Abstract: 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.

Abstract: In this paper we construct multidimensional codes with high dimension. The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small radius. We also consider small number of errors in a small area. The clusters which are discussed are mainly spheres such as semi-crosses and crosses. Also considered are clusters with small number of errors such as 2-bursts, two errors in various clusters, and three errors on a line. Our main focus is on the redundancy of the codes when the most dominant parameter is the dimension of the code.

Abstract: This paper deals with derivation of bounds for linear codes that are able to detect and locate errors which occur during the process of transmission. The kind of errors considered are known as repeated burst errors. An illustration for such kind of a code has also been provided.

Abstract: Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure protection. As can be seen, the simple interleaved RS codes have substantially lower inefficiency over a wide range of transmission lengths.

Abstract: A class of binary quasi-cyclic burst error-correcting codes based upon product codes is introducedAn expression for the maximum burst error-correcting capability for each code in the class is givenA decoding algorithm for the class of codes is set forthIn certain cases the codes reduce to Gilbert codes,which are cyclicOften codes exist in the class which have the same block length and number of check bits as the Gilbert codes but correct longer bursts of errors than Gilbert codesComputer simulation shows that the decoding algorithm works well

Abstract: In this paper, we shall construct a long cyclic binary code from small codes. The generator polynomial of the cyclic combination of sub codes is derived and shown to be a simple function of the generator polynomials of the subcodes. We will show that binary cyclic codes of length 5n can be obtained from 5 cyclic codes of length n by two methods. For both the methods the length of codes must be even. We conclude with detailed examples of binary codes of even length and their generators for which exact results are obtained.

Abstract: An assignment scheme exploits the Media Access Control (MAC) layer protocol features under various MAC layer call scenarios. In one embodiment, the Hamming distance between pairs of critical Data Units are assigned to codewords with a minimum distance of dmin2=8 bits, thereby increasing the hard decision error correcting capability from 1 bit to 3 bits when deciding between these pairs of Data Units. The method for assigning data unit identification (DUID) codes by a radio operating within a wireless communication system includes determining by the radio whether an expected burst is a 4 Voice Burst with Encryption Synchronization Signaling (4V); when the expected burst is 4V, decoding the DUID within the received burst using an increased minimum distance; and when the expected burst is not 4V, decoding the DUID within the received burst using a minimum distance.

Abstract: In this paper, the generator polynomial of linear cyclic codes on ring Z Pm are studied, and we prove that the depth spectrum of linear cyclic codes C l = (pl−1f l )(degf l = n−k, l = 1, 2 · · · ,m) has consisted exactly k non zero values and give the depth spectrum of linear cyclic codes on ring Z Pm

Abstract: This paper obtains bounds for linear codes which are capable to correct the errors blockwise which occur during the process of transmission. The kind of errors considered are known as repeated burst errors of length b(fixed), introduced by Dass and Garg (2009). An illustration for such kind of codes has also been provided. Mathematics Subject Classification: 94B20, 94B25, 94B65

Abstract: Enumerating burst errors enables to obtain bounds on parameters of codes. Recently, Jain in [ 5 ] established a Reiger’s type bound for burst error correcting matrix codes over finite fields with respect to a non Hamming metric. Here, we extend these results to array codes over finite rings. Further, we also introduce a new constructive method for counting burst errors that avoids solving Diophantine inequalities in order to compute burst errors for each given weight. Finally, we apply our results on establishing some bounds for array codes over finite rings.

Abstract: This paper presents a study of linear codes which are capable to detect and locate errors which are repeated low-density bursts of length b(flxed) with weight w or less. An illustration for such a kind of code has also been provided.

Abstract: Quantum error correction is an important research area of quantum information. This paper proposes one kind of quantum CSS code for burst errors. Two construction methods are given of the proposed CSS code obtaining from classical cyclic code. Using these methods, a group of CSS codes of length 15 and 30 suitable for burst errors are obtained. In conclusion, the capability of correcting burst errors of the quantum CSS codes is much larger than their capability of correcting random errors.

Abstract: This paper presents the non-existence of (8,4)-2 burst error correcting perfect code over GF(2). An (n,k) linear code is said to be perfect if for some positive integer b, it corrects all b and fewer errors and no more. Mathematics Subject Classification: 94B20

Abstract: Linear and cyclic codes are typically used to combat substitution errors. However, synchronization errors, associated with the deletion and insertion of symbols, can cause severe performance degradation unless the coding scheme possesses the capability to recover from such errors. It is shown that linear codes of rate greater than 1/2 cannot correct deletion or insertion errors but there are linear codes of rate 1/2 that can correct these errors. Although cyclic codes, except for repetition codes, cannot correct deletion or insertion errors, two approaches are investigated to yield codes, based on cyclic codes, that can correct these errors. In the first approach, it is shown that a binary or nonbinary cyclic code of rate at most 1/3 or 1/2, respectively, can be extended by one symbol to make it capable of correcting synchronization errors. In the second approach, a cyclic code of rate at most 1/2 is expurgated by appropriately deleting codewords such that the expurgated code is capable of correcting synchronization errors. It is shown that deleting codewords costs at most two information bits if the code is binary and one information symbol if the code is nonbinary.