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Efficient Encoding of LowDensity ParityCheck Codes
, 2001
"... Lowdensity paritycheck (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 185 (3 self)
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for LDPC codes. More generally, we consider the encoding problem for codes specified by sparse paritycheck matrices. We show how to exploit the sparseness of the paritycheck matrix to obtain efficient encoders. For the @Q TAregular LDPC code, for example, the complexity of encoding is essentially
Paritycheck codes and their representations
, 2015
"... Linear codes can be represented by paritycheck matrices. Let Fq be the finite field with q elements, where q is a power of a prime. A linear code C of length n over Fq is a subspace of Fnq. Elements of C are called codewords. All codes considered here are linear codes. Given a code C of length n, t ..."
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, there exists a matrix H 2 Fr⇥nq for some r whose nullspace is C, meaning C = NS(H). The matrix H is called a paritycheck matrix for C, because y 2 C if and only if HyT = 0. The code C is sometimes called a paritycheck code. If H is sparse, then C is a lowdensity paritycheck (LDPC) code. Gretchen L
LowDensity ParityCheck Code Design Techniques to Simplify Encoding
, 2007
"... This work describes a method for encoding lowdensity paritycheck (LDPC) codes based on the accumulate–repeat–4–jagged–accumulate (AR4JA) scheme, using the lowdensity paritycheck matrix H instead of the dense generator matrix G. The use ..."
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This work describes a method for encoding lowdensity paritycheck (LDPC) codes based on the accumulate–repeat–4–jagged–accumulate (AR4JA) scheme, using the lowdensity paritycheck matrix H instead of the dense generator matrix G. The use
1 GF(2 m) LowDensity ParityCheck Codes Derived
, 2005
"... Abstract — Based on the ideas of cyclotomic cosets, idempotents and MattsonSolomon polynomials, we present a new method to construct GF(2 m), where m> 0 cyclic lowdensity paritycheck codes. The construction method produces the dual code idempotent which is used to define the paritycheck matrix ..."
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Cited by 1 (1 self)
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matrix of the lowdensity paritycheck code. An interesting feature of this construction method is the ability to increment the code dimension by adding more idempotents and so steadily decrease the sparseness of the paritycheck matrix. We show that the constructed codes can achieve performance very
On the Statistical Theory of TurboCodes
"... A statistical theory of turbocodes, treated as a special family of convolutional codes with a lowdensity paritycheck matrix, is developed. The basic ideas are: the representation of the transposed paritycheck matrix of turbocodes as a product of a sparse (multiple) scrambler matrix and the tran ..."
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A statistical theory of turbocodes, treated as a special family of convolutional codes with a lowdensity paritycheck matrix, is developed. The basic ideas are: the representation of the transposed paritycheck matrix of turbocodes as a product of a sparse (multiple) scrambler matrix
Construction of Short Block Length Irregular LowDensity ParityCheck Codes
, 2004
"... We present a construction algorithm for short block length irregular lowdensity paritycheck (LDPC) codes. Based on a novel interpretation of stopping sets in terms of the paritycheck matrix, we present an approximate trellisbased search algorithm that detects many stopping sets. Growing the parit ..."
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Cited by 31 (11 self)
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We present a construction algorithm for short block length irregular lowdensity paritycheck (LDPC) codes. Based on a novel interpretation of stopping sets in terms of the paritycheck matrix, we present an approximate trellisbased search algorithm that detects many stopping sets. Growing
Complete enumeration of stopping sets of fullrank paritycheck matrices of Hamming codes
 IEEE Transactions on Information Theory
, 2007
"... Abstract — Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three f ..."
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Cited by 8 (1 self)
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for a fullrank paritycheck matrix of the Hamming code. In this correspondence, we derive an expression for the number of stopping sets of any given size for the same paritycheck matrix. Index Terms – Hamming code, linear code, paritycheck matrix, stopping set enumerator, weight enumerator.
Results on ParityCheck Matrices with Optimal Stopping and/or DeadEnd Set Enumerators
, 2006
"... The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the paritycheck matrix representing the code. In this paper, we introduce the notion of dea ..."
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Cited by 4 (1 self)
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The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the paritycheck matrix representing the code. In this paper, we introduce the notion
Performance of LowDensity ParityCheck Codes for Burst Erasure Channels
"... Performance of lowdensity paritycheck (LDPC) codes with maximum likelihood decoding (MLD) for solid burst erasures is discussed. The columns of the paritycheck matrix of LDPC codes are permuted to increase the distance between elements (DBEs) which are defined as a number of symbol positions betwe ..."
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Performance of lowdensity paritycheck (LDPC) codes with maximum likelihood decoding (MLD) for solid burst erasures is discussed. The columns of the paritycheck matrix of LDPC codes are permuted to increase the distance between elements (DBEs) which are defined as a number of symbol positions
Results 11  20
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47,550