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Pseudocodewords of Tanner Graphs

Christine A. Kelley, Deepak Sridhara
2007 IEEE Transactions on Information Theory  
This papers presents a detailed analysis of pseudocodewords of Tanner graphs.  ...  The results obtained provide some insights in relating the structure of the Tanner graph to the pseudocodeword distribution and suggest ways of designing Tanner graphs with good minimum pseudocodeword  ...  Remark 6.1: Theorem 6.1 considers only the set of lift-realizable pseudocodewords of a Tanner graph.  ... 
doi:10.1109/tit.2007.907501 fatcat:y76otn7b45hw3a22v3ckfluxzm

Pseudocodewords of Tanner graphs [article]

Christine A. Kelley, Deepak Sridhara
2007 arXiv   pre-print
This papers presents a detailed analysis of pseudocodewords of Tanner graphs.  ...  The results obtained provide some insights in relating the structure of the Tanner graph to the pseudocodeword distribution and suggest ways of designing Tanner graphs with good minimum pseudocodeword  ...  Section 5 analyzes the structure of pseudocodewords realizable in lifts of general Tanner graphs.  ... 
arXiv:cs/0504013v4 fatcat:gfxhs5yl75akpjqp3ie7s5o5d4

Pseudocodeword-free criterion for codes with cycle-free Tanner graph

Wittawat Kositwattanarerk
2018 Designs, Codes and Cryptography  
In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant  ...  Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.  ...  This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.  ... 
doi:10.1007/s10623-018-0476-3 fatcat:xaq6yknd5bdc7dbrvq2zffqkxy

Pseudocodeword-Free Criterion for Codes with Cycle-Free Tanner Graph [article]

Wittawat Kositwattanarerk
2017 arXiv   pre-print
In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant  ...  Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.  ...  This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.  ... 
arXiv:1706.06648v1 fatcat:wcn5cdvy2vfxhk3q5c4q4ed7ji

Analysis of Connections Between Pseudocodewords

Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric Psota, Lance C. Perez, Judy L. Walker
2009 IEEE Transactions on Information Theory  
Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given.  ...  This allows for further analysis of when graph cover pseudocodewords induce computation tree pseudocodewords.  ...  More specifically, the Tanner graph in Figure 3 is a 4-cover of the Tanner graph in Figure 1 , so the configuration in Figure 3 is a realization of a graph cover pseudocodeword.  ... 
doi:10.1109/tit.2009.2025529 fatcat:cyec37c5wze55drufrzyejinuu

Towards universal cover decoding

Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric Psota, Lance C. Perez, Judy L. Walker
2008 2008 International Symposium on Information Theory and Its Applications  
Given a Tanner graph T , the universal cover of T can also be thought of as an infinite Tanner graph. This relationship is given by Definition 2.2. and F := F ( T ) = f ∈F π −1 (f ).  ...  We conclude this section by examining the costs of another class of universal cover pseudocodewords, defined below. Definition 3.5. Let T be a Tanner graph and let T be the universal cover of T .  ... 
doi:10.1109/isita.2008.4895386 fatcat:qkjdnfk4pfde7jt7liepwy2upa

Connections between computation trees and graph covers

D. Dreher, J.L. Walker
2009 2009 Information Theory and Applications Workshop  
Connections between graph cover pseudocodewords and computation tree pseudocodewords are investigated with the aim of bridging the gap between the theoretically attractive analysis of graph covers and  ...  the more intractable analysis of iterative message-passing algorithms that are intuitively linked to graph covers.  ...  A configuration e c on a 4-cover e T of the Tanner graph T of Example 3.1. Fig. 1 . 1 The Tanner graph T and a computation tree configuration (c, R) for the Tanner graph T of Example 3.1.  ... 
doi:10.1109/ita.2009.5044971 fatcat:w7p3zc3z3ra45frihsxemsktai

Average min-sum decoding of LDPC codes

Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric Psota, Lance C. Perez, Judy L. Walker
2008 2008 5th International Symposium on Turbo Codes and Related Topics  
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  ...  Simulations have shown that the outputs of minsum (MS) decoding generally behave in one of two ways: the output either eventually stabilizes at a codeword or eventually cycles through a finite set of vectors  ...  on the Tanner graph, it does not distinguish between the Tanner graph itself and any finite, unramified cover of the Tanner graph.  ... 
doi:10.1109/turbocoding.2008.4658725 fatcat:mecdixehcff75ldp4lr5uz2l4a

On the pseudocodeword weight and parity-check matrix redundancy of linear codes

Christine A. Kelley, Deepak Sridhara
2007 2007 IEEE Information Theory Workshop  
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  ...  The minimum pseudocodeword weight wmin of a linear graph-based code is more influential in determining decoding performance when decoded via iterative and linear programming decoding algorithms than the  ...  This single cycle Tanner graph also has no non-codeword pseudocodewords.  ... 
doi:10.1109/itw.2007.4313040 fatcat:xlduof3m7rg6nnhv5bqjfdjjfm

Characterization of Graph-cover Pseudocodewords of Codes over F_3 [article]

Vitaly Skachek
2010 arXiv   pre-print
These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords.  ...  The knowledge of the boundaries of the fundamental cone could help in studying various properties of the pseudocodewords, such as their minimum pseudoweight, pseudoredundancy of the codes, etc.  ...  The Tanner graph of a linear code C over F is an equivalent characterization of the code's parity-check matrix H.  ... 
arXiv:1007.3808v1 fatcat:4iyxa5nx6zftpnojxd2kf5vj5i

Exposing Pseudoweight Layers in Regular LDPC Code Ensembles [article]

Mark F. Flanagan
2009 arXiv   pre-print
Simulation results for the pseudoweight distribution of two regular LDPC code ensembles are presented for graph covers of low degree.  ...  A solution is presented for the asymptotic growth rate of the AWGN-pseudoweight distribution of regular low-density parity-check (LDPC) code ensembles for a selected graph cover degree M >= 1.  ...  Also, pseudocodewords arising from finite covers of the Tanner graph were shown to be equivalent to those responsible for failure of LP decoding [7] , [8] .  ... 
arXiv:0908.1298v1 fatcat:abfbmji2ufdqje2klfgi4f4znu

Pseudocodewords of Parity-Check Codes Over Fields of Prime Cardinality

Wittawat Kositwattanarerk, Gretchen L. Matthews
2014 IEEE Transactions on Information Theory  
In order to understand this choice of representation, we need to analyze the pseudocodewords of the Tanner graph of a code.  ...  Nonetheless, the performance of these decoders depends crucially on the Tanner graph representation of the code.  ...  The codewords of C(H) Figure 5.1 shows the Tanner graph T (H) and the codeword (1, 0, 2, 1) on the Tanner graph.  ... 
doi:10.1109/tit.2014.2331677 fatcat:qaznggjzu5af7hahtct5hhlswq

LP Pseudocodewords of Cycle Codes are Half-Integral [article]

Nathan Axvig
2012 arXiv   pre-print
In particular, the components of any such pseudocodeword can only assume values of zero, one-half, or one.  ...  Restricting to the class of cycle codes, we provide necessary conditions for a vector to be a linear programming pseudocodeword.  ...  Along the way, we will see that LP pseudocodewords also have a close relationship with unions of vertexdisjoint simple cycles in the Tanner graph.  ... 
arXiv:1212.2953v1 fatcat:2lyh6tui6ze4lbtl2hu4zy4rqu

Lower Bounds on the Minimum Pseudodistance for Linear Codes with q-ary PSK Modulation over AWGN [article]

Vitaly Skachek, Mark F. Flanagan
2008 arXiv   pre-print
We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum "pseudodistance") for coded modulation systems using linear codes with q-ary phase-shift keying (PSK) modulation  ...  In the case of a linear-programming based receiver, the minimum pseudodistance may be used to form an exact bound on the codeword error rate of the system.  ...  Let P 0 = (f i (k)) i∈I;k∈{1,2,··· ,q−1} be the normalized pseudocodeword matrix of a graph-cover pseudocodeword p corresponding to some M -cover of the Tanner graph of H.  ... 
arXiv:0803.3777v2 fatcat:gn45bsbfgzcnrphjudpr7xuqe4

Lower bounds on the minimum pseudodistance for linear codes with q-ary PSK modulation over AWGN

Vitaly Skachek, Mark F. Flanagan
2008 2008 5th International Symposium on Turbo Codes and Related Topics  
We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum "pseudodistance") for coded modulation systems using linear codes with q-ary phase-shift keying (PSK) modulation  ...  In the case of a linearprogramming based receiver, the minimum pseudodistance may be used to form an exact bound on the codeword error rate of the system.  ...  Let P 0 = (f i (k)) i∈I;k∈{1,2,··· ,q−1} be the normalized pseudocodeword matrix of a graph-cover pseudocodeword p corresponding to some M -cover of the Tanner graph of H.  ... 
doi:10.1109/turbocoding.2008.4658737 fatcat:v4tjfr6775dvrntns7jatkulgu
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