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Exchange of Limits: Why Iterative Decoding Works

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We study the stability of low-density parity-check codes under blockwise or bitwise maximum a posteriori decoding, where transmission takes place over a binary-input memoryless output-symmetric channel. Our study stems from the consideration of constructin ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

On the Universality of Low-Density Parity-Check Block Codes

Rüdiger Urbanke, Wei Liu

An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this pape ...

IEEE2020

From LDPC Block to LDPC Convolutional Codes: Capacity, Stability, and Universality

Wei Liu

In his landmark paper "A Mathematical Theory of Communication," the founding father of information theory and coding theory, Claude E. Shannon, established the largest rate at which reliable communication is possible and he revealed that the key to this re ...

EPFL2019

The Stability Condition of LDPC Codes Under MAP Decoding

Rüdiger Urbanke, Wei Liu

We determine the stability condition of low-density parity-check codes under both bitwise and blockwise maximum a posteriori decoding. As a consequence, we prove that the stability condition determines an upper bound on both the bitwise and the blockwise m ...

IEEE2018

Fast Low-Complexity Decoders for Low-Rate Polar Codes

Alexios Konstantinos Balatsoukas Stimming, Pascal Giard

Polar codes are capacity-achieving error-correcting codes with an explicit construction that can be decoded with low-complexity algorithms. In this work, we show how the state-of-the-art low-complexity decoding algorithm can be improved to better accommoda ...

2018

Fast-SSC-Flip Decoding of Polar Codes

Andreas Peter Burg, Pascal Giard

Polar codes are widely considered as one of the most exciting recent discoveries in channel coding. For short to moderate block lengths, their error-correction performance under list decoding can outperform that of other modern error-correcting codes. Howe ...

2018

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Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of codes has not been ...

Ieee2017

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 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

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