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04/24/2023
Fast Methods for Ranking Synthetic BECs
We gather existing methods that are used to compare and rank the BECs sy...
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04/16/2023
Density Devolution for Ordering Synthetic Channels
Constructing a polar code is all about selecting a subset of rows from a...
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04/16/2023
Optimal Self-Dual Inequalities to Order Polarized BECs
1 - (1-x^M) ^ 2^M > (1 - (1-x)^M) ^2^M is proved for all x ∈ [0,1] and a...
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07/10/2022
Accelerating Polarization via Alphabet Extension
Polarization is an unprecedented coding technique in that it not only ac...
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04/25/2022
Sub-4.7 Scaling Exponent of Polar Codes
Polar code visibly approaches channel capacity in practice and is thereb...
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01/12/2022
Tropical Group Testing
Polymerase chain reaction (PCR) testing is the gold standard for diagnos...
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07/13/2021
Complexity and Second Moment of the Mathematical Theory of Communication
The performance of an error correcting code is evaluated by its error pr...
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11/30/2020
Parity-Checked Strassen Algorithm
To multiply astronomic matrices using parallel workers subject to stragg...
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06/30/2020
Multilinear Algebra for Minimum Storage Regenerating Codes
An (n, k, d, α)-MSR (minimum storage regeneration) code is a set of n no...
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06/16/2020
Multilinear Algebra for Distributed Storage
An (n, k, d, α, β, M)-ERRC (exact-repair regenerating code) is a collect...
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12/19/2019
Polar Codes' Simplicity, Random Codes' Durability
Over any discrete memoryless channel, we build codes such that: for one,...
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05/30/2019
Log-logarithmic Time Pruned Polar Coding
A pruned variant of polar coding is proposed for binary erasure channels...
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12/19/2018
Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability
A general framework is proposed that includes polar codes over arbitrary...
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12/19/2018
Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels
A pruned variant of polar coding is reinvented for all binary erasure ch...
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06/06/2018