A Lower Bound on the Probability of Error of Polar Codes over BMS Channels

Boaz Shuval, Ido Tal

Research output: Contribution to journalArticlepeer-review


Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-wise manner. A decoding error occurs when at least one bit is erroneously decoded. The various codeword bits are correlated, yet performance analysis of polar codes ignores this dependence: the upper bound is based on the union bound, and the lower bound is based on the worst-performing bit. Improvement of the lower bound is afforded by considering error probabilities of two bits simultaneously. These are difficult to compute explicitly due to the large alphabet size inherent to polar codes. In this paper, we propose a method to lower-bound the error probabilities of bit pairs. We develop several transformations on pairs of synthetic channels that make the resultant synthetic channels amenable to alphabet reduction. Our method yields lower bounds that significantly improve upon currently known lower bounds for polar codes under successive-cancellation decoding.

Original languageEnglish
Article number8490744
Pages (from-to)2021-2045
Number of pages25
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2019


  • Channel polarization
  • channel upgrading
  • lower bounds
  • polar codes
  • probability of error

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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