Polar coded computing: The role of the scaling exponent
Fathollahi D, Mondelli M. 2022. Polar coded computing: The role of the scaling exponent. 2022 IEEE International Symposium on Information Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 2154–2159.
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https://doi.org/10.48550/arXiv.2201.10082
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Conference Paper
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Author
Fathollahi, Dorsa;
Mondelli, MarcoISTA
Department
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 –1/μ ), and (ii) this upper bound can be improved to roughly O(n –1/2 ) by considering polar codes with large kernels. We conjecture that these bounds could be improved to O(n –2/μ ) and O(n –1 ), respectively, and provide a heuristic argument as well as numerical evidence supporting this view.
Publishing Year
Date Published
2022-08-03
Proceedings Title
2022 IEEE International Symposium on Information Theory
Publisher
IEEE
Acknowledgement
D. Fathollahi and M. Mondelli were partially supported by the 2019 Lopez-Loreta Prize. The authors thank Hamed Hassani and Hessam Mahdavifar for helpful discussions.
Volume
2022
Page
2154-2159
Conference
ISIT: Internation Symposium on Information Theory
Conference Location
Espoo, Finland
Conference Date
2022-06-26 – 2022-07-01
ISBN
ISSN
IST-REx-ID
Cite this
Fathollahi D, Mondelli M. Polar coded computing: The role of the scaling exponent. In: 2022 IEEE International Symposium on Information Theory. Vol 2022. IEEE; 2022:2154-2159. doi:10.1109/ISIT50566.2022.9834712
Fathollahi, D., & Mondelli, M. (2022). Polar coded computing: The role of the scaling exponent. In 2022 IEEE International Symposium on Information Theory (Vol. 2022, pp. 2154–2159). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834712
Fathollahi, Dorsa, and Marco Mondelli. “Polar Coded Computing: The Role of the Scaling Exponent.” In 2022 IEEE International Symposium on Information Theory, 2022:2154–59. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834712.
D. Fathollahi and M. Mondelli, “Polar coded computing: The role of the scaling exponent,” in 2022 IEEE International Symposium on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 2154–2159.
Fathollahi D, Mondelli M. 2022. Polar coded computing: The role of the scaling exponent. 2022 IEEE International Symposium on Information Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 2154–2159.
Fathollahi, Dorsa, and Marco Mondelli. “Polar Coded Computing: The Role of the Scaling Exponent.” 2022 IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022, pp. 2154–59, doi:10.1109/ISIT50566.2022.9834712.
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arXiv 2201.10082