An Iteratively Decodable Tensor Product Code with Application to Data Storage

Alhussien, Hakim; Moon, Jaekyun

doi:10.1109/jsac.2010.100212

Cited by 5 publications

(7 citation statements)

References 38 publications

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“…This phenomenon of degeneracy is quite different from the decoding of classical TPCs [22], [24], [39] where the decoding fails if the number of errors in one sub-block exceeds the error correction ability of the inner codes. As such, AQCTPCs can correct many more X-errors than their classical TPC counterparts.…”

Section: Resultsmentioning

confidence: 89%

“…and GCCs show large potential applications, e.g., in data transmission systems [36] and Flash memory [37], [38]. TPCs and GTPCs exhibit large advantages in magnetic storage systems [39]- [42], Flash memory [43], [44] and in constructing locally repairable codes for distributed storage systems [45]- [47]. In [48], it is shown that Polar codes can be treated as GCCs for a fast encoding.…”

Section: Classical Concatenated Codesmentioning

confidence: 99%

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Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances

Fan

Wang

et al. 2021

IEEE Trans. Commun.

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In many quantum channels, dephasing errors occur more frequently than the amplitude errorsa phenomenon that has been exploited for performance gains and other benefits through asymmetric quantum codes (AQCs). In this paper, we present a new construction of AQCs by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Especially, we derive a first family of binary AQCs with the Zdistance larger than half the block length. Third, AQCTPCs can be efficiently decoded although they

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Section: Resultsmentioning

confidence: 89%

Section: Classical Concatenated Codesmentioning

confidence: 99%

Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances

Fan

Wang

et al. 2021

IEEE Trans. Commun.

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“…L c = 40 and N = 1200, a shortened EPCC of rate 0.68 would incur a staggering rate penalty of 1.7 dB. An alternative concatenation approach that avoids the rate penalty of serial concatenation to a short inner EPCC is discussed in [26].…”

Section: Snr Gain As Function Of L C and M Cmentioning

confidence: 99%

The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs

Alhussien¹,

Moon²

2011

IEEE Trans. Inform. Theory

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The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates. Index TermsInter-symbol interference, turbo equalization, dominant error events, error pattern correcting code, maximum-likelihood bit error rate bound, error weight enumerator, list decoding, dicode channel.

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“…Based on the choice of the component codes, TPCs can be designed to provide error-correction, error-detection or error-location properties. Recently, several classes of TPCs have been considered to be used in data storage systems, e.g., in magnetic recording [1,10,9], in Flash memory [13,26] and in the construction of locally repairable codes which are applied in distributed storage systems [23,22]. In [1], an iteratively decodable TPC by concatenating an error-pattern correction code with a q-ary LDPC code was proposed.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, several classes of TPCs have been considered to be used in data storage systems, e.g., in magnetic recording [1,10,9], in Flash memory [13,26] and in the construction of locally repairable codes which are applied in distributed storage systems [23,22]. In [1], an iteratively decodable TPC by concatenating an error-pattern correction code with a q-ary LDPC code was proposed. The tensor product concatenating scheme could significantly improve the efficiency of the inner parity code while retaining a similar performance.…”

Section: Introductionmentioning

confidence: 99%

On Quantum Tensor Product Codes

Fan¹,

Li²,

Hsieh³

et al. 2016

Preprint

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We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

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An Iteratively Decodable Tensor Product Code with Application to Data Storage

Cited by 5 publications

References 38 publications

Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances

Asymmetric Quantum Concatenated and Tensor Product Codes With Large Z-Distances

The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs

On Quantum Tensor Product Codes

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