Publications related to Finite fields And Error-Correcting Codes

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Design and Decoding of Irregular LDPC Codes Based on Discrete Message Passing

Andreas Peter Burg

We consider discrete message passing (MP) decoding of low-density parity check (LDPC) codes based on information-optimal symmetric look-up table (LUT). A link between discrete message labels and the associated log-likelihood ratio values (defined in terms ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore, Chen Feng

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

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

Approximation-aware Rewriting of AIGs for Error Tolerant Applications

Mathias Soeken, Arun Chandrasekharan

Approximation circuits offer superior performance (speed and area) compared to traditional circuits at the cost of computational accuracy. The accuracy of the results in approximation circuits is evaluated based on several error metrics such as worst-case ...

Assoc Computing Machinery2016

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

Algebraic twists of modular forms and Hecke orbits

Philippe Michel

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistri ...

Springer Verlag2015

Universal Polar Codes

Rüdiger Urbanke, Seyed Hamed Hassani

Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless outputsymmetric channel. Further, both the encoding and the decoding can be accomplished in O(N log(N)) real operations, where N is the blocklength. O ...

Ieee2014

Finite fields And Error-Correcting Codes

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Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Design and Decoding of Irregular LDPC Codes Based on Discrete Message Passing

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Arithmetic and geometric structures in cryptography

Patching And Weak Approximation In Isometry Groups

Multiple-field based code generator and decoder for communications systems

Approximation-aware Rewriting of AIGs for Error Tolerant Applications

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

Algebraic twists of modular forms and Hecke orbits

Universal Polar Codes

Approximation-aware Rewriting of AIGs for Error Tolerant Applications

Multiple-field based code generator and decoder for communications systems

Patching And Weak Approximation In Isometry Groups

Algebraic twists of modular forms and Hecke orbits

Universal Polar Codes

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Design and Decoding of Irregular LDPC Codes Based on Discrete Message Passing

Arithmetic and geometric structures in cryptography

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

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals