arXiv subjects

David Tse

Publications and source records attributed to David Tse.

At least 73 records · Page 4Linked to original sources

arXiv2015

The two-unicast problem

We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity constraints on the directed edges of the network. We propose a simple outer bound for the problem that we call the Generalized Network Sharing (GNS) bound. We show this bound is the tightest edge-cut bound for two-unicast networks and is tight in several bottleneck cases, though it is not tight in general. We also show that the problem of computing the GNS bound is NP-complete. Finally, we show that despite its seeming simplicity, the two-unicast problem is as hard as the most general network coding problem. As a consequence, linear coding is insufficient to achieve capacity for general two-unicast networks, and non-Shannon inequalities are necessary for characterizing capacity of general two-unicast networks.

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arXiv2015

Minimum HGR Correlation Principle: From Marginals to Joint Distribution

Given low order moment information over the random variables $\mathbf{X} = (X_1,X_2,\ldots,X_p)$ and $Y$, what distribution minimizes the Hirschfeld-Gebelein-Rényi (HGR) maximal correlation coefficient between $\mathbf{X}$ and $Y$, while remains faithful to the given moments? The answer to this question is important especially in order to fit models over $(\mathbf{X},Y)$ with minimum dependence among the random variables $\mathbf{X}$ and $Y$. In this paper, we investigate this question first in the continuous setting by showing that the jointly Gaussian distribution achieves the minimum HGR correlation coefficient among distributions with the given first and second order moments. Then, we pose a similar question in the discrete scenario by fixing the pairwise marginals of the random variables $\mathbf{X}$ and $Y$. To answer this question in the discrete setting, we first derive a lower bound for the HGR correlation coefficient over the class of distributions with fixed pairwise marginals. Then we show that this lower bound is tight if there exists a distribution with certain {\it additive} structure satisfying the given pairwise marginals. Moreover, the distribution with the additive structure achieves the minimum HGR correlation coefficient. Finally, we conclude by showing that the event of obtaining pairwise marginals containing an additive structured distribution has a positive Lebesgue measure over the probability simplex.

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arXiv2015

An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems

This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric vehicles. We cast the problem as an optimization program, where the objective is to minimize the losses in the network subject to constraints on bus voltage magnitudes, limits on active and reactive power injections, transmission line thermal limits and losses. We provide sufficient conditions under which the optimization problem can be solved via its convex relaxation. Using data from existing networks, we show that these sufficient conditions are expected to be satisfied by most networks. We also provide an efficient distributed algorithm to solve the problem. The algorithm adheres to a communication topology described by a graph that is the same as the graph that describes the electrical network topology. We illustrate the operation of the algorithm, including its robustness against communication link failures, through several case studies involving 5-, 34-, and 123-bus power distribution systems.

math.OC↗

arXiv2015

Optimal Haplotype Assembly from High-Throughput Mate-Pair Reads

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.

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arXiv2015

Do Read Errors Matter for Genome Assembly?

While most current high-throughput DNA sequencing technologies generate short reads with low error rates, emerging sequencing technologies generate long reads with high error rates. A basic question of interest is the tradeoff between read length and error rate in terms of the information needed for the perfect assembly of the genome. Using an adversarial erasure error model, we make progress on this problem by establishing a critical read length, as a function of the genome and the error rate, above which perfect assembly is guaranteed. For several real genomes, including those from the GAGE dataset, we verify that this critical read length is not significantly greater than the read length required for perfect assembly from reads without errors.

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arXiv2014

Interference alignment for the MIMO interference channel

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.

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arXiv2014

A RM-Polar Codes

In this letter we propose a new hybrid code called "RM-Polar" codes. This new codes are constructed by combining the construction of Reed-Muller (RM) code and Polar code. It has much larger minimum Hamming distance than Polar codes, therefore it has much better error performance than Polar codes.

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arXiv2014

Network Risk Limiting Dispatch: Optimal Control and Price of Uncertainty

Increased uncertainty due to high penetration of renewables imposes significant costs to the system operators. The added costs depend on several factors including market design, performance of renewable generation forecasting and the specific dispatch procedure. Quantifying these costs has been limited to small sample Monte Carlo approaches applied specific dispatch algorithms. The computational complexity and accuracy of these approaches has limited the understanding of tradeoffs between different factors. {In this work we consider a two-stage stochastic economic dispatch problem. Our goal is to provide an analytical quantification and an intuitive understanding of the effects of uncertainties and network congestion on the dispatch procedure and the optimal cost.} We first consider an uncongested network and calculate the risk limiting dispatch. In addition, we derive the price of uncertainty, a number that characterizes the intrinsic impact of uncertainty on the integration cost of renewables. Then we extend the results to a network where one link can become congested. Under mild conditions, we calculate price of uncertainty even in this case. We show that risk limiting dispatch is given by a set of deterministic equilibrium equations. The dispatch solution yields an important insight: congested links do not create isolated nodes, even in a two-node network. In fact, the network can support backflows in congested links, that are useful to reduce the uncertainty by averaging supply across the network. We demonstrate the performance of our approach in standard IEEE benchmark networks.

math.OC↗

arXiv2014

Near-optimal Assembly for Shotgun Sequencing with Noisy Reads

Recent work identified the fundamental limits on the information requirements in terms of read length and coverage depth required for successful de novo genome reconstruction from shotgun sequencing data, based on the idealistic assumption of no errors in the reads (noiseless reads). In this work, we show that even when there is noise in the reads, one can successfully reconstruct with information requirements close to the noiseless fundamental limit. A new assembly algorithm, X-phased Multibridging, is designed based on a probabilistic model of the genome. It is shown through analysis to perform well on the model, and through simulations to perform well on real genomes.

q-bio.GN↗

arXiv2013

Parallel Decoders of Polar Codes

In this letter, we propose parallel SC (Successive Cancellation) decoder and parallel SC-List decoder for polar codes. The parallel decoder is composed of M=2^m(m>=1) component decoders working in parallel and each component decoder decodes a Polar code of a block size of 1/M of the original Polar code. Therefore the parallel decoder has M times faster decoding speed. Our simulation results show that the parallel decoder has almost the same error-rate performance as the conventional non-parallel decoder.

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arXiv2013

Geometry of Power Flows and Optimization in Distribution Networks

We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation constraints. The geometrical object of interest is the set of Pareto-optimal points of the injection region. If the voltage magnitudes are fixed, the injection region of a tree network can be written as a linear transformation of the product of two-bus injection regions, one for each line in the network. Using this decomposition, we show that under the practical condition that the angle difference across each line is not too large, the set of Pareto-optimal points of the injection region remains unchanged by taking the convex hull. Moreover, the resulting convexified optimal power flow problem can be efficiently solved via }{ semi-definite programming or second order cone relaxations. These results improve upon earlier works by removing the assumptions on active power lower bounds. It is also shown that our practical angle assumption guarantees two other properties: (i) the uniqueness of the solution of the power flow problem, and (ii) the non-negativity of the locational marginal prices. Partial results are presented for the case when the voltage magnitudes are not fixed but can lie within certain bounds.

math.OC↗

arXiv2013

A Local Control Approach to Voltage Regulation in Distribution Networks

This paper address the problem of voltage regulation in power distribution networks with deep penetration of distributed energy resources (DERs) without any explicit communication between the buses in the network. We cast the problem as an optimization problem with the objective of minimizing the distance between the bus voltage magnitudes and some reference voltage profile. We present an iterative algorithm where each bus updates the reactive power injection provided by their DER. The update at a bus only depends on the voltage magnitude at that bus, and for this reason, we call the algorithm a local control algorithm. We provide sufficient conditions that guarantee the convergence of the algorithm and these conditions can be checked a priori for a set of feasible power injections. We also provide necessary conditions establishing that longer and more heavily loaded networks are inherently more difficult to control. We illustrate the operation of the algorithm through case studies involving 8-,34- and 123-bus test distribution systems.

math.OC↗

arXiv2013

Optimal DNA shotgun sequencing: Noisy reads are as good as noiseless reads

We establish the fundamental limits of DNA shotgun sequencing under noisy reads. We show a surprising result: for the i.i.d. DNA model, noisy reads are as good as noiseless reads, provided that the noise level is below a certain threshold which can be surprisingly high. As an example, for a uniformly distributed DNA sequence and a symmetric substitution noisy read channel, the threshold is as high as 19%.

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arXiv2013

Optimal Assembly for High Throughput Shotgun Sequencing

We present a framework for the design of optimal assembly algorithms for shotgun sequencing under the criterion of complete reconstruction. We derive a lower bound on the read length and the coverage depth required for reconstruction in terms of the repeat statistics of the genome. Building on earlier works, we design a de Brujin graph based assembly algorithm which can achieve very close to the lower bound for repeat statistics of a wide range of sequenced genomes, including the GAGE datasets. The results are based on a set of necessary and sufficient conditions on the DNA sequence and the reads for reconstruction. The conditions can be viewed as the shotgun sequencing analogue of Ukkonen-Pevzner's necessary and sufficient conditions for Sequencing by Hybridization.

q-bio.GN↗

arXiv2013

Information Theory of DNA Shotgun Sequencing

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technology and the statistics of the DNA sequence, what is the minimum number of reads required for reliable reconstruction? This number provides a fundamental limit to the performance of {\em any} assembly algorithm. For a simple statistical model of the DNA sequence and the read process, we show that the answer admits a critical phenomena in the asymptotic limit of long DNA sequences: if the read length is below a threshold, reconstruction is impossible no matter how many reads are observed, and if the read length is above the threshold, having enough reads to cover the DNA sequence is sufficient to reconstruct. The threshold is computed in terms of the Renyi entropy rate of the DNA sequence. We also study the impact of noise in the read process on the performance.

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arXiv2012

Asynchronous Capacity per Unit Cost

The capacity per unit cost, or equivalently minimum cost to transmit one bit, is a well-studied quantity. It has been studied under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with small amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, we show that the minimum cost to transmit B bits of information asynchronously is (B + \bar{H})k_sync, where k_sync is the synchronous minimum cost per bit and \bar{H} is a measure of timing uncertainty equal to the entropy for most reasonable arrival time distributions. This result holds when the transmitter can stay idle at no cost and is a particular case of a general result which holds for arbitrary cost functions.

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arXiv2012

Coding and System Design for Quantize-Map-and-Forward Relaying

In this paper we develop a low-complexity coding scheme and system design framework for the half duplex relay channel based on the Quantize-Map-and-Forward (QMF) relay- ing scheme. The proposed framework allows linear complexity operations at all network terminals. We propose the use of binary LDPC codes for encoding at the source and LDGM codes for mapping at the relay. We express joint decoding at the destination as a belief propagation algorithm over a factor graph. This graph has the LDPC and LDGM codes as subgraphs connected via probabilistic constraints that model the QMF relay operations. We show that this coding framework extends naturally to the high SNR regime using bit interleaved coded modulation (BICM). We develop density evolution analysis tools for this factor graph and demonstrate the design of practical codes for the half-duplex relay channel that perform within 1dB of information theoretic QMF threshold.

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arXiv2012

An Adaptive Successive Cancellation List Decoder for Polar Codes with Cyclic Redundancy Check

In this letter, we propose an adaptive SC (Successive Cancellation)-List decoder for polar codes with CRC. This adaptive SC-List decoder iteratively increases the list size until the decoder outputs contain at least one survival path which can pass CRC. Simulation shows that the adaptive SC-List decoder provides significant complexity reduction. We also demonstrate that polar code (2048, 1024) with 24-bit CRC decoded by our proposed adaptive SC-List decoder with very large list size can achieve a frame error rate FER=0.001 at Eb/No=1.1dB, which is about 0.2dB from the information theoretic limit at this block length.

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