Improved reconciliation with polar codes in quantum key distribution

Sunghoon Lee, Jooyoun Park, Jun Heo

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing (CPP). Information reconciliation is a part of CPP in which parties are given correlated variables and attempt to eliminate the discrepancies between them while disclosing a minimum amount of information. The elegant reconciliation protocol known as Cascade was developed specifically for QKD in 1992 and has become the de-facto standard for all QKD implementations. However, the protocol is highly interactive. Thus, other protocols based on linear block codes such as Hamming codes, low-density parity-check (LDPC) codes, and polar codes have been researched. In particular, reconciliation using LDPC codes has been mainly studied because of its outstanding performance. Nevertheless, with small block size, the bit error rate performance of polar codes under successive-cancellation list (SCL) decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art turbo and LDPC codes. In this study, we demonstrate the use of polar codes to improve the performance of information reconciliation in a QKD system with small block size. The best decoder for polar codes, a CRC-aided SCL decoder, requires CRC-precoded messages. However, messages that are sifted keys in QKD are obtained arbitrarily as a result of a characteristic of the QKD protocol and cannot be CRC-precoded. We propose a method that allows arbitrarily obtained sifted keys to be CRC precoded by introducing a virtual string. Thus the best decoder can be used for reconciliation using polar codes and improves the efficiency of the protocol.

Original languageEnglish
Pages (from-to)795-813
Number of pages19
JournalQuantum Information and Computation
Issue number9-10
Publication statusPublished - 2018 Aug

Bibliographical note

Funding Information:
This work was supported by the ICT R&D program of MSIP/IITP [1711028311, Reliable crypto-system standards and core technology development for secure quantum key distribution network].

Publisher Copyright:
© Rinton Press.


  • Information reconciliation
  • Polar codes
  • Quantum key distribution
  • Small block size
  • Successive-cancellation list decoder

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Computational Theory and Mathematics


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