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- W4289713086 abstract "We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes is investigated. In this paper, we focus on polar codes and unveil a connection between the average execution time and the scaling exponent μ of the family of codes. In the finite-length characterization of polar codes, the scaling exponent is a key object capturing the speed of convergence to capacity. In particular, we show that (i) the gap between the normalized average execution time of polar codes and that of optimal MDS codes is O(n <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>–1/μ</sup> ), and (ii) this upper bound can be improved to roughly O(n <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>–1/2</sup> ) by considering polar codes with large kernels. We conjecture that these bounds could be improved to O(n <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>–2/μ</sup> ) and O(n <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>–1</sup> ), respectively, and provide a heuristic argument as well as numerical evidence supporting this view." @default.
- W4289713086 created "2022-08-04" @default.
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- W4289713086 date "2022-06-26" @default.
- W4289713086 modified "2023-09-25" @default.
- W4289713086 title "Polar Coded Computing: The Role of the Scaling Exponent" @default.
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- W4289713086 doi "https://doi.org/10.1109/isit50566.2022.9834712" @default.
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