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: Contribution to journalArticlepeer-review

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(N1-1/μ + N/P log2 log2 N/P), where N is the block length of the code and μ is the scaling exponent of the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where P = N/2, the latency of SSC decoding is O(N1-1/μ), which is sublinear in the block length. This recovers a result from our earlier work. Second, in a fully-serial implementation where P = 1, the latency of SSC decoding scales as O(N log2 log2 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 log2 log2 N. Third, in a semi-parallel implementation, the smallest P that gives the same latency as that of the fully-parallel implementation is P = N1/μ. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.

Original languageEnglish (US)
JournalIEEE Transactions on Wireless Communications
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics

Keywords

  • Codes
  • Complexity theory
  • Decoding
  • Error probability
  • Hardware
  • latency
  • Polar codes
  • Polar codes
  • successive-cancellation decoding
  • Wireless communication

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