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Low-density parity-check codes with rates very close to the capacity of the q-ary symmetric channel for large q

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Hardware implementation aspects of polar decoders and ultra high-speed LDPC decoders

Alexios Konstantinos Balatsoukas Stimming

The goal of channel coding is to detect and correct errors that appear during the transmission of information. In the past few decades, channel coding has become an integral part of most communications standards as it improves the energy-efficiency of tran ...

EPFL2016

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

A Multi-Gbps Unrolled Hardware List Decoder Systematic Polar Code

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming, Thomas Christoph Müller, Pascal Giard

Polar codes are a new class of block codes with an explicit construction that provably achieve the capacity of various communications channels, even with the low-complexity successive-cancellation (SC) decoding algorithm. Yet, the more complex successive-c ...

2016

Hardware Decoders for Polar Codes: An Overview

Andreas Peter Burg, Pascal Giard

Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from error-correction performa ...

Ieee2016

Polar Codes for Arbitrary DMCs and Arbitrary MACs

Emre Telatar, Rajai Nasser

Polar codes are constructed for arbitrary channels by imposing an arbitrary quasi-group structure on the input alphabet. Just as with usual polar codes, the block error probability under successive cancellation decoding is O(2^(-N^(1/2-epsilon))), where N ...

Institute of Electrical and Electronics Engineers2016

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

Optimal Computational Split-state Non-malleable Codes

Divesh Aggarwal, Divya Gupta

Non-malleable codes are a generalization of classical error-correcting codes where the act of "corrupting" a codeword is replaced by a "tampering" adversary. Non-malleable codes guarantee that the message contained in the tampered codeword is either the or ...

Springer Int Publishing Ag2016

Approximate Decoding for Network Coded Inter-dependent Data

Pascal Frossard, Nikolaos Thomos, Hyung Gon Park

In this paper, we consider decoding of loss tolerant data encoded by network coding and transmitted over error-prone networks. Intermediate network nodes typically perform the random linear network coding in a Galois field and a Gaussian elimination is use ...

Elsevier Science Bv2016

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