Turbo-XZ Algorithm: Low-Latency Decoders for Quantum LDPC Codes

Nithin Raveendran, Emmanuel Boutillon, Bane Vasic

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

Abstract

We propose a low latency hardware-friendly decoding framework for Calderbank-Shor-Steane (CSS) quantum low-density parity-check (QLDPC) codes under the depolarizing noise model. With a given latency constraint, the proposed decoder, referred to generally as the Turbo-XZ decoding algorithm utilizes the correlation of Pauli X and Z errors. In this framework, we introduce early stopping and switching decoders to meet latency constraints and improve error correction performance for different decoders including the bit-flip (BF), fixed BF (proposed hardware-friendly variant of BF), and normalized min-sum algorithm (nMSA). This decoding framework allows various tradeoffs in terms of latency, complexity, and decoding performance which are discussed briefly. Simulation results show that the BF-Turbo-XZ decoder performs close to (and beyond in some cases) the nMSA version with lower complexity and latency. Our proposed fixed BF approach reduces complexity with minimal performance degradation. For example with a generalized bicycle code, nMSA performs better for higher depolarizing values (p>0.02) at a higher cost, while low-complexity BF-Turbo-XZ decoders are better at low depolarizing values.

Original languageEnglish (US)
Title of host publication2023 12th International Symposium on Topics in Coding, ISTC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798350326116
DOIs
StatePublished - 2023
Event12th International Symposium on Topics in Coding, ISTC 2023 - Brest, France
Duration: Sep 4 2023Sep 8 2023

Publication series

Name2023 12th International Symposium on Topics in Coding, ISTC 2023

Conference

Conference12th International Symposium on Topics in Coding, ISTC 2023
Country/TerritoryFrance
CityBrest
Period9/4/239/8/23

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Safety, Risk, Reliability and Quality

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