Sameer Pawar

Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesnt+nr-1 where T is the number of time slots over which coding takes place and nt,nr are the number of transmit and receive antennas, respectively. For T nt case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all Tgesnt is the same as that previously known to hold for Tgesnt+n r-1

Securing Dynamic Distributed Storage Systems Against Eavesdropping and Adversarial Attacks

We address the problem of securing distributed storage systems against eavesdropping and adversarial attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from an intruder who may come at different time instances during the lifetime of the storage system to observe and possibly alter the data stored on some nodes. In this scenario, we give upper bounds on the maximum amount of information that can be stored safely on the system. For an important operating regime of the distributed storage system, which we call the bandwidth-limited regime, we show that our upper bounds are tight and provide explicit code constructions. Moreover, we provide a way to short list the malicious nodes and expurgate the system.

Codes can reduce queueing delay in data centers

In this paper, we quantify how much codes can reduce the data retrieval latency in storage systems. By combining a simple linear code with a novel request scheduling algorithm, which we call Blocking-one Scheduling (BoS), we show analytically that it is possible to use codes to reduce data retrieval delay by up to 17% over currently popular replication-based strategies. Although in this work we focus on a simplified setting where the storage system stores a single content, the methodology developed can be applied to more general settings with multiple contents. The results also offer insightful guidance to the design of storage systems in data centers and content distribution networks.

DRESS codes for the storage cloud: Simple randomized constructions

We introduce an efficient family of exact regenerating codes for data storage in large-scale distributed systems. We refer to these new codes as Distributed Replication-based Exact Simple Storage (DRESS) codes. A key property of DRESS codes is their very efficient distributed and uncoded repair and growth processes that have minimum bandwidth, reads and computational overheads. This property is essential for large-scale systems with high reliability and availability requirements. DRESS codes will first encode the file using a Maximum Distance Separable (MDS) code, then place multiple replicas of the coded packets on different nodes in the system. We propose a simple and flexible randomized scheme for placing those replicas based on the balls-and-bins model. Our construction showcases the power of the probabilistic approach in constructing regenerating codes that can be efficiently repaired and grown.

On secure distributed data storage under repair dynamics

We address the problem of securing distributed storage systems against passive eavesdroppers that can observe a limited number of storage nodes. An important aspect of these systems is node failures over time, which demand a repair mechanism aimed at maintaining a targeted high level of system reliability. If an eavesdropper observes a node that is added to the system to replace a failed node, it will have access to all the data downloaded during repair, which can potentially compromise the entire information in the system.We are interested in determining the secrecy capacity of distributed storage systems under repair dynamics, i.e., the maximum amount of data that can be securely stored and made available to a legitimate user without revealing any information to any eavesdropper. We derive a general upper bound on the secrecy capacity and show that this bound is tight for the bandwidth-limited regime which is of importance in scenarios such as peer-to-peer distributed storage systems. We also provide a simple explicit code construction that achieves the capacity for this regime.

Diversity-multiplexing tradeoff of the half-duplex relay channel

We show that the diversity-multiplexing tradeoff of a half-duplex single-relay channel with identically distributed Rayleigh fading channel gains meets the 2 by 1 MISO bound. We generalize the result to the case when there are N non-interfering relays and show that the diversity-multiplexing tradeoff is equal to the N + 1 by 1 MISO bound.

Deterministic algorithm for the cooperative data exchange problem

In this paper we study the problem of data exchange, where each node in the system has a number of linear combinations of the data packets. Communicating over a public channel, the goal is for all nodes to reconstruct the entire set of the data packets in minimal total number of bits exchanged over the channel. We present a novel divide and conquer based architecture that determines the number of bits each node should transmit. This along with the well known fact, that it is sufficient for the nodes to broadcast linear combinations of their local information, provides a polynomial time deterministic algorithm for reconstructing the entire set of the data packets at all nodes in minimal amount of total communication.

Codes for a distributed caching based Video-on-Demand system

We study the role of codes in the optimization and design of a large-scale Video-on-Demand (VoD) system based on distributed caching, that we have architected and built at Berkeley. We show how network codes can convert a combinatorial problem into a tractable one, and enable a fully distributed algorithm that jointly optimizes the three-fold problem of cache content placement, cache-to-users topology selection, and cache-to-users rate-allocation. While a description of the general VoD system optimization and design can be found in [1], this paper focuses on the critical role of codes in enabling our VoD system. Specifically, we motivate and describe a specific class of network codes, called DRESS codes, that offer desirable tradeoffs between cache-to-user and cache-to-cache communication aspects of the problem needed to sustain a scalable VoD system.

Cooperative multiplexing in the multiple antenna half duplex relay channel

Cooperation between terminals has been proposed to improve the reliability and throughput of wireless communication. While recent work has shown that relay cooperation provides increased diversity, increased multiplexing gain over that offered by direct link has largely been unexplored. In this work we show that cooperative multiplexing gain can be achieved by using a half duplex relay. We capture relative distances between terminals in the high SNR diversity multiplexing tradeoff (DMT) framework. The DMT performance is then characterized for a network having a single antenna half-duplex relay between a single-antenna source and two-antenna destination. Our results show that the achievable multiplexing gain using cooperation can be greater than that of the direct link and is a function of the relative distance between source and relay compared to the destination. Moreover, for multiplexing gains less than 1, a simple scheme of the relay listening 1/3 of the time and transmitting 2/3 of the time can achieve the 2 by 2 MIMO DMT.

A hybrid DFT-LDPC framework for fast, efficient and robust compressive sensing

We use a hybrid mix of the Discrete Fourier Transform (DFT), an old workhorse in digital signal processing, and Low Density Parity Check (LDPC) codes, a recent workhorse in coding theory, to generate a linear measurement lens through which to perform compressive sensing (CS) of sparse high-dimensional signals. This novel hybrid DFT-LDPC framework represents a new family of sparse measurement matrices, and induces a fast algorithm (dubbed the Short-and-Wide Iterative Fast Transform based or SWIFT algorithm) for robustly recovering a high-dimensional k-sparse signal x, in Cn, from a near-optimal (upto a small constant multiple of k) number of linear observations, with a decoding complexity of k steps, under high signal-to-noise-ratio (SNR). A key attribute of our sensing framework and the SWIFT recovery algorithm is that both the sensing efficiency (number of measurements) and the recovery efficiency (decoding complexity) are independent of the ambient signal dimension n for the noiseless and high-SNR noisy regimes, which is particularly attractive when k <;<; n. This contrasts existing solutions1 in the CS literature based on the class of Linear Programming (LP)-based optimization techniques and the class of expander graph based greedy-pursuit (sketching) algorithms; for both these classes, both the number of measurements and the decoding complexity depend explicitly on the ambient signal dimension n, even for the noiseless and high-SNR regimes. We provide both an explicit constructions of the DFT-LDPC based matrix framework and an analytical characterization of the SWIFT recovery algorithm. Although our analytical characterization is for asymptotic values of k, n and for high SNR regime, our simulation results validate the efficiency of the SWIFT algorithm even for the low-to-moderate SNR regimes and modest problem dimensions (e.g., k = 250 and n = 20000), beyond what we can currently prove analytically.