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A note on double insertion/deletion correcting codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第1期49卷 269-273页

作者： Swart, TG Ferreira, HC Rand Afrikaans Univ Lab Cybernet Dept Elect & Elect Engn ZA-2006 Auckland Pk South Africa

By using a run-length representation of sequences, ways to determine sub- and supersequences are discussed. This is then used in determining the number of sub- and supersequences of a sequence after double insertions or deletions. It is also used in creating subsequence/supersequence books that are searched to find new double insertion/deletion correcting code books with higher cardinalities than those already known.

关键词： block codes error-correction coding forward error correction synchronization

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On maximum-length linear congruential-sequences-based low-density parity-check codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2005年第12期53卷 1977-1980页

作者： Sun, J Takeshita, OY Qualcomm Inc San Diego CA 92121 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

This letter extends a low-density parity-check code construction using maximum-length linear congruential sequences by Prabhakar and Narayanan. The corresponding bipartite graphs of their construction were guaranteed to have a girth larger than four by a sufficient condition. However, their sufficient condition was limited to regular codes and data-node degree equal to three. The extension in this letter allows arbitrary data-node degrees and is applicable to irregular codes. Further, simpler sufficient conditions are derived and larger girths are addressed.

关键词： error-correction coding graph theory low-density parity-check (LDPC) codes permutation sequences

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Runlength limited codes for single error-detection and single error-correction with mixed type errors

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IEEE TRANSACTIONS ON INFORMATION THEORY 1998年第4期44卷 1588-1592页

作者： Perry, P Li, MC Lin, MC Zhang, Z Univ Guam Dept Math Mangilao GU 96923 USA Univ So Calif Los Angeles CA 90089 USA Natl Taiwan Univ Dept Elect Engn Taipei 10764 Taiwan

Runlength-limited (RLL) codes are used in magnetic recording. The error patterns that occur with peak detection magnetic recording systems when using a runlength-limited code consist of both symmetric errors and shift errors, We will refer to shift errors and symmetric errors collectively as mixed-type errors. In this correspondence, a method of providing error control for mixed-type errors that occur in a runlength-limited code comprised of(d, k) constrained sequences is examined. The coding scheme is to choose parity blocks to insert in the constrained information sequence. The parity blocks are chosen to satisfy the constraints and to provide some error control. The cases of single error detection and single error correction are investigated, where the single error is allowed to be a shift error or a symmetric error. Bounds are discussed on the possible lengths for the parity blocks. It is shown that the single error-detection codes are the best possible in terms of the length of the parity blocks.

关键词： error-correction coding error-detection coding RLL codes

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An efficient chase decoder for turbo product codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2004年第6期52卷 896-898页

作者： Argon, C McLaughlin, SW Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

In this letter, we propose an efficient decoding algorithm for turbo product codes as introduced by Pyndiah. The proposed decoder has no performance degradation and reduces the complexity of the original decoder by an order of magnitude. We concentrate on extended Bose-Chaudhuri-Hocquengem codes as the constituent row and column codes because of their already low implementation complexity. For these component codes, we observe that the weight and reliability factors can be fixed, and that there is no need for normalization. Furthermore, as opposed to previous efficient decoders, the newly proposed decoder naturally scales with a test-pattern parameter p that can change as a function of iteration number, i.e., the efficient Chase algorithm presented here uses conventionally ordered test patterns, and the syndromes, even parities, and extrinsic metrics are obtained with a minimum number of operations.

关键词： block turbo code chase algorithm error-correction coding iterative decoding turbo code turbo product code (TPC)

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Improved High Code-Rate Soft BCH Decoder Architectures With One Extra error Compensation

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2013年第11期21卷 2160-2164页

作者： Lin, Yi-Min Chang, Hsie-Chia Lee, Chen-Yi Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90005 USA Natl Chiao Tung Univ Dept Elect Engn Hsinchu 30050 Taiwan Natl Chiao Tung Univ Inst Elect Hsinchu 30050 Taiwan

Compared with traditonal hard Bose-Chaudhuri-Hochquenghem (BCH) decoders, soft BCH decoders provide better error-correcting performance but much higher hardware complexity. In this brief, an improved soft BCH decoding algorithm is presented to achieve both competitive hardware complexity and better error-correcting performance by dealing with least reliable bits and compensating one extra error outside the least reliable set. For BCH (255, 239;2) and (255, 231;3) codes, our proposed soft BCH decoders can achieve up to 0.75-dB coding gain with one extra error compensation and 5% less complexity than the traditional hard BCH decoders.

关键词： Bose-Chaudhuri-Hochquenghem (BCH) codes error-correction coding soft decoding

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ASYMPTOTIC BOUNDS FOR UNIDIRECTIONAL BYTE error-CORRECTING CODES

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1993年第9期E76A卷 1437-1441页

作者： SAITOH, Y IMAI, H Univ of Tokyo Tokyo Japan

Asymptotic bounds are considered for unidirectional byte error-correcting codes. Upper bounds are developed from the concepts of the Singleton, Plotkin, and Hamming bounds. Lower bounds are also derived from a combination of the generalized concatenated code construction and, the Varshamov-Gilbert bound. As the result, we find that there exist codes of low rate better than those on the basis of Hamming distance with respect to unidirectional byte error-correction.

关键词： ASYMPTOTIC BOUND error-correction coding GENERALIZED CONCATENATED coding UNIDIRECTIONAL BYTE error VARSHAMOV-GILBERT BOUND

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Design of 4/6 ITI-mitigating error correction modulation code for ultra-high-density bit-patterned media recording systems

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ELECTRONICS LETTERS 2020年第18期56卷 931-933页

作者： Nguyen, C. D. Phenikaa Univ Fac Elect & Elect Engn Hanoi 12116 Vietnam Phenikaa Res & Technol Inst PRATI A&A Green Phoenix Grp JSC 167 Hoang Ngan Hanoi 11313 Vietnam

A design of 4/6 intertrack-interference (ITI)-mitigating error correction modulation code for bit-patterned media recording systems is proposed in this Letter. Generally, coding schemes in data storage devices are usually accomplished using a combination of error-correction coding and modulation coding. However, an interesting approach is that the modulation code itself has the capability of correcting errors. Such a modulation code design will reduce the total size and complexity of the data storage devices. In this Letter, the authors design a new 4/6 modulation code, where the code not only mitigates the effect of ITI but also maintains minimum Hamming distance of 2 to build up a trellis structure providing error correction capability of the proposed code. Simulation results show that the proposed design outperforms prior arts. For instance, the performance of the proposed design is better than that of a conventional 4/6 modulation code about 8 dB at a bit error rate of 10(-7)under 20% read-head offtrack for the area density of 4 Tb/in(2).

关键词： error statistics intersymbol interference error correction codes Viterbi decoding magnetic recording error correction channel coding modulation coding modulation coding correcting errors modulation code design data storage devices authors design error correction capability bit error rate ultra-high-density bit-patterned media bit-patterned media recording systems error-correction coding noise figure 8 0 dB

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Reliable Communication over Non-Binary Insertion/Deletion Channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第12期60卷 3597-3608页

作者： Yazdani, Raman Ardakani, Masoud Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2V4 Canada

We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the received sequence and all symbols are corrupted by additive white Gaussian noise. To this end, we utilize the inherent redundancy achievable in non-binary symbol sets by first expanding the symbol set and then allocating part of the bits associated with each symbol to watermark symbols. The watermark sequence, known at the receiver, is then used by a forward-backward algorithm to provide soft information for an outer code which decodes the transmitted sequence. Through numerical results and discussions, we evaluate the performance of the proposed solution and show that it leads to significant system ability to detect and correct insertions/deletions. We also provide estimates of the maximum achievable information rates of the system, compare them with the available bounds, and construct practical codes capable of approaching these limits.

关键词： Concatenated coding error-correction coding insertion/deletion channels watermark codes hidden Markov models (HMM)

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Rate adaptation of convolutional coded optical CDMA systems for improved goodput

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OPTICS COMMUNICATIONS 2004年第4-6期240卷 315-327页

作者： Juan, L Mutafungwa, E Aalto Univ Commun Lab FIN-02015 Espoo Finland

Rate adaptation is a technique that enables the selection of the most suitable error-correction coding rate according to the real-time channel quality, therefore increasing the overall throughput. We propose the use of rate adaptive convolutional codes for amplitude encoded, binary on-off keyed optical code-division multiple access (OCDMA) systems. Conventional OCDMA systems have a bit error probability floor due to optical multiple-user interference (OMUI). A convolutional coded OCDMA system (CC-OCDMA) lowers the error floors with increased coding rates but at the expense of reduced goodput (throughput minus the redundancy bits or symbols). However, by exploiting the variation of OMUI with user number, it is shown here that rate adaptation offers larger and consistent goodput improvements compared to fixed coding rate CC-OCDMA systems for various traffic profiles. This advantage is also observed in comparisons with OCDMA systems using improved receiver designs and 2D wavelength/time signatures codes. Based on the analytical results obtained here and the commercial availability of convolutional coding chipsets, rate-adaptive convolutional coding for OCDMA systems is worth to be considered for practical implementation. (C) 2004 Elsevier B.V. All rights reserved.

关键词： optical code-division multiple access multiple-user interference error-correction coding goodput analysis

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Algorithm-based low-power/high-speed Reed-Solomon decoder design

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2000年第11期47卷 1254-1270页

作者： Raghupathy, A Liu, KJR Univ Maryland Dept Elect Engn College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA

With the spread of Reed-Solomon (RS) codes to portable wireless applications, low-power RS decoder design has become important. This paper discusses how the Berlekamp Massey Decoding algorithm can be modified and mapped to obtain a low-power architecture. In addition, architecture level modifications that speed-up the syndrome and error computations are proposed. Then the VLSI architecture and design of the proposed low-power/high-speed decoder is presented, The proposed design is compared with a normal design that does not use these algorithm/architecture modifications. The power reduction when compared to the normal design is estimated. The results indicate a power reduction of about 40% or a speed-up of 1,34.

关键词： Berlekamp Massey algorithm Channel coding decoding error-correction coding Forney's method high-speed integrated circuits low power systems parallel algorithms parallel architectures Reed-Solomon codes very-large-scale integration

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