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Pseudocodeword weights for non-binary LDPC codes
2006
2006 IEEE International Symposium on Information Theory
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The tree-based lower bounds on the minimum pseudocodeword weight are shown to also hold for q-ary LDPC codes on these channels. ...
Pseudocodewords of q-ary LDPC codes are examined and the weight of a pseudocodeword on the q-ary symmetric channel is defined. ...
In [3] and [4] , the performance of non-binary LDPC codes, defined over larger finite fields and over integer rings, is investigated and compared with that of binary LDPC codes. ...
doi:10.1109/isit.2006.262072
dblp:conf/isit/KelleySR06
fatcat:o2wmymxos5ai7g6ukpbhh4ic4y
On the pseudocodeword weight and parity-check matrix redundancy of linear codes
2007
2007 IEEE Information Theory Workshop
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We provide some upper bounds on the BSCpseudoweight redundancy and illustrate the concept with some results for Hamming codes, tree-based and finite geometry LDPC codes, Reed-Muller codes and Hadamard ...
Moreover, unlike the minimum distance which is unique to the code regardless of representation, the set of pseudocodewords, and therefore also the minimum pseudocodeword weight, depends on the graph representation ...
We point out that this does not contradict the above theorem, as non-codeword pseudocodewords may also assume weights ≥ d(C). Theorem 2.1 says that any binary linear code has φ(C) ≤ 2 n−k . ...
doi:10.1109/itw.2007.4313040
fatcat:xlduof3m7rg6nnhv5bqjfdjjfm
Pseudocodewords of Tanner Graphs
2007
IEEE Transactions on Information Theory
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Lower bounds on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN channel. ...
weight. ...
Example 3.1: Some graphs with known t-values are: t ≤ 2 for cycle codes [1] , [2] , t = 1 for LDPC codes whose Tanner graphs are trees, and t ≤ 2 for LDPC graphs having a single cycle, and t ≤ s for ...
doi:10.1109/tit.2007.907501
fatcat:y76otn7b45hw3a22v3ckfluxzm
Pseudocodewords of Tanner graphs
[article]
2007
arXiv
pre-print
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Lower bounds on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN channel. ...
weight. ...
Let G represent a binary LDPC code C with minimum distance d min . Then G is called a Tanner graph (or, LDPC constraint graph) of C. ...
arXiv:cs/0504013v4
fatcat:gfxhs5yl75akpjqp3ie7s5o5d4
Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights
[article]
2006
arXiv
pre-print
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We also present some bounds on pseudocodeword weight for p-ary LDPC codes. ...
Treating these codes as p-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes ...
Moreover, we expect that p-ary LDPC codes to have larger minimum pseudocodeword weights than corresponding binary LDPC codes. ...
arXiv:cs/0510009v2
fatcat:jwxiqhje6ncqjitrsurvg3a73y
Eigenvalue bounds on the pseudocodeword weight of expander codes
2007
Advances in Mathematics of Communications
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For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. ...
Furthermore, Tanner's parity-oriented eigenvalue lower bound on the minimum distance is generalized to yield a new lower bound on the minimum pseudocodeword weight. ...
We also thank Reviewer 1 for providing the more intuitive definition of a stopping set in a generalized LDPC code. ...
doi:10.3934/amc.2007.1.287
fatcat:rwnfklidyffblm5uoipekeml6y
Eigenvalue bounds on the pseudocodeword weight of expander codes
[article]
2007
arXiv
pre-print
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For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. ...
Furthermore, Tanner's parity-oriented eigenvalue lower bound on the minimum distance is generalized to yield a new lower bound on the minimum pseudocodeword weight. ...
We also thank Reviewer 1 for providing the more intuitive definition of a stopping set in a generalized LDPC code. ...
arXiv:0708.2462v1
fatcat:5r7thuq535cjxnzrjwznougqpe
LP Decoding
[chapter]
2008
Encyclopedia of Algorithms
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We also discuss the application of LP decoding to binary linear codes. We define the notion of a relaxation being symmetric for a binary linear code. ...
We describe the notion of pseudocodewords under LP decoding, unifying many known characterizations for specific codes and channels. ...
The fractional distance of a -symmetric polytope È for a binary linear code is equal to the minimum weight of a non-zero vertex of È. ...
doi:10.1007/978-0-387-30162-4_216
fatcat:4hhkbkxsfjahvi255da774qm7a
LP Decoding
[chapter]
2016
Encyclopedia of Algorithms
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We also discuss the application of LP decoding to binary linear codes. We define the notion of a relaxation being symmetric for a binary linear code. ...
We describe the notion of pseudocodewords under LP decoding, unifying many known characterizations for specific codes and channels. ...
The fractional distance of a C-symmetric polytope P for a binary linear code C is equal to the minimum weight of a non-zero vertex of P. ...
doi:10.1007/978-1-4939-2864-4_216
fatcat:bce4u46mbrggjg2hdqkslrtqke
Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs
2014
IEEE Transactions on Information Theory
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We consider both random and constrained edgeweight labeling, and refer to the former as the unconstrained non-binary protograph-based LDPC codes (U-NBPB codes) and the latter as the constrained non-binary ...
This paper provides a comprehensive analysis of non-binary low-density parity check (LDPC) codes built out of protographs. ...
Ben-Yue Chang for help with the original formulation of NB-EXIT tool and for help with the design methodology of finite-length NBPB codes. ...
doi:10.1109/tit.2014.2316215
fatcat:72qisp7jn5abrghxtg2fkaihwy
Average min-sum decoding of LDPC codes
2008
2008 5th International Symposium on Turbo Codes and Related Topics
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Finally, AMS pseudocodewords are introduced and analyzed and their relationship to graph cover and LP pseudocodewords is explored, with particular focus on the AMS pseudocodewords of regular LDPC codes ...
and cycle codes. ...
In particular, for all non-codeword outputs in the range shown, the binary value assigned to the fourth coordinate is 1. ...
doi:10.1109/turbocoding.2008.4658725
fatcat:mecdixehcff75ldp4lr5uz2l4a
Using Linear Programming to Decode Binary Linear Codes
2005
IEEE Transactions on Information Theory
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We describe a method for approximate ML decoding of an arbitrary binary linear code, based on a linear programming (LP) relaxation that is defined by a factor graph or parity check representation of the ...
code. ...
Fractional Distance A classical quantity associated with a code is its distance, which for a linear code is equal to the minimum weight of any non-zero codeword. ...
doi:10.1109/tit.2004.842696
fatcat:qf3estqpnvcqdocjtlnjw7d3cm
Guessing Facets: Polytope Structure and Improved LP Decoding
[article]
2007
arXiv
pre-print
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We begin by showing that for expander codes, every fractional pseudocodeword always has at least a constant fraction of non-integral bits. ...
We then prove that for expander codes, the active set of any fractional pseudocodeword is smaller by a constant fraction than the active set of any codeword. ...
Previous work by Koetter and Vontobel [9] established that for any bit-check regular LDPC code, there exist pseudocodewords for the additive white Gaussian noise (AWGN) channel with sublinear weight. ...
arXiv:0709.3915v1
fatcat:yl2tmsv67bcgvby6fzpzjp6ygm
Minimum Pseudo-Weight and Minimum Pseudo-Codewords of LDPC Codes
[article]
2006
arXiv
pre-print
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Then, we show that the lower bound of Kashyap and Vardy on the stopping distance of an LDPC code is also a lower bound on the pseudo-weight of a pseudo-codeword of this LDPC code with girth 4, and this ...
Using these results we further show that for some LDPC codes, there are no other minimum pseudo-codewords except the real multiples of minimum codewords. ...
Sridhara for kindly affording the preprint [10] , and Mr. X. Ge for his calculation of the minimum distance in Example 6 by computer. ...
arXiv:cs/0606051v2
fatcat:rremtpnt7vab3liovte22kpt34
Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC
[article]
2018
arXiv
pre-print
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In this paper, we consider ensembles of periodically time-varying spatially coupled LDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graph covers of a fixed degree. ...
We show that for certain (J,K)-regular SC-LDPC code ensembles and a fixed cover degree, the typical minimum pseudoweight of the unterminated (and associated tail-biting/terminated) SC-LDPC code ensembles ...
The pseudodistance, w m min , for finite covers of a fixed degree m of G is defined as the minimum pseudoweight among all non-zero pseudocodewords from the degree-m covers. ...
arXiv:1809.04253v1
fatcat:lexailglpvgivirkb74e7jpmra
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