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6 papers · 1 filter
Spectral Graph Analysis of Quasi-Cyclic Codes
Roxana Smarandache, Mark F. Flanagan
In this paper we analyze the bound on the additive white Gaussian noise channel (AWGNC) pseudo-weight of a (c,d)-regular linear block code based on the two largest eigenvalues of H…
Exposing Pseudoweight Layers in Regular LDPC Code Ensembles
Mark F. Flanagan
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 de…
Comparing Measures of Sparsity
Niall P. Hurley, Scott T. Rickard
Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal anal…
On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes
Mark F. Flanagan, Enrico Paolini, Marco Chiani +1
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expr…
A Few More Quadratic APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin +1
We present two infinite families of APN functions where the degree of the field is divisible by 3 but not 9. Our families contain two already known families as special cases. We al…
Linear-programming Decoding of Non-binary Linear Codes
Mark F. Flanagan, Vitaly Skachek, Eimear Byrne +1
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' p…