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Statistical physics methods for sparse graph codes

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Decoder Partitioning: Towards Practical List Decoding of Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming SG standard. As such, a lot of attention has been devoted to the development of decoding algori ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Near-Optimal Noisy Group Testing via Separate Decoding of Items

Volkan Cevher, Jonathan Mark Scarlett

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and more. In this pa ...

2018

Near-Optimal Noisy Group Testing via Separate Decoding of Items

Volkan Cevher, Jonathan Mark Scarlett

In this paper, we revisit an efficient algorithm for noisy group testing in which each item is decoded separately (Malyutov and Mateev, 1980), and develop novel performance guarantees via an information-theoretic framework for general noise models. For the ...

IEEE2018

Coding for Communications and Secrecy

Mani Bastaniparizi

Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...

EPFL2017

From Polar to Reed-Muller Codes

Marco Mondelli

The year 2016, in which I am writing these words, marks the centenary of Claude Shannon, the father of information theory. In his landmark 1948 paper "A Mathematical Theory of Communication", Shannon established the largest rate at which reliable communica ...

EPFL2016

Analysis of Spatially Coupled Systems using the Potential Functional with Applications to Coding Theory

Rafah El-Khatib

For the past 70 years or so, coding theorists have been aiming at designing transmission schemes with efficient encoding and decoding algorithms that achieve the capacity of various noisy channels. It was not until the '90s that graph-based codes, such as ...

EPFL2016

Multiuser Random Coding Techniques for Mismatched Decoding

Jonathan Mark Scarlett, Albert Guillén i Fàbregas

This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensem ...

Institute of Electrical and Electronics Engineers2016

Re-proving Channel Polarization Theorems

Mine Alsan

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Arikan proved that this class of codes, ...

EPFL2015

Sparse Probabilistic Models

Andrei Giurgiu

This thesis is concerned with a number of novel uses of spatial coupling, applied to a class of probabilistic graphical models. These models include error correcting codes, random constraint satisfaction problems (CSPs) and statistical physics models calle ...

EPFL2015

A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

Rüdiger Urbanke

Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially ...

Institute of Electrical and Electronics Engineers2015