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Universal Polar Codes

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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

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

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

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

LLR-Based Successive Cancellation List Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming

We show that successive cancellation list decoding can be formulated exclusively using log-likelihood ratios. In addition to numerical stability, the log-likelihood ratio based formulation has useful properties that simplify the sorting step involved in su ...

Institute of Electrical and Electronics Engineers2015

Finite-Length Scaling for Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Consider a binary-input memoryless output-symmetric channel W. Such a channel has a capacity, call it I (W), and for any R < I (W) and strictly positive constant P-e we know that we can construct a coding scheme that allows transmission at rate R with an e ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Generalized Codes on Graphs and Applications in Content Distribution

Masoud Alipour Babaei

The contribution of this thesis is twofold. In the first part, we generalize and analyze two classes of error correcting codes: LDPC codes and product codes. We generalize graphical codes by considering checks being arbitrary codes instead of single pariti ...

EPFL2013

Windowed Decoding of Spatially Coupled Codes

Rüdiger Urbanke

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as fo ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Conditions for Robustness of Polar Codes in the Presence of Channel Mismatch

Mine Alsan

A challenging problem related to the design of polar codes is "robustness against channel parameter variations'', as stated in Arıkan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as a mismatch decodi ...

2013