Publications related to Binary Golay code

Symmetry in design and decoding of polar-like codes

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

On the Efficiency of Polar-Like Decoding for Symmetric Codes

Rüdiger Urbanke, Kirill Ivanov

The recently introduced polar codes constitute a breakthrough in coding theory due to their capacity-achieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures based on the Plo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

On Codes Decoding a Constant Fraction of Errors on the BSC

Jan Hazla

We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is succe ...

ASSOC COMPUTING MACHINERY2021

New Results On The Pseudoredundancy

Jens Markus Zumbrägel, 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

On the Computational Complexity of Blind Detection of Binary Linear Codes

Alexios Konstantinos Balatsoukas Stimming, Aris Filos Ratsikas

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes C of a given dimension k, for which t ...

IEEE2019

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

Design rules for optimizing unipolar coded Brillouin optical time-domain analyzers

Luc Thévenaz, Zhisheng Yang, Marcelo Alfonso Soto Hernandez, Simon Adrien Zaslawski, Zonglei Li

The performance of unipolar unicolor coded Brillouin optical time-domain analysis (BOTDA) is evaluated based on both Simplex and Golay codes. Four major detrimental factors that limit the system performance, including decoded-gain trace distortion, coding ...

2018

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

Considerations for Rank-based Cryptosystems

Anna-Lena Horlemann, Joachim Rosenthal

Cryptosystems based on rank metric codes have been considered as an alternative to McEliece cryptosystems due to the relative difficulty of solving the rank syndrome decoding problem. Generic attacks have recently seen several improvements, notably in the ...

Ieee2016

Linear Programming Decoding of Spatially Coupled Codes

Rüdiger Urbanke, Badih Ghazi

For a given family of spatially coupled codes, we prove that the linear programming (LP) threshold on the binary-symmetric channel (BSC) of the tail-biting graph cover ensemble is the same as the LP threshold on the BSC of the derived spatially coupled ens ...

Ieee-Inst Electrical Electronics Engineers Inc2014

LDPC Codes for 2D Arrays

Mohammad Amin Shokrollahi, Yuval Cassuto

Binary codes over 2D arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper, we propose a new framework for probabilistic construction of codes on 2D arrays. Instead of a p ...

Institute of Electrical and Electronics Engineers2014

Function computation via subspace coding

Christina Fragouli, Lorenzo Keller, Nikhil Karamchandani

This paper considers function computation in a network where intermediate nodes perform randomized network coding, through appropriate choice of the subspace codebooks at the source nodes. Unlike traditional network coding for comput- ing functions, that r ...

2013

Non-coherent Network Coding: An Arbitrarily Varying Channel Approach

Mahdi Jafari Siavoshani

In this paper, we propose an "arbitrarily varying channel" (AVC) approach to study the capacity of non-coherent transmission in a network that employs randomized linear network coding. The network operation is modeled by a matrix channel over a finite fiel ...

Ieee2012

Network Coding : Theoretical Designs Directed to Applications

Mahdi Jafari Siavoshani

The demand for higher throughput and better efficiency are two important challenges for future communication networks. During the past decades, a lot of research studies have been devoted to investigating and proposing near optimal and efficient schemes an ...

EPFL2012

On the capacity of non-coherent network coding

Christina Fragouli, Suhas Diggavi, Mahdi Jafari Siavoshani, Soheil Mohajerzefreh

We consider the problem of multicasting information from a source to a set of receivers over a network where interme- diate network nodes perform randomized linear network coding operations on the source packets. We propose a channel model for the noncoher ...

2011

Phase Transitions for Mutual Information

Mohammad Amin Shokrollahi, Amir Hesam Salavati, Krishna Kumar, Raj Kumar Krishna Kumar

We consider ensembles of binary linear error correcting codes, obtained by sampling each column of the generator matrix G or parity check matrix H independently from the set of all binary vectors of weight d (of appropriate dimension). We investigate the c ...

IEEE2010

Joint Identity-Message Coding for Sensor Networks

Aikaterini Argyraki, Christina Fragouli, Suhas Diggavi, Lorenzo Keller, Mahdi Jafari Siavoshani

In a significant class of sensor-network applications, the identities of the reporting sensors constitute the bulk of the communicated data, whereas the message itself can be as small as a single bit—for instance, in many cases, sensors are used to detect ...

Institute of Electrical and Electronics Engineers2010

Function computation via subspace coding

Christina Fragouli, Lorenzo Keller, Nikhil Karamchandani

This paper considers function computation in a network where intermediate nodes perform randomized network coding, through appropriate choice of the subspace codebooks at the source nodes. Unlike traditional network coding for computing functions, that req ...

2010

Compressed network coding vectors

Aikaterini Argyraki, Christina Fragouli, Lorenzo Keller, Mahdi Jafari Siavoshani

In networks that employ network coding, two main approaches have been proposed in the literature to allow the receivers to recover the source information: (i) use of coding vectors, that keep track of the linear combinations the received packets contain, a ...

2009