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48,307
An Authentication Scheme Based on an Low-Density Parity-Check Matrix
"... Abstract — In 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 ensemble. I. ..."
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Abstract — In 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 ensemble. I.
Codes with a circulant parity check matrix
"... In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the first row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We ..."
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In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the first row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We
DRAFT SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Parity-Check Matrix Calculation for
, 2008
"... Joint source-channel coding schemes based on oversampled filter banks were recently proposed. Oversampled filter banks are considered as error-correcting codes, extending the notion of code-subspace, parity-check matrix, and syndrom to the domain of real and complex numbers. We here present an effic ..."
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Joint source-channel coding schemes based on oversampled filter banks were recently proposed. Oversampled filter banks are considered as error-correcting codes, extending the notion of code-subspace, parity-check matrix, and syndrom to the domain of real and complex numbers. We here present
Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix
, 2005
"... An iterative algorithm is presented for soft input soft output (SISO) decoding of Reed-Solomon (RS) codes. The proposed algorithm works at the bit level using the binary parity check matrix associated with the RS code. The novelty in the proposed algorithm is in reducing a submatrix of the binary pa ..."
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Cited by 27 (1 self)
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An iterative algorithm is presented for soft input soft output (SISO) decoding of Reed-Solomon (RS) codes. The proposed algorithm works at the bit level using the binary parity check matrix associated with the RS code. The novelty in the proposed algorithm is in reducing a submatrix of the binary
A Parity Check Matrix Design for Irregular LDPC Codes with 2K Block Length
, 2009
"... This paper outlines the work on another design of a parity check matrix for Irregular LDPC codes. The design is based on the pattern of Modified Array and Interleaved Modified Array LDPC codes. The application of matrix transposition Quasi-cyclic shifting has resulted in the reduction of 1’s. The d ..."
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This paper outlines the work on another design of a parity check matrix for Irregular LDPC codes. The design is based on the pattern of Modified Array and Interleaved Modified Array LDPC codes. The application of matrix transposition Quasi-cyclic shifting has resulted in the reduction of 1’s
(1) Let Gi,Hi be the generator matrix and parity check matrix of Ci respectively, (i=1,2). Without loss of generality,
"... between two distinct codewords, then C is called an [n,k,d] linear code over F 2. A linear code C is always specified by an n by k generator matrix G whose entries are all zeroes and ones. The generator matrix G maps k bits of information to a set of binary vectors of length n, called codewords. Bin ..."
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. Binary linear codes can be alternatively (but equivalently) formulated by so called parity matrix, which is used to perform error-correction. The parity matrix H of a linear code [n,k] is an (n−k)×n matrix such that Hx=0 for all those and only those vectors x in the code C. The rows of H are n−k linearly
Moderate-density parity-check codes
- CoRR
"... Abstract—We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of one’s of the parity-check matrix of the codes presented is typically higher than the number of one’s of the parity-check matrix of low-den ..."
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Cited by 1 (0 self)
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Abstract—We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of one’s of the parity-check matrix of the codes presented is typically higher than the number of one’s of the parity-check matrix of low
Efficient Encoding of Low-Density Parity-Check Codes
, 2001
"... Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. In this paper, we consider the encoding problem for LDPC ..."
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Cited by 184 (3 self)
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for LDPC codes. More generally, we consider the encoding problem for codes specified by sparse parity-check matrices. We show how to exploit the sparseness of the parity-check matrix to obtain efficient encoders. For the @Q TA-regular LDPC code, for example, the complexity of encoding is essentially
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