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Reed-Muller codes polarize

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Symmetry in design and decoding of polar-like codes

Kirill Ivanov

The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...

EPFL2022

Optima Age Over Erasure Channels

Emre Telatar, Elie Najm, Rajai Nasser

Previous works on age of information and erasure channels have dealt with specific models and computed the average age or average peak age for certain settings. In this paper, given a source that produces a letter every T-s seconds and an erasure channel t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

Michael Christoph Gastpar, Erixhen Sula

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, ou ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Emmanuel Abbé, Min Ye

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM code ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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

Permutation-based Decoding of Reed-Muller Codes in Binary Erasure Channel

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...

IEEE2019

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

Optimal Age over Erasure Channels

Emre Telatar, Elie Najm, Rajai Nasser

Given a source that produces a letter every T-s seconds and an erasure channel that can be used every T-c seconds, we ask what is the coding strategy that minimizes the time-average "age of information" that an observer of the channel output incurs. We wil ...

IEEE2019

High-Dimensional Inference on Dense Graphs with Applications to Coding Theory and Machine Learning

Mohamad Baker Dia

We are living in the era of "Big Data", an era characterized by a voluminous amount of available data. Such amount is mainly due to the continuing advances in the computational capabilities for capturing, storing, transmitting and processing data. However, ...

EPFL2018

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