Abstract: A syndrome S is found from a received information D and a parity check matrix for correcting burst errors up to b bits. The syndrome S is inputted to p sets of burst error pattern generation circuits that correspond to information frames overlapping each other by (b - 1) bits and each having a length of 2b bits. If a burst error is included entirely in any one of the p sets of burst error pattern generation circuits, then the burst error pattern is outputted. An error pattern calculation circuit executes OR respectively on overlapping bits output from the error pattern generation circuits. By executing exclusive OR on an output of the error pattern calculation circuit and received information D, corrected information Ds is obtained. As a result, a burst error in the received information can be detected and corrected.

Abstract: Binary two-dimensional arrays are considered, where the patches of errors contain more than one symbol from the same codeword, i.e. arrays with repetitions. The relative digit positions in each codeword are taken into account when performing interleaving, and burst error-correcting codes are used instead of random error-correcting codes.

Abstract: In some applications, such as in holographic memories, high-speed parallel decoding is strongly required for burst error correction and detection. From this viewpoint, this paper demonstrates a parallel decoding method for burst error control codes and presents the decoding circuit implemented by combinational circuits, not by LFSRs.

Abstract: Various communication and storage systems are likely corrupted by bursts of noise These bursts may be long in duration, resulting in a significant degradation for the system performance Reed-Solomon (RS) codes are proven to be very effective in correcting burst errors According to the Singleton bound, the maximum length of burst errors that can be corrected by an (n, k) RS code is (n-k)/2 symbols However, it turns out that, if correlation between erroneous symbols within bursts is considered and well used, the variables for burst locations will be decreased and, accordingly, decoding capability may be enhanced with increased length of correctable bursts As such, we propose a new burst-error-correcting algorithm It is shown that, for (n, k) RS codes, this algorithm can correct continuous burst errors with length that approaches to n-k symbols with fairly low miscorrection probability, achieving a good performance over long-burst channels

Abstract: It 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

Abstract: The error location function of codes was first proposed by Wolf and Elspas in 1963 lying midway between error correction and error detection. In 1982, Dass proposed burst error locating codes. These codes, however, have a problem that they cannot locate burst errors which occur at the boundary of the two adjacent subblocks. From this point, the authors proposed a new class of burst error locating codes indicating an erroneous frame, called single bit error correcting and l-bit burst error locating codes, or SEC-B/sub l/EL codes. Here, the frame is a set of continuous symbols in a codeword and adjacent frames are partially overlapped in order to make any burst errors not exceeding the maximum size of the frame be included in at least one frame. The proposed codes, however, have more check-bits than burst error correcting fire codes for longer information-bit length. This paper proposes a new code design method of the SEC-B/sub l/EL codes having less check-bits than the burst error correcting fire codes.

Abstract: We propose a quantum error correcting code for burst error.% By using the quantum interleaver, any quantum burst-errors that have occurred are spread over the interleaved code word, so that we can construct good quantum burst-error correcting codes without increasing the redundancy of the code.