Mainak Chowdhury

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions.

QualComp: a new lossy compressor for quality scores based on rate distortion theory.

BackgroundNext Generation Sequencing technologies have revolutionized many fields in biology by reducing the time and cost required for sequencing. As a result, large amounts of sequencing data are being generated. A typical sequencing data file may occupy tens or even hundreds of gigabytes of disk space, prohibitively large for many users. This data consists of both the nucleotide sequences and per-base quality scores that indicate the level of confidence in the readout of these sequences. Quality scores account for about half of the required disk space in the commonly used FASTQ format (before compression), and therefore the compression of the quality scores can significantly reduce storage requirements and speed up analysis and transmission of sequencing data.ResultsIn this paper, we present a new scheme for the lossy compression of the quality scores, to address the problem of storage. Our framework allows the user to specify the rate (bits per quality score) prior to compression, independent of the data to be compressed. Our algorithm can work at any rate, unlike other lossy compression algorithms. We envisage our algorithm as being part of a more general compression scheme that works with the entire FASTQ file. Numerical experiments show that we can achieve a better mean squared error (MSE) for small rates (bits per quality score) than other lossy compression schemes. For the organism PhiX, whose assembled genome is known and assumed to be correct, we show that it is possible to achieve a significant reduction in size with little compromise in performance on downstream applications (e.g., alignment).ConclusionsQualComp is an open source software package, written in C and freely available for download at https://sourceforge.net/projects/qualcomp.

Design and performance of noncoherent massive SIMO systems

A system with a single antenna transmitter and a large number of antennas at the receiver is considered. For this system we propose a simple noncoherent communication scheme based on energy detection that does not require knowledge of instantaneous channel state information at either the transmitter or the receiver. We also propose a constellation design based on the minimum distance criterion for this system and present numerical results to demonstrate the performance of this scheme for representative fading and noise statistics. Moreover, we show that this constellation design has the same scaling law performance as a system with perfect channel knowledge at the receiver.

Constellation design in noncoherent massive SIMO systems

An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. For this system we propose an average energy-detection-based one-shot noncoherent communication scheme which does not use the instantaneous channel state information at either the transmitter or the receiver. We provide a constellation design that is asymptotically optimal in terms of achievable error exponent (in the number of receiver antennas) with an increasing constellation size. We also present numerical results on how this design performs in non-asymptotic regimes. Since the channel statistics may not be precisely known, we present a robust constellation design scheme which takes into account possible uncertainty in the large scale statistics and compare numerically its performance with the constellation design assuming perfect knowledge of channel and noise statistics. In terms of achievable symbol error rates, the robust constellation design is shown to perform almost as well as the scheme designed with perfectly known statistics despite mismatch in the channel statistics.

CSI is not needed for optimal scaling in multiuser massive SIMO systems

An uplink system with a fixed number of single antenna transmitters and a single receiver with a large number of antennas is considered. For this system we propose an energy-based noncoherent communication scheme that does not use instantaneous channel state information at either the transmitter or the receiver: only the channel and noise statistics are used.We show that, in terms of the scaling law of achievable symmetric rates for two users, our schemes performance is no different from that achievable with perfect CSI (channel state information) at the transmitters and the receiver. We also provide a simple constellation design using the design criterion of minimum distance and present numerical results on how these designs perform in non-asymptotic regimes with typical channel and noise statistics.

Optimal Pricing to Manage Electric Vehicles in Coupled Power and Transportation Networks

We study the system-level effects of the introduction of large populations of Electric Vehicles (EVs) on the power and transportation networks. We assume that each EV owner solves a decision problem to pick a cost-minimizing charge and travel plan. This individual decision takes into account traffic congestion in the transportation network, affecting travel times, as well as congestion in the power grid, resulting in spatial variations in electricity prices for battery charging. We show that this decision problem is equivalent to finding the shortest path on an “extended” transportation graph, with virtual arcs that represent charging options. Using this extended graph, we study the collective effects of a large number of EV owners individually solving this path planning problem. We propose a scheme in which independent power and transportation system operators can collaborate to manage each network towards a socially optimum operating point while keeping the operational data of each system private. We further study the optimal reserve capacity requirements for pricing in the absence of such collaboration. We showcase numerically that a lack of attention to interdependencies between the two infrastructures can have adverse operational effects.

Benefits of Storage Control for Wind Power Producers in Power Markets

We consider a wind power producer (WPP) participating in a dynamically evolving two settlement power market. We study the utility of energy storage for a WPP in maximizing its expected profit. With random wind and price processes, the optimal forward contract and storage charging/discharging decisions are formulated as solutions of an infinite horizon stochastic optimal control problem. For the asymptotically small storage capacity regime, we precisely characterize the maximum profit increase brought by utilizing energy storage. We prove that, in this regime, an optimal policy uses storage to compensate for power delivery shortfall/surplus in real time, without changing the forward contracts from the optimal ones in the absence of energy storage. This policy also serves as an approximately optimal policy for the case of relatively small storage capacity. We also design a policy based on model predictive control (MPC) that is approximately optimal for general storage capacities. We numerically evaluate the developed policies for wind and price processes with representative statistics from real world data. It is observed that, as expected, the simple small storage approximation policy performs closely to the optimum when storage is relatively small, while the more complex stochastic MPC policy performs better for larger storage capacities.

Scaling Laws for Noncoherent Energy-Based Communications in the SIMO MAC

We consider a one-shot communication setting in which several single antenna transmitters communicate with a receiver with a large number of antennas, i.e., the receiver decodes transmitted information at the end of every symbol time. Motivated by the optimal noncoherent detector in a Rayleigh fading channel, we consider a noncoherent energy-based communication scheme that does not require any knowledge of instantaneous channel state information at either the transmitter or the receiver; it uses only the statistics of the channel and noise. We show that, for general channel fading statistics, the performance of the considered one-shot multiuser noncoherent scheme is the same, in a scaling law sense, as that of the optimal coherent scheme exploiting perfect channel knowledge and coding across time. Furthermore, we present a numerical evaluation of the performance of this scheme in representative fading and noise statistics.

Time-slotted transmission over molecular timing channels

Abstract This work studies time-slotted communication over molecular timing (MT) channels. The transmitter, assumed to be perfectly synchronized in time with the receiver, is required to send K bits to the receiver using K information particles. It releases a single information particle in each time-slot , where the information is encoded in the time of release . The receiver decodes the transmitted information based on the random time of arrivals of the information particles during a finite-time observation window. The maximum-likelihood (ML) detector is derived in terms of the permanent of a matrix involving the arrival times, and shown to have an exponential computational complexity, thus, rendering it impractical. Therefore, two additional (practical) detectors are presented: The first is a symbol-by-symbol detector. The second is a sequence detector which is based on the Viterbi algorithm (VA), yet, the VA is used differently than in its common application in electromagnetic communications where the channels are linear. Numerical simulations indicate that the proposed sequence detection algorithm significantly improves the performance compared to the symbol-by-symbol detector. For a short number of transmitted symbols, the numerical results indicate that the performance of the proposed sequence detector closely approaches the performance of the highly complicated ML detector. Finally, the proposed sequence detector is numerically compared with a one-shot transmission scheme that releases all K particles simultaneously to send a single symbol out of a constellation of size 2 K . It is shown that while for a small number of bits the one-shot scheme is better, when the number of bits is medium to large, the sequence detector achieves significantly better performance.

On Time-Slotted Communication over Molecular Timing Channels

This work studies time-slotted communication over molecular timing (MT) channels. The transmitter, assumed to be perfectly synchronized in time with the receiver, releases a single information particle in each time slot, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrivals of the information particles during a finite-time reception window. The maximum-likelihood (ML) detector is derived and shown to have an exponential computational complexity, thus, rendering it impractical. In addition, two practical detectors are presented: The first is a symbol-by-symbol detector. The second is a sequence detector which is based on the Viterbi algorithm (VA), yet, the VA is used differently than in its common application in ML detection where information is transmitted over linear channels with memory. Numerical simulations indicate that the proposed sequence detection algorithm significantly improves the performance compared to the symbol-by-symbol detector. Furthermore, for a short number of transmitted symbols it closely approaches the highly complicated ML detector.