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Computational Hardness and Explicit Constructions of Error Correcting Codes

Related publications (68)

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Static Worst-Case Resource Analysis for Substrate Pallets

Simon Nicolas Perriard

We present saft, the first attempt of a static analyzer that extracts the asymptotic function complexity for the Polkadot/Substrate ecosystem, where the burden of accounting for computation resource consumption is put on the developer. saft is a tool meant ...

2023

Latency Interfaces for Systems Code

Rishabh Ramesh Iyer

This thesis demonstrates that it is feasible for systems code to expose a latency interface that describes its latency and related side effects for all inputs, just like the code's semantic interface describes its functionality and related side effects.Sem ...

EPFL2023

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

Relaxed Locally Correctable Codes With Nearly-Linear Block Length And Constant Query Complexity

Alessandro Chiesa

Locally correctable codes (LCCs) are error correcting codes C : \Sigmak \rightarrow \Sigman which admit local algorithms that correct any individual symbol of a corrupted codeword via a minuscule number of queries. For systematic codes, this notion is stro ...

SIAM PUBLICATIONS2022

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2022

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

Fast Block Sequential Decoding of Polar Codes

Kirill Ivanov

A reduced complexity sequential decoding algorithm for polar (sub) codes is described. The proposed approach relies on a decomposition of the polar (sub) code being decoded into a number of outer codes, and on-demand construction of codewords of these code ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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

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

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