Publications related to Compute-and-Forward: Harnessing Interference Through Structured Codes

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 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

On the Power and Limitations of Branch and Cut

Mika Tapani Göös

The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formu ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

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

Reliable decoding of motor state transitions during imagined movement

José del Rocio Millán Ruiz, Ricardo Andres Chavarriaga Lozano, Bastien Orset

Current non-invasive Brain Machine interfaces commonly rely on the decoding of sustained motor imagery activity. This approach enables a user to control brain-actuated devices by triggering predetermined motor actions. However, despite of its broad range o ...

IEEE2019

PolarBear: A 28-nm FD-SOI ASIC for Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming, Thomas Christoph Müller, Andrea Bonetti, Pascal Giard

Polar codes are a recently proposed class of block codes that provably achieve the capacity of various communication channels. They received a lot of attention as they can do so with low-complexity encoding and decoding algorithms, and they have an explici ...

2017

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Van Thang Pham

We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of th ...

Academic Press Inc Elsevier Science2017

Approximate Decoding for Network Coded Inter-dependent Data

Pascal Frossard, Nikolaos Thomos, Hyung Gon Park

In this paper, we consider decoding of loss tolerant data encoded by network coding and transmitted over error-prone networks. Intermediate network nodes typically perform the random linear network coding in a Galois field and a Gaussian elimination is use ...

Elsevier Science Bv2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Multiple-field based code generator and decoder for communications systems

Mohammad Amin Shokrollahi, Lorenz Minder

A method of encoding data for transmission from a source to a destination over a communications channel is provided. The method operates on an ordered set of input symbols and includes generating a plurality of redundant symbols from the input symbols base ...

2016

Compute-and-Forward: Harnessing Interference Through Structured Codes

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Symmetry in design and decoding of polar-like codes

On Codes Decoding a Constant Fraction of Errors on the BSC

On the Power and Limitations of Branch and Cut

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Reliable decoding of motor state transitions during imagined movement

PolarBear: A 28-nm FD-SOI ASIC for Decoding of Polar Codes

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Approximate Decoding for Network Coded Inter-dependent Data

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Multiple-field based code generator and decoder for communications systems

On the Power and Limitations of Branch and Cut

Symmetry in design and decoding of polar-like codes

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

PolarBear: A 28-nm FD-SOI ASIC for Decoding of Polar Codes

Reliable decoding of motor state transitions during imagined movement

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

On Codes Decoding a Constant Fraction of Errors on the BSC

Approximate Decoding for Network Coded Inter-dependent Data

Multiple-field based code generator and decoder for communications systems