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105,806
LowDensity ParityCheck Codes
, 1963
"... Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been the equipment ..."
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Cited by 1349 (1 self)
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Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been the equipment complexity and the computation time required to decode the noisy received data.
The Capacity of LowDensity ParityCheck Codes Under MessagePassing Decoding
, 2001
"... In this paper, we present a general method for determining the capacity of lowdensity paritycheck (LDPC) codes under messagepassing decoding when used over any binaryinput memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chos ..."
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Cited by 569 (9 self)
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In this paper, we present a general method for determining the capacity of lowdensity paritycheck (LDPC) codes under messagepassing decoding when used over any binaryinput memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly
Design of capacityapproaching irregular lowdensity paritycheck codes
 IEEE TRANS. INFORM. THEORY
, 2001
"... We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
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Cited by 581 (6 self)
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We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming
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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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
ParityCheck Code Decoder
, 2002
"... Because of their excellent errorcorrecting performance, lowdensity paritycheck (LDPC) codes have recently attracted a lot of attention. In this paper, we are interested in the practical LDPC code decoder hardware implementations. The direct fully parallel decoder implementation usually incurs too ..."
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Because of their excellent errorcorrecting performance, lowdensity paritycheck (LDPC) codes have recently attracted a lot of attention. In this paper, we are interested in the practical LDPC code decoder hardware implementations. The direct fully parallel decoder implementation usually incurs
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 184 (3 self)
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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
On Sparse Parity Check Matrices
, 1999
"... We consider the extremal problem to determine the maximal number N(m; k; r) of columns of a 01matrix with m rows and at most r ones in each column such that each k columns are linearly independent modulo 2. For each fixed k 1 and r 1, we shall prove a probabilistic lower bound N(m; k; r) = \Omeg ..."
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Cited by 2 (0 self)
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We consider the extremal problem to determine the maximal number N(m; k; r) of columns of a 01matrix with m rows and at most r ones in each column such that each k columns are linearly independent modulo 2. For each fixed k 1 and r 1, we shall prove a probabilistic lower bound N(m; k; r) = \Omega\Gamma m kr=2(k\Gamma1) ); for k a power of 2, we prove an upper bound N(m; k; r) = O(m dkr=(k\Gamma1)e=2 ) which matches the lower bound for infinitely many values of r. We give some explicit constructions. 1 Introduction We shall consider matrices M over the twoelement field GF 2 . If each k column vectors of M are linearly independent, we say that the columns are kwise independent. By a (k; r)matrix we mean a matrix, where the column vectors are kwise independent and each column contains at most r ones. We denote by N(m; k; r) the maximal number of columns in a (k; r)matrix with m rows. The aim of this paper is to give estimates on the growth of the function N(m; k; r). Matric...
Moderatedensity paritycheck codes
 CoRR
"... Abstract—We propose a new type of short to moderate blocklength, linear errorcorrecting codes, called moderatedensity paritycheck (MDPC) codes. The number of one’s of the paritycheck matrix of the codes presented is typically higher than the number of one’s of the paritycheck matrix of lowden ..."
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Cited by 1 (0 self)
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Abstract—We propose a new type of short to moderate blocklength, linear errorcorrecting codes, called moderatedensity paritycheck (MDPC) codes. The number of one’s of the paritycheck matrix of the codes presented is typically higher than the number of one’s of the paritycheck matrix of low
Improved lowdensity paritycheck codes using irregular graphs
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—We construct new families of errorcorrecting codes based on Gallager’s lowdensity paritycheck codes. We improve on Gallager’s results by introducing irregular paritycheck matrices and a new rigorous analysis of harddecision decoding of these codes. We also provide efficient methods for ..."
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Cited by 224 (15 self)
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Abstract—We construct new families of errorcorrecting codes based on Gallager’s lowdensity paritycheck codes. We improve on Gallager’s results by introducing irregular paritycheck matrices and a new rigorous analysis of harddecision decoding of these codes. We also provide efficient methods
Results 1  10
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105,806