Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes

Seyyed Ali Hashemi, Marco Mondelli, Arman Fazeli, Alexander Vardy, John Cioffi, Andrea Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements P that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is O\left(N^{1-1/\mu}+ \frac{N}{P}\log_{2}\log_{2}\frac{N}{P}\right), where N is the block length of the code and \mu is the scaling exponent of polar codes for the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where P=\frac{N}{2}, the latency of SSC decoding is O\left(N^{1-1/\mu}\right), which is sublinear in the block length. This recovers a result from an earlier work. Second, in a fully-serial implementation where P=1, the latency of SSC decoding scales as O(N\, \log_{2}\log_{2}N). The multiplicative constant is also calculated: we show that the latency of SSC decoding when P=1 is given by (2+o(1))N\, \log_{2}\log_{2}N. Third, in a semi-parallel implementation, the smallest P that gives the same latency as that of the fully-parallel implementation is P=N^{1/\mu}. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.

Original languageEnglish (US)
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2369-2374
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - Jul 12 2021
Externally publishedYes
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: Jul 12 2021Jul 20 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period7/12/217/20/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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