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# Near-hashing-bound multiple-rate quantum turbo short-block codes

Chandra, Daryus, Babar, Zunaira, Ng, Soon and Hanzo, Lajos (2019) Near-hashing-bound multiple-rate quantum turbo short-block codes. IEEE Access, 7, 52712-52730.

Record type: Article

## Abstract

Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate, since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated quantum turbo code (QTC) design exhibiting a high quantum coding rate. The high quantum coding rate is achieved by combining the quantum-domain version of short-block codes (SBCs) also known as single parity check (SPC) codes as the outer codes and quantum unity-rate codes (QURCs) as the inner codes. Despite its design simplicity, the proposed QTC yields a near-hashing-bound error correction performance. For instance, compared to the best half-rate QTC known in the literature, namely the QIrCC-QURC scheme, which operates at the distance of $D = 0.037$ from the quantum hashing bound, our novel QSBC-QURC scheme can operate at the distance of $D = 0.029$. It is worth also mentioning that this is the first instantiation of QTCs capable of adjusting the quantum encoders according to the quantum coding rate required for mitigating the Pauli errors given the different depolarizing probabilities of the quantum channel.

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IEEE_QSBC - Accepted Manuscript
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near-hashing - Version of Record

Accepted/In Press date: 12 April 2019
e-pub ahead of print date: 15 April 2019
Keywords: quantum error detection codes, quantum error correction codes, concatenated codes, iterative decoding, topological codes, quantum turbo codes, short-block codes

## Identifiers

Local EPrints ID: 430418
URI: http://eprints.soton.ac.uk/id/eprint/430418
ISSN: 2169-3536
PURE UUID: f58e02d9-e813-49b0-9052-18850527a27d
ORCID for Daryus Chandra: orcid.org/0000-0003-2406-7229
ORCID for Zunaira Babar: orcid.org/0000-0002-7498-4474
ORCID for Soon Ng: orcid.org/0000-0002-0930-7194
ORCID for Lajos Hanzo: orcid.org/0000-0002-2636-5214

## Catalogue record

Date deposited: 30 Apr 2019 16:30

## Contributors

Author: Daryus Chandra
Author: Zunaira Babar
Author: Soon Ng
Author: Lajos Hanzo