List Decoding of Polar Codes

Ido Tal, Alexander Vardy

Research output: Contribution to journalArticlepeer-review


We describe a successive-cancellation list decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Arikan. In the proposed list decoder, L decoding paths are considered concurrently at each decoding stage, where L is an integer parameter. At the end of the decoding process, the most likely among the L paths is selected as the single codeword at the decoder output. Simulations show that the resulting performance is very close to that of maximum-likelihood decoding, even for moderate values of L. Alternatively, if a genie is allowed to pick the transmitted codeword from the list, the results are comparable with the performance of current state-of-the-art LDPC codes. We show that such a genie can be easily implemented using simple CRC precoding. The specific list-decoding algorithm that achieves this performance doubles the number of decoding paths for each information bit, and then uses a pruning procedure to discard all but the L most likely paths. However, straightforward implementation of this algorithm requires Ω (Ln2) time, which is in stark contrast with the O(n log n) complexity of the original successive-cancellation decoder. In this paper, we utilize the structure of polar codes along with certain algorithmic transformations in order to overcome this problem: we devise an efficient, numerically stable, implementation of the proposed list decoder that takes only O(Ln log n) time and O(Ln) space.

Original languageEnglish
Article number7055304
Pages (from-to)2213-2226
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 1 May 2015


  • List decoding
  • polar codes
  • successive cancellation decoding

All Science Journal Classification (ASJC) codes

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


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