Burst Error Correction Research Articles

Improving Burst Error Tolerance of LDPC-Centric Coding Systems in Read Channel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We report on the use of low-density parity check (LDPC)-centric error correction coding (ECC) for magnetic recording read channel in the presence of significant burst errors. Since an LDPC code by itself is severely vulnerable to burst errors due to its soft-decision probability-based decoding, we focus on LDPC-centric concatenated coding in which LDPC code is used as inner code. To improve the burst error tolerance, we propose a hybrid LDPC-centric concatenated coding strategy in which one inner LDPC codeword is replaced by another codeword with much stronger burst error correction capability. This special inner codeword reveals the burst error location information, which can be leveraged by the inner LDPC code decoding to largely improve the overall robustness to burst errors. Using a hybrid BCH-LDPC/RS concatenated coding system as a test vehicle, we demonstrate a significant performance advantage over its RS-only and LDPC-only counterparts in the presence of three different types of burst errors. </para>

AN UPPER BOUND ON THE NUMBER OF PARITY CHECKS FOR BURST ERROR DETECTION AND CORRECTION IN EUCLIDEAN CODES

There are three standard weight functions on a linear code viz. Hamming weight, Lee weight, and Euclidean weight. Euclidean weight function is useful in connection with the lattice constructions (2) where the minimum norm of vectors in the lattice is related to the min- imum Euclidean weight of the code. In this paper, we obtain an upper bound over the number of parity check digits for Euclidean weight codes detecting and correcting burst errors.

Localization of a Target with Three Degrees of Freedom Using a Low Cost Wireless Infrared Sensor Network

The estimation of the position of a mobile target on a plane as well as its orientation is an important aspect for many applications. The indoor or outdoor localization of such a target has been widely addressed in the literature but if a third degree of freedom like rotation has to be also taken into consideration the difficulty in estimating the target position and orientation is significantly increased. A network consisting of only a small number of low cost infrared transmitters/receivers is used in this paper to estimate the position of a mobile target on a plane as well as its draft orientation with an angular step of 45o or less. The distance and orientation estimation is based on the success rate that infrared patterns are retrieved at the target. This success rate parameter is calculated by simple ultra low cost microcontrollers. The architectural complexity and cost of the overall localization system is significantly lower than other approaches without sacrificing speed and accuracy. An error correction scheme like Turbo decoding is applied in order to increase the reliability and stability of the results by correcting burst errors introduced by real time noise.

Performance analysis of burst-mode receivers with clock phase alignment and forward error correction for GPON

We experimentally demonstrate the performance analysis of burst-mode receivers (BMRx) in a 622 Mb/s 20-km gigabit-capable passive optical network (GPON) uplink. Our receiver features automatic phase acquisition using a clock phase aligner (CPA), and forward-error correction using (255, 239) Reed-Solomon (RS) codes. The BMRx provides instantaneous (0 preamble bit) phase acquisition and a packet-loss ratio (PLR) < 10?6 for any phase step (±2? rads) between consecutive packets, while also supporting more than 600 consecutive identical digits (CIDs). The receiver also accomplishes a 3-dB coding gain at a bit-error rate (BER) of 10?10. The CPA makes use of a phase picking algorithm and an oversampling clock-and-data recovery circuit operated at 2× the bit rate. The receiver meets the GPON physical media dependent layer specifications defined in the ITU-T recommendation G.984.2 standard. We investigate the PLR performance of the system and quantify it as a function of the phase step between consecutive packets, received signal power, CID immunity, and BER, while also assessing the tradeoffs in preamble length, power penalty, and pattern correlator error resistance. We also study the impact of mode-partition noise in the GPON uplink in terms of the effective PLR and BER coding gain performance of the system. In addition, we demonstrate how the CPA and the RS(255, 239) codes can be used in tandem for dynamic burst-error correction giving reliable BERs in bursty channels.

Experimental Study on 42.7-Gb/s Forward-Error-Correction Performance Under Burst Errors

We describe a novel method to experimentally investigate the performances of forward-error-correction (FEC) codes in the presence of burst errors with various burst length and duty cycle. Using this method, we observe that the coding gains of two commercial 42.7-Gb/s FEC codes are greatly reduced by long and dense error bursts. A correlation between the FEC performance and the FEC burst-error correction length is clearly shown. In addition, the measurement also shows an increase in coding gain in cases with certain short error bursts as compared to the reference case of steady-state white Gaussian noise.

ON THE GENERALIZED-LEE-RT-PSEUDO-METRIC (THE GLRTP-METRIC) ARRAY CODES CORRECTING BURST ERRORS

In [16], the author introduced a new pseudo-metric on the space Matm×s(Zq) which is the module space of all m × s matrices with entries from the finite ring Zq generalizing the classical Lee metric (see [17]) and the array RT- metric (see [19]) and named this pseudo-metric as the Generalized-Lee-RT-Pseudo-Metric (or the GLRTP-Metric). In this paper, we obtain some lower bounds for two dimensional array codes correcting burst errors (see [10]) with weight constraints under the GLRTP-metric.

A 100-Gb/s-Physical-Layer Architecture for Higher-Speed Ethernet for VSR and Backplane Applications

A high-speed physical-layer architecture for next-generation higher-speed Ethernet for VSR and backplane applications was developed. VSR and backplane networks provide 100-Gb/s data transmission in mega data centers and blade servers, which have new and broad potential markets of LAN technologies. It supports 100-Gb/s-throughput, high-reliability, and low-latency data transmission, making it well suited to VSR and backplane applications for intra-building and intra-cabinet networks. Its links comprise ten 10-Gb/s high-speed serial lanes. Payload data are transmitted by ribbon fiber cables for very short reach and by copper channels for the backplane board. Ten lanes convey 320-bit data synchronously (32 bits x 10 lanes) and parity data of forward-error correction code (newly developed (544, 512) code FEC), providing highly reliable (BER<1E-22) data transmission with a burst-error correction with low latency (31.0 ns on the transmitter (Tx) side and 111.6 ns on the receiver (Rx) side). A 64B/66B code-sequence-based skew compensation mechanism, which provides low-latency compensation for the lane-to-lane skew (less than 51ns), is used for parallel transmission. Testing this physical-layer architecture in an ASIC showed that it can provide 100-Gb/s data transmission with a 772-kgate circuit, which is small enough for implementation in a single LSI.

Inaudible watermarking via phase manipulation of random frequencies

Watermarking technology can be beneficial in digital rights protection. However, the industry's acceptance of the technology has been lukewarm as experts have been able to hear audible artifacts introduced during the watermarking process. In this paper, we present what we believe to be a truly inaudible solution to this problem. Our proposed watermarking technique embeds the watermark signal in the phase of an audio signal, with secrecy as to which frequency components carry the watermark bits, achieved via a pseudorandom generator. Inaudibility is realized by exploiting the human auditory system's insensitivity to absolute phase. Further, our algorithm includes a novel mechanism for segmenting an audio signal into variable frame-lengths to provide robustness against de-synchronization attacks such as jitter and time-scaling. It uses a short-time Fourier transform to first characterize local changes in the frequency content of an audio signal, from which, pairs of frequencies satisfying specified conditions are identified, to mark the start and end of a segment. The insertion of synchronization marks adds further robustness against such attacks. Robustness against other common attacks may be further enhanced through the use of concatenated error-control codes which enable the correction of random and/or burst errors, which may be introduced during an attack.

Sufficient Condition over the Number of Parity Checks for Burst Error Detection/Correction in Linear Lee Weight Codes

Lee weight is more appropriate for some practical situations than Hamming weight as it takes into account the magnitude of each digit of the word. In this paper, we obtain a sufficient bound over the number of parity check digits for codes detecting burst errors and also for codes correcting burst errors with Lee weight.

CT bursts—from classical to array coding

R.T. Chien and D.T. Tang [On definition of a burst, IBM J. Res. Develop. 9 (1965) 292–293] introduced the concept of Chien and Tang bursts (CT bursts) for classical coding systems where codes are subsets (or subspaces) of the space F q n , the space of all n-tuples with entries from a finite field F q . In this paper, we extend the notion of CT bursts for array coding systems where array codes are subsets (or subspaces) of the space Mat m × s ( F q ) , the linear space of all m × s matrices with entries from a finite field F q , endowed with a non-Hamming metric [M.Yu. Rosenbloom, M.A. Tsfasman, Codes for m-metric, Problems Inform. Transmission 33 (1997) 45–52]. We also obtain some bounds on the parameters of array codes for the detection and correction of CT burst errors.

Optimal Interleaving Schemes for Two-Dimensional Arrays

Given an mtimesn array of k single random error correction (or erasure) codewords, each having length l such that mn=kl, we construct optimal interleaving schemes that provide the maximum burst error correction power such that an arbitrarily shaped error burst of size t can be corrected for the largest possible value of t. We show that for all such mtimesn arrays, the maximum possible interleaving distance, or equivalently, the largest value of t such that an arbitrary error burst of size up to t can be corrected, is bounded by lfloorradic2krfloor if kleslceil(min{m,n}) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /2rceil, and by min{m,n}+lfloor(k-lceil(min{m,n}) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> /2rceil)/min{m,n}rfloor if kgeslceil(min{m,n}) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /2rceil. We generalize the cyclic shifting algorithm developed by the authors in a previous paper and construct, in several special cases, optimal interleaving arrays achieving these upper bounds. Additionally, for codewords of variable lengths, we solve a related array coloring problem for which the same upper bounds hold and can be achieved

Campopiano-type bounds in non-Hamming array coding

Campopiano [C.N. Campopiano, Bounds on burst error correcting codes, IRE Trans. IT-8 (1962) 257–259] obtained an upper bound for burst error correction in classical coding systems where codes are subsets/subspaces of the space F q n , the space of all n-tuples with entries from a finite field F q equipped with the Hamming metric. In [S. Jain, Bursts in m-metric array codes, Linear Algebra Appl., in press], the author introduced the notion of burst errors for m-metric array coding systems where m-metric array codes are subsets/subspaces of the space Mat m× s ( F q ), the linear space of all m × s matrices with entries from a finite field F q , endowed with a non-Hamming metric and obtained some lower bounds for burst error correction. In this paper, we obtain various construction upper bounds on the parameters of m-metric array codes for the detection and correction of burst errors.

A simple baseband transmission scheme for power line channels

We propose a simple pulse-amplitude modulation (PAM)-based coded modulation scheme that overcomes two major constraints of power line channels, viz., severe insertion-loss and impulsive noise. The scheme combines low-density parity-check (LDPC) codes, along with cyclic random-error and burst-error correction codes to achieve high-spectral efficiency, low decoding complexity, and a high degree of immunity to impulse noise. To achieve good performance in the presence of intersymbol interference (ISI) on static or slowly time-varying channels, the proposed coset-coding is employed in conjunction with Tomlinson-Harashima precoding and spectral shaping at the transmitter. In Gaussian noise, the scheme performs within 2 dB of unshaped channel capacity at a bit-error rate (BER) of 10/sup -11/, even with (3,6)-regular LDPC codes of modest length (1000-2000 bits). To mitigate errors due to impulse noise (a combination of synchronous and asynchronous impulses), a multistage interleaver is proposed, each stage tailored to the error-correcting property of each layer of the coset decomposition. In the presence of residual ISI, colored Gaussian noise, as well as severe synchronous and asynchronous impulse noise, the gap to Shannon capacity of the scheme to a Gaussian-noise-only channel is 5.5 dB at a BER of 10/sup -7/.

Bursts in m-metric array codes

Fire [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959] introduced the concept of bursts for classical codes where codes are subsets/subspaces of the space F q n , the space of all n-tuples with entries from a finite field F q . In this paper, we introduce the notion of bursts for m-metric array codes where m-metric array codes are subsets/subspaces of the space Mat m× s ( F q ), the linear space of all m × s matrices with entries from a finite field F q , endowed with a non-Hamming metric. We also obtain some bounds (analogous to Fire’s bound [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959], Rieger’s bound [S.H. Reiger, Codes for the correction of clustered errors, IRE-Trans., IT-6 (1960), 16–21] etc. in classical codes) on the parameters of m-metric array codes for the detection and correction of burst errors.

Optimal Interleaving on Tori

This paper studies t‐interleaving on two‐dimensional tori. Interleaving has applications in distributed data storage and burst error correction, and is closely related to Lee metric codes. A t‐interleaving of a graph is defined as a vertex coloring in which any connected subgraph of t or fewer vertices has a distinct color at every vertex. We say that a torus can be perfectly t‐interleaved if its t‐interleaving number (the minimum number of colors needed for a t‐interleaving) meets the sphere‐packing lower bound, $\lceil t^2/2 \rceil$. We show that a torus is perfectly t‐interleavable if and only if its dimensions are both multiples of $\frac{t^2+1}{2}$ (if t is odd) or t (if t is even). The next natural question is how much bigger the t‐interleaving number is for those tori that are not perfectly t‐interleavable, and the most important contribution of this paper is to find an optimal interleaving for all sufficiently large tori, proving that when a torus is large enough in both dimensions, its t‐interleaving number is at most just one more than the sphere‐packing lower bound. We also obtain bounds on t‐interleaving numbers for the cases where one or both dimensions are not large, thus completing a general characterization of t‐interleaving numbers for two‐dimensional tori. Each of our upper bounds is accompanied by an efficient t‐interleaving scheme that constructively achieves the bound.

Uniform latin square interleaving for correcting two-dimensional burst errors

A Latin square is widely used as an interleaving algorithm with an error-correcting code to correct burst errors in storage and communication systems. In a storage system, there are two types of burst errors; successive errors occurring on one track, i.e. a 1-dimensional burst error, and 1-dimensional burst errors occurring over successive tracks, i.e. a 2-dimensional burst error. The 1-dimensional burst error is usually caused by surface contamination or thermal asperity in the read head and the 2-dimensional burst error is usually caused by defects in the recording medium. We introduce here a new class of Latin square, a uniform Latin square, that can improve 2-dimensional error-correction capability compared with that of the conventional Latin squares.

The Burst Error Correcting Capabilities of a Simple Array Code

We propose a simple decoder for a widely used array code, known as the EVENODD code, which is originally designed to correct phased burst errors, to make it useful for correcting nonphased errors. The proposed scheme is capable of correcting almost all bursts up to a certain length. We show that the failure rate is sufficiently small and approaches zero as the block length increases. The redundancy of the code is twice the maximal burst length, which is a lower bound for the redundancy of a true burst-error-correcting code. Both the encoder and the decoder have very low complexity, both in terms of number of operations and in terms of computer code size

Bound for solid burst error correction with Lee weight

In this paper, we obtain bound for codes correcting solid burst errors with Lee weight over Z q and show that this bound is same as the corresponding bound with Hamming weight over Z2 and Z3. We also obtain some special/particular cases of this bound. Finally, we obtain Lee weight bound for solid bursts with limited intensity.

Parallel decoding for burst error control codes

AbstractIt is well known that sequential decoding methods for burst error control codes use Linear Feedback Shift Registers (LFSR). However, a parallel decoding method employing only combinational logic is preferable in certain applications, such as semiconductor memory systems and holographic memory systems, where a huge amount of data needs to be read or written at ultrahigh speed. This paper proposes a parallel decoding method for linear burst error control codes including the Fire code. In order to obtain the error pattern, this decoding method uses an inverse matrix of a nonsingular matrix which includes a sub‐matrix of the parity check matrix. Burst error correction is possible because correct burst error patterns are obtained only from frames that completely include the burst error pattern. Furthermore, this decoding method can also be applied to single byte error correcting codes with less hardware. The implementation of decoding circuits for burst and byte error control codes are illustrated in this paper. And their hardware complexity is also evaluated to show that the proposed method requires less hardware than the existing parallel decoding method. Finally, we will discuss about how the proposed decoding method can be extended to correct multiple burst or byte errors. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 38–48, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10094

Greedy loop transversal codes for correcting error bursts

The greedy loop transversal algorithm is used to construct linear codes in a binary channel for the correction of error bursts. The dimensions of the codes constructed are compared with the dimensions of the corresponding white noise greedy loop transversal codes, and with the dimensions of the few previously best-known codes for the burst-error patterns. The dimensions of the greedy loop transversal codes for burst-error correction match or exceed the dimensions of these previously known codes.