is used for both EH and information decoding. Assuming a generalized function for energy consumption, we maximize the total number of information bits decoded, under both average and peak power constraints at the transmitter, by carefully optimizing the power used for EH, power used for information transmission, fraction of time for EH, and code rate. For transmission over a single block, we find there exist problem parameters for which either maximizing power for information transmission or maximizing power for EH is optimal. In the general case, the optimal solution is a tradeoff of the two. For transmission over multiple blocks, we give an upper bound on performance and give sufficient and necessary conditions to achieve this bound. Finally, we give some numerical results to illustrate our results and analysis.

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arXiv2017

Layered Coding for Energy Harvesting Communication Without CSIT

Due to stringent constraints on resources, it may be infeasible to acquire the current channel state information at the transmitter in energy harvesting communication systems. In this paper, we optimize an energy harvesting transmitter, communicating over a slow fading channel, using layered coding. The transmitter has access to the channel statistics, but does not know the exact channel state. In layered coding, the codewords are first designed for each of the channel states at different rates, and then the codewords are either time-multiplexed or superimposed before the transmission, leading to two transmission strategies. The receiver then decodes the information adaptively based on the realized channel state. The transmitter is equipped with a finite-capacity battery having non-zero internal resistance. In each of the transmission strategies, we first formulate and study an average rate maximization problem with non-causal knowledge of the harvested power variations. Further, assuming statistical knowledge and causal information of the harvested power variations, we propose a sub-optimal algorithm, and compare with the stochastic dynamic programming based solution and a greedy policy.

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arXiv2017

Bounds on the Size and Asymptotic Rate of Subblock-Constrained Codes

The study of subblock-constrained codes has recently gained attention due to their application in diverse fields. We present bounds on the size and asymptotic rate for two classes of subblock-constrained codes. The first class is binary constant subblock-composition codes (CSCCs), where each codeword is partitioned into equal sized subblocks, and every subblock has the same fixed weight. The second class is binary subblock energy-constrained codes (SECCs), where the weight of every subblock exceeds a given threshold. We present novel upper and lower bounds on the code sizes and asymptotic rates for binary CSCCs and SECCs. For a fixed subblock length and small relative distance, we show that the asymptotic rate for CSCCs (resp. SECCs) is strictly lower than the corresponding rate for constant weight codes (CWCs) (resp. heavy weight codes (HWCs)). Further, for codes with high weight and low relative distance, we show that the asymptotic rates for CSCCs is strictly lower than that of SECCs, which contrasts that the asymptotic rate for CWCs is equal to that of HWCs. We also provide a correction to an earlier result by Chee et al. (2014) on the asymptotic CSCC rate. Additionally, we present several numerical examples comparing the rates for CSCCs and SECCs with those for constant weight codes and heavy weight codes.

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arXiv2017

Energy Harvesting Communication Using Finite-Capacity Batteries with Internal Resistance

Modern systems will increasingly rely on energy harvested from their environment. Such systems utilize batteries to smoothen out the random fluctuations in harvested energy. These fluctuations induce highly variable battery charge and discharge rates, which affect the efficiencies of practical batteries that typically have non-zero internal resistances. In this paper, we study an energy harvesting communication system using a finite battery with non-zero internal resistance. We adopt a dual-path architecture, in which harvested energy can be directly used, or stored and then used. In a frame, both time and power can be split between energy storage and data transmission. For a single frame, we derive an analytical expression for the rate optimal time and power splitting ratios between harvesting energy and transmitting data. We then optimize the time and power splitting ratios for a group of frames, assuming non-causal knowledge of harvested power and fading channel gains, by giving an approximate solution. When only the statistics of the energy arrivals and channel gains are known, we derive a dynamic programming based policy and, propose three sub-optimal policies, which are shown to perform competitively. In summary, our study suggests that battery internal resistance significantly impacts the design and performance of energy harvesting communication systems and must be taken into account.

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arXiv2017

Polar Coding for the Binary Erasure Channel with Deletions

We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a list decoding algorithm with a cyclic redundancy check for this case. The decoding complexity is $O(N^2\log N)$, where $N$ is the blocklength of the code. An important contribution is an optimization of the amount of redundancy added to minimize the overall error probability. Our theoretical results are corroborated by numerical simulations which show that the list size can be reduced to one and the original message can be recovered with high probability as the length of the code grows.

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arXiv2017

Discrete Lossy Gray-Wyner Revisited: Second-Order Asymptotics, Large and Moderate Deviations

In this paper, we revisit the discrete lossy Gray-Wyner problem. In particular, we derive its optimal second-order coding rate region, its error exponent (reliability function) and its moderate deviations constant under mild conditions on the source. To obtain the second-order asymptotics, we extend some ideas from Watanabe's work (2015). In particular, we leverage the properties of an appropriate generalization of the conditional distortion-tilted information density, which was first introduced by Kostina and Verdú (2012). The converse part uses a perturbation argument by Gu and Effros (2009) in their strong converse proof of the discrete Gray-Wyner problem. The achievability part uses two novel elements: (i) a generalization of various type covering lemmas; and (ii) the uniform continuity of the conditional rate-distortion function in both the source (joint) distribution and the distortion level. To obtain the error exponent, for the achievability part, we use the same generalized type covering lemma and for the converse, we use the strong converse together with a change-of-measure technique. Finally, to obtain the moderate deviations constant, we apply the moderate deviations theorem to probabilities defined in terms of information spectrum quantities.

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arXiv2016

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

We derive the optimal second-order coding region and moderate deviations constant for successive refinement source coding with a joint excess-distortion probability constraint. We consider two scenarios: (i) a discrete memoryless source (DMS) and arbitrary distortion measures at the decoders and (ii) a Gaussian memoryless source (GMS) and quadratic distortion measures at the decoders. For a DMS with arbitrary distortion measures, we prove an achievable second-order coding region, using type covering lemmas by Kanlis and Narayan and by No, Ingber and Weissman. We prove the converse using the perturbation approach by Gu and Effros. When the DMS is successively refinable, the expressions for the second-order coding region and the moderate deviations constant are simplified and easily computable. For this case, we also obtain new insights on the second-order behavior compared to the scenario where separate excess-distortion proabilities are considered. For example, we describe a DMS, for which the optimal second-order region transitions from being characterizable by a bivariate Gaussian to a univariate Gaussian, as the distortion levels are varied. We then consider a GMS with quadratic distortion measures. To prove the direct part, we make use of the sphere covering theorem by Verger-Gaugry, together with appropriately-defined Gaussian type classes. To prove the converse, we generalize Kostina and Verdú's one-shot converse bound for point-to-point lossy source coding. We remark that this proof is applicable to general successively refinable sources. In the proofs of the moderate deviations results for both scenarios, we follow a strategy similar to that for the second-order asymptotics and use the moderate deviations principle.

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arXiv2016

On Error Exponents and Moderate Deviations for Lossless Streaming Compression of Correlated Sources

We derive upper and lower bounds for the error exponents of lossless streaming compression of two correlated sources under the blockwise and symbolwise settings. We consider the linear scaling regime in which the delay is a scalar multiple of the number of symbol pairs of interest. We show that for rate pairs satisfying certain constraints, the upper and lower bounds for the error exponent of blockwise codes coincide. For symbolwise codes, the bounds coincide for rate pairs satisfying the aforementioned constraints and a certain condition on the symbol pairs we wish to decode---namely, that their indices are asymptotically comparable to the blocklength. We also derive moderate deviations constants for blockwise and symbolwise codes, leveraging the error exponent results, and using appropriate Taylor series expansions. In particular, for blockwise codes, we derive an information spectrum-type strong converse, giving the complete characterization of the moderate deviations constants. For symbolwise codes, under an additional requirement on the backoff from the first-order fundamental limit, we can show that the moderate deviations constants are the same as the blockwise setting.

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arXiv2015

Subblock-Constrained Codes for Real-Time Simultaneous Energy and Information Transfer

Consider an energy-harvesting receiver that uses the same received signal both for decoding information and for harvesting energy, which is employed to power its circuitry. In the scenario where the receiver has limited battery size, a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy. In this paper, we consider a discrete memoryless channel and characterize achievable information rates when the energy content in each codeword is regularized by ensuring that sufficient energy is carried within every subblock duration. In particular, we study constant subblock-composition codes (CSCCs) where all subblocks in every codeword have the same fixed composition, and this subblock-composition is chosen to maximize the rate of information transfer while meeting the energy requirement. Compared to constant composition codes (CCCs), we show that CSCCs incur a rate loss and that the error exponent for CSCCs is also related to the error exponent for CCCs by the same rate loss term. We show that CSCC capacity can be improved by allowing different subblocks to have different composition while still meeting the subblock energy constraint. We provide numerical examples highlighting the tradeoff between delivery of sufficient energy to the receiver and achieving high information transfer rates. It is observed that the ability to use energy in real-time imposes less of penalty than the ability to use information in real-time.

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arXiv2014

Analyzing DISH for Multi-Channel MAC Protocols in Wireless Networks

For long, node cooperation has been exploited as a data relaying mechanism. However, the wireless channel allows for much richer interaction between nodes. One such scenario is in a multi-channel environment, where transmitter-receiver pairs may make incorrect decisions (e.g., in selecting channels) but idle neighbors could help by sharing information to prevent undesirable consequences (e.g., data collisions). This represents a Distributed Information SHaring (DISH) mechanism for cooperation and suggests new ways of designing cooperative protocols. However, what is lacking is a theoretical understanding of this new notion of cooperation. In this paper, we view cooperation as a network resource and evaluate the availability of cooperation via a metric, $p_{co}$, the probability of obtaining cooperation. First, we analytically evaluate $p_{co}$ in the context of multi-channel multi-hop wireless networks. Second, we verify our analysis via simulations and the results show that our analysis accurately characterizes the behavior of $p_{co}$ as a function of underlying network parameters. This step also yields important insights into DISH with respect to network dynamics. Third, we investigate the correlation between $p_{co}$ and network performance in terms of collision rate, packet delay, and throughput. The results indicate a near-linear relationship, which may significantly simplify performance analysis for cooperative networks and suggests that $p_{co}$ be used as an appropriate performance indicator itself. Throughout this work, we utilize, as appropriate, three different DISH contexts --- model-based DISH, ideal DISH, and real DISH --- to explore $p_{co}$.

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arXiv2014

A Metric for DISH Networks: Analysis, Implications, and Applications

In wireless networks, node cooperation has been exploited as a data relaying mechanism for decades. However, the wireless channel allows for much richer interaction among nodes. In particular, Distributed Information SHaring (DISH) represents a new improvement to multi-channel MAC protocol design by using a cooperative element at the control plane. In this approach, nodes exchange control information to make up for other nodes' insufficient knowledge about the environment, and thereby aid in their decision making. To date, what is lacking is a theoretical understanding of DISH. In this paper, we view cooperation as a network resource and evaluate the availability of cooperation, $p_{co}$. We first analyze $p_{co}$ in the context of a multi-channel multi-hop wireless network, and then perform simulations which show that the analysis accurately characterizes $p_{co}$ as a function of underlying network parameters. Next, we investigate the correlation between $p_{co}$ and network metrics such as collision rate, packet delay, and throughput. We find a near-linear relationship between $p_{co}$ and the metrics, which suggests that $p_{co}$ can be used as an appropriate performance indicator itself. Finally, we apply our analysis to solving a channel bandwidth allocation problem, where we derive optimal schemes and provide general guidelines on bandwidth allocation for DISH networks.

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arXiv2014

Energy-Efficient Strategies for Cooperative Multi-Channel MAC Protocols

Distributed Information SHaring (DISH) is a new cooperative approach to designing multi-channel MAC protocols. It aids nodes in their decision making processes by compensating for their missing information via information sharing through other neighboring nodes. This approach was recently shown to significantly boost the throughput of multi-channel MAC protocols. However, a critical issue for ad hoc communication devices, i.e., energy efficiency, has yet to be addressed. In this paper, we address this issue by developing simple solutions which (1) reduce the energy consumption (2) without compromising the throughput performance, and meanwhile (3) maximize cost efficiency. We propose two energy-efficient strategies: in-situ energy conscious DISH which uses existing nodes only, and altruistic DISH which needs additional nodes called altruists. We compare five protocols with respect to the strategies and identify altruistic DISH to be the right choice in general: it (1) conserves 40-80% of energy, (2) maintains the throughput advantage gained from the DISH approach, and (3) more than doubles the cost efficiency compared to protocols without applying the strategy. On the other hand, our study shows that in-situ energy conscious DISH is suitable only in certain limited scenarios.

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arXiv2014

Second-Order Coding Rates for Conditional Rate-Distortion

This paper characterizes the second-order coding rates for lossy source coding with side information available at both the encoder and the decoder. We first provide non-asymptotic bounds for this problem and then specialize the non-asymptotic bounds for three different scenarios: discrete memoryless sources, Gaussian sources, and Markov sources. We obtain the second-order coding rates for these settings. It is interesting to observe that the second-order coding rate for Gaussian source coding with Gaussian side information available at both the encoder and the decoder is the same as that for Gaussian source coding without side information. Furthermore, regardless of the variance of the side information, the dispersion is $1/2$ nats squared per source symbol.

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arXiv2014

Fading Two-Way Relay Channels: Physical-Layer Versus Digital Network Coding

In this paper, we consider three transmit strategies for the fading three-node, two-way relay network (TWRN) -- physical-layer network coding (PNC), digital network coding (DNC) and codeword superposition (CW-Sup). The aim is to minimize the total average energy needed to deliver a given pair of required average rates. Full channel state information is assumed to be available at all transmitters and receivers. The optimization problems corresponding to the various strategies in fading channels are formulated, solved and compared. For the DNC-based strategies, a simple time sharing of transmission of the network-coded message and the remaining bits of the larger message (DNC-TS) is considered first. We extend this approach to include a superposition strategy (DNC-Sup), in which the network-coded message and the remainder of the longer source message are superimposed before transmission. It is demonstrated theoretically that DNC-Sup outperforms DNC-TS and CW-Sup in terms of total average energy usage. More importantly, it is shown in simulation that DNC-Sup performs better than PNC if the required rate is low and worse otherwise. Finally, an algorithm to select the optimal strategy in terms of energy usage subject to different rate pair requirements is presented.

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arXiv2014

A Case Where Interference Does Not Affect The Channel Dispersion

In 1975, Carleial presented a special case of an interference channel in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this work, we show that if the inequalities in the conditions that Carleial stated are strict, the dispersions are similarly unaffected. More precisely, in this work, we characterize the second-order coding rates of the Gaussian interference channel in the strictly very strong interference regime. In other words, we characterize the speed of convergence of rates of optimal block codes towards a boundary point of the (rectangular) capacity region. These second-order rates are expressed in terms of the average probability of error and variances of some modified information densities which coincide with the dispersion of the (single-user) Gaussian channel. We thus conclude that the dispersions are unaffected by interference in this channel model.

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arXiv2012

Digital Network Coding Aided Two-way Relaying: Energy Minimization and Queue Analysis

In this paper, we consider a three node, two-way relay system with digital network coding over static channels where all link gains are assumed to be constant during transmission. The aim is to minimize total energy consumption while ensuring queue stability at all nodes, for a given pair of random packet arrival rates. Specifically, we allow for a set of transmission modes and solve for the optimal fraction of resources allocated to each mode, including multiaccess uplink transmission mode and network coding broadcasting mode. In addition, for the downlink, we find the condition to determine whether superposition coding with excess data over the better link and network coded data for both users is energy efficient and the corresponding optimization is formulated and solved. To tackle the queue evolution in this network, we present a detailed analysis of the queues at each node using a random scheduling method that closely approximates the theoretical design, through a two-dimensional Markov chain model.

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