Publications related to Non-binary LDPC codes and EXIT like functions

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Successive Refinement of Gaussian Projections

Michael Christoph Gastpar, Guillaume Jean Op 't Veld

Successive refinement is a technique to encode a source iteratively, improving the distortion at each step. If the code rates of all steps combined can be as efficient as coding only for the final distortion in one go, then the source is said to be success ...

2014

Mass distributions marginalized over per-event errors

Frédéric Guillaume Dupertuis

We present generalizations of the Crystal Ball function to describe mass peaks in which the per event mass resolution is unknown and marginalized over. The presented probability density functions are tested using a series of toy Monte Carlo samples generat ...

Elsevier Science Bv2014

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Is non-unique decoding necessary?

Vinod Malathidevi Prabhakaran, Shirin Saeedi Bidokhti

In multi-terminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique decoding ...

Institute of Electrical and Electronics Engineers2014

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Martin Vetterli, Robin Scheibler, Saeid Haghighatshoar

A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT, where N is a power of two and K = O(N^α), scales sub- linearly in N for some 0 < α < 1. Assuming a ...

2013

Message-Passing Algorithms: Reparameterizations and Splittings

Nicholas Ruozzi

The max-product algorithm, a local message-passing scheme that attempts to compute the most probable assignment (MAP) of a given probability distribution, has been successfully employed as a method of approximate inference for applications arising in codin ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Scaling Exponent of List Decoders with Applications to Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Motivated by the significant performance gains which polar codes experience when they are decoded with successive cancellation list decoders, we study how the scaling exponent changes as a function of the list size L. In particular, we fix the block error ...

Ieee2013

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

Rüdiger Urbanke, Seyed Hamed Hassani

We consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel W. In particular, we study the asymptotics of the cumulative distribution, P(Z(n ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Non-binary LDPC codes and EXIT like functions

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Successive Refinement of Gaussian Projections

Mass distributions marginalized over per-event errors

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Is non-unique decoding necessary?

Generalized Codes on Graphs and Applications in Content Distribution

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Message-Passing Algorithms: Reparameterizations and Splittings

Scaling Exponent of List Decoders with Applications to Polar Codes

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Mass distributions marginalized over per-event errors

Successive Refinement of Gaussian Projections

Scaling Exponent of List Decoders with Applications to Polar Codes

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Is non-unique decoding necessary?

A Fast Hadamard Transform for Signals with Sub-linear Sparsity

Generalized Codes on Graphs and Applications in Content Distribution

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Message-Passing Algorithms: Reparameterizations and Splittings

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization