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Phase Transitions for Mutual Information

Publications associées (77)

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New Results On The Pseudoredundancy

Zihui Liu

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...

2019

Improved decoding of second-order Reed-Muller codes

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...

IEEE2019

Reed-Muller codes polarize

Emmanuel Abbé, Min Ye

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are gen ...

IEEE COMPUTER SOC2019

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

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

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels

Rüdiger Urbanke, Seyed Hamed Hassani, Shrinivas Kudekar, Yury Polyanskiy

Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...

IEEE2018

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

A New Coding Paradigm for the Primitive Relay Channel

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

We present a coding paradigm that provides a new achievable rate for the primitive relay channel by combining compress-and-forward and decode-and-forward with a chaining construction. In the primitive relay channel model, the source broadcasts a message to ...

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

The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances: A Proof From the Polymer Expansion

Nicolas Macris, Marc Vuffray

The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...

Ieee-Inst Electrical Electronics Engineers Inc2016