TY - GEN

T1 - Coded convolution for parallel and distributed computing within a deadline

AU - Dutta, Sanghamitra

AU - Cadambe, Viveck

AU - Grover, Pulkit

N1 - Funding Information:
ment of Electrical & Computer Engineering, Carnegie Mellon University, Pittsburgh, USA. V. Cadambe is with the Department of Electrical Engineering at Pennsylvania State University, University Park, USA. This work was supported in part by NSF-CNS-1702694 and Systems on Nanoscale Information fabriCs (SONIC), one of the six SRC STARnet Centers, sponsored by MARCO and DARPA. F. Franchetti, D. Popovici, T. M. Low, Y. Yang, P. Venkatesh and H. Jeong are thanked for suggestions.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - We consider the problem of computing the convolution of two long vectors using parallel processors in the presence of 'stragglers'. Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides improved resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target 'deadline' time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e., the behavior of the 'tail'. Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems.

AB - We consider the problem of computing the convolution of two long vectors using parallel processors in the presence of 'stragglers'. Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides improved resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target 'deadline' time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e., the behavior of the 'tail'. Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems.

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U2 - 10.1109/ISIT.2017.8006960

DO - 10.1109/ISIT.2017.8006960

M3 - Conference contribution

AN - SCOPUS:85034107899

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2403

EP - 2407

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -