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On the pseudocodeword weight and parity-check matrix redundancy of linear codes
2007 IEEE Information Theory Workshop, 2007The minimum pseudocodeword weight w min of a linear graph-based code is more influential in determining decoding performance when decoded via iterative and linear programming decoding algorithms than the classical minimum distance d min under standard maximum-likelihood decoding Moreover, unlike the minimum distance which is unique to the code ...
Christine A. Kelley, Deepak Sridhara
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A simple parity check matrix LDPC code for perpendicular magnetic recording channels
2013 10th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, 2013In LDPC code design, the structure of code's parity check matrix can be very crucial to code performance. In this paper, we have investigated a simple designed parity check matrix when the code is applied to a PMR channel of a storage system. Belief propagation algorithm and min-sum algorithm are two major decoding algorithms used to benchmarked the ...
Sekson Timakul, Somsak Choochuay
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An authentication scheme based on an low-density parity-check matrix
Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 2005In this paper, an authentication scheme based on an LDPC (low-density parity-check) matrix is presented. Upper bounds on probabilities of impersonate attack and substitution attack have been derived using combinatorial argument on an LDPC ...
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Parity Check Matrix Partitioning for Layered Decoding of QC-LDPC Codes
2021 IEEE Globecom Workshops (GC Wkshps), 2021Teng Lu, Xuan He, Peng Kang, Xiaohu Tang
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Wide-Sense Time-Invariant Block Codes in Their Parity Check Matrix
2014A wide-sense time-invariant block code in its parity check matrix exhibits more than one parity check polynomial periodically repeating. Quasi-cyclic codes are revisited from this point of view. Reordered forms of quasi-cyclic codes are treated. Shortening or lengthening, with respect to the quasi-cyclic condition, are possible here only with steps of ...
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A Turbo-Decoding Message-Passing Algorithm for Sparse Parity-Check Matrix Codes
IEEE Transactions on Signal Processing, 2006A turbo-decoding message-passing (TDMP) algorithm for sparse parity-check matrix (SPCM) codes such as low-density parity-check, repeat-accumulate, and turbo-like codes is presented. The main advantages of the proposed algorithm over the standard decoding algorithm are 1) its faster convergence speed by a factor of two in terms of decoding iterations, 2)
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Strict-Sense Time-Invariant Convolutional Codes in Their Parity Check Matrix
2014The syndrome former sub-matrix is introduced. The generator matrix of a convolutional code can be constructed by means of a procedure called null ex-OR sum of clusters of syndromes. Inversely, it is possible to operate by means of the column construction of the parity check matrix. The importance of a parity check matrix in minimal form is stressed.
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Wide-Sense Time-Invariant Convolutional Codes in Their Parity Check Matrix
2014The circuit for syndrome calculation in a convolutional code is introduced. The most general method for obtaining the parity check matrix in a convolutional code, starting from its generator matrix, is presented. The minimal encoder circuit is discussed. Wide-sense time-invariant convolutional codes form a closed ensemble.
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On the parity-check matrix of generalized concatenated code
Science China Information Sciences, 2019Sha Shi +4 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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