Serially Concatenated Unity-Rate Codes Improve Quantum Codes Without Coding-Rate Reduction

Babar, Zunaira; Nguyen, Hung Viet; Botsinis, Panagiotis; Alanis, Dimitrios; Chandra, Daryus; Ng, Soon Xin; Hanzo, Lajos

doi:10.1109/lcomm.2016.2593874

Cited by 7 publications

(22 citation statements)

References 14 publications

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“…Furthermore, while the CSS-type codes independently correct bit-flip and phaseflip errors, the non-CSS codes jointly correct bit-flip and phaseflip errors. The advent of stabilizer formalism sparked a major revolution in the history of quantum coding, leading to the development of various code families, which includes Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes [94]- [99], toric codes [100]- [102], Quantum Reed-Muller codes [106], Quantum Reed-Solomon codes (QRS) [107], Quantum Low Density Parity Check (QLDPC) codes [110], [164]- [166], Quantum Convolutional Codes (QCC) [114], [167]- [169], Quantum Turbo Codes (QTC) [120], [121], Quantum IRregular Convolutional Codes (QIRCC) [3] as well Quantum Unity Rate Codes (QURC) [139].…”

Section: B Quantum Coding Theory 1) Design Objectivesmentioning

confidence: 99%

“…Hence, the QTCs of [120], [121] exhibit a bounded minimum distance, since they rely on non-recursive non-catastrophic QCCs. For the sake of designing near-capacity QTCs, Babar et al [136] developed EXIT charts for the quantum domain, while a Quantum IrRegular Convolutional Code (QIRCC) structure and Quantum Unity Rate Code (QURC) were proposed in [3] and [139], respectively. Recently, a Fully-Parallel Quantum Turbo Decoder (FPQTD) was conceived in [140], which substantially reduces the decoding latency.…”

Section: B Quantum Coding Theory 1) Design Objectivesmentioning

confidence: 99%

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Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples

Babar

Chandra

Nguyen

et al. 2019

IEEE Commun. Surv. Tutorials

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Quantum Error Correction Codes (QECCs) can be constructed from the known classical coding paradigm by exploiting the inherent isomorphism between the classical and quantum regimes, while also addressing the challenges imposed by the strange laws of quantum physics. In this spirit, this paper provides deep insights into the duality of quantum and classical coding theory, hence aiming for bridging the gap between them. Explicitly, we survey the rich history of both classical as well as quantum codes. We then provide a comprehensive slow-paced tutorial for constructing stabilizer-based QECCs from arbitrary binary as well as quaternary codes, as exemplified by the dual-containing and non-dual-containing Calderbank-Shor-Steane (CSS) codes, non-CSS codes and entanglement-assisted codes. Finally, we apply our discussions to two popular code families, namely to the family of Bose-Chaudhuri-Hocquenghem (BCH) as well as of convolutional codes and provide detailed design examples for both their classical as well as their quantum versions.

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Section: B Quantum Coding Theory 1) Design Objectivesmentioning

confidence: 99%

Section: B Quantum Coding Theory 1) Design Objectivesmentioning

confidence: 99%

Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples

Babar

Chandra

Nguyen

et al. 2019

IEEE Commun. Surv. Tutorials

Self Cite

View full text Add to dashboard Cite

show abstract

“…QBER curves of the half-rate QSBC-QURC scheme having n = {500, 1000, 2000} physical qubits after 16 decoding iterations using Monte Carlo simulations is portrayed in Fig 9. For the sake of benchmarking, we also simulated the QIrCC-QURC scheme from [10] and we added the QBER curves to Fig. 9.…”

Section: B Quantum Bit Error Rate (Qber)mentioning

confidence: 99%

“…Explicitly, as for the QIrCC-QURC scheme, the outer code is constituted by a set of QCCs exhibiting strong error correction performance despite failing to converge fully. The seed transformation of the QCCs that assembles the QIrCC is given in Table II [10]. For more detailed descriptions on QIrCCs, we refer the motivated reader to [16].…”

Section: B Quantum Bit Error Rate (Qber)mentioning

confidence: 99%

“…Hence, this is the first instantiation of high-rate, scalable, short-length, and high-rate QEDCs. • We amalgamate the QSBCs with the QURCs [10] for the sake of constructing soft-decision-aided QECCs without sacrificing the quantum coding rate, which results in a low-complexity high-rate QTC design. We refer to the resultant construction as a QSBC-QURC scheme.…”

Section: Introductionmentioning

confidence: 99%

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Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes

Chandra

Babar

et al. 2019

IEEE Access

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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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Reordered Exponential Golomb Error Correction Code for Universal Near-Capacity Joint Source-Channel Coding

Hamilton,

El-Hajjar,

Maunder

2023

IEEE Access

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Joint Source-Channel Coding (JSCC) is a powerful technique that allows for the efficient transmission of information by simultaneously considering the characteristics of both the source and the channel. The recently proposed Exponential Golomb Error Correction (ExpGEC) and Rice Error Correction (REC) codes provide generalized JSCC schemes for the near capacity coding of symbols drawn from large or infinite alphabets. Yet these require impractical decoding structures, with large buffers and inflexible system design, this was mitigated by the introduction of the Reordered Elias Gamma Error Correction (REGEC) which itself had limited flexibility with regards to source distribution. In this paper, we propose a novel Reordered Exponential Golomb Error Correction (RExpGEC) coding scheme, which is a JSCC technique designed for flexible and practical near-capacity performance. The proposed RExpGEC encoder and decoder are presented and its performance is analysed using Extrinsic Information Transfer (EXIT) charts. The flexibility of the RExpGEC is shown via the novel trellis encoder and decoder design. Finally, the Symbol Error Rate (SER) performance of RExpGEC code is compared when integrated into the novel RExpGEC-URC-QPSK scheme against other comparable JSCC and Separate Source Channel Coding (SSCC) benchmarkers. Specifically the RExpGEC-URC-QPSK scheme is compared against the REGEC-URC-QPSK scheme, and a serial concatenation of the Exponential Golomb and Convolution Code, which becomes the novel Exp-CC-URC-QPSK scheme. Our simulation results demonstrate the performance gains and flexibility of the proposed RExpGEC-URC-QPSK scheme against the benchmarkers in providing reliable and efficient communications. Specifically, the RExpGEC-URC-QPSK scheme outperforms the SSCC in a uncorrelated Rayleigh fading channel by 2 to 3.6 dB (dependent on source distribution). Furthermore, the RExpGEC-URC-QPSK scheme consistently operates within 2.5 dB of channel capacity when measuring E b /N 0 , whilst providing flexibility in SNR performance when compared to the REGEC-URC-QPSK scheme. These performance gains come at the cost of complexity, whereby the RExpGEC-URC-QPSK scheme is 3.6 times more complex than Exp-CC-URC-QPSK scheme under certain conditions. This paper highlights the unique capabilities of RExpGEC as a high performance, practical and flexible JSCC technique.

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Serially Concatenated Unity-Rate Codes Improve Quantum Codes Without Coding-Rate Reduction

Abstract: Abstract-Inspired by the astounding performance of the unity

Cited by 7 publications

References 14 publications

Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples

Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples

Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes

Reordered Exponential Golomb Error Correction Code for Universal Near-Capacity Joint Source-Channel Coding

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