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Polar Code Moderate Deviation: Recovering the Scaling Exponent
TLDR
It is shown that polar coding is able to produce a series of codes that achieve capacity on symmetric binary-input memoryless channels and the latest result in the moderate deviation regime does not imply the scaling exponent regime as a special case.
Polar Codes’ Simplicity, Random Codes’ Durability
TLDR
The core theme is to incorporate polar coding with large, random, dynamic kernels (which boosts the performance to random’s realm), and the putative codes are optimal in the following manner.
Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability
TLDR
As a corollary, a grafted variant of polar coding almost catches up the code rate and error probability of random codes with complexity slightly larger than $N\log N$ over BEC.
Log-Logarithmic Time Pruned Polar Coding
TLDR
A pruned variant of polar coding is proposed for binary erasure channel (BEC) and has the lowest per-bit time complexity among all capacity-achieving codes known to date.
Multilinear Algebra for Distributed Storage
TLDR
This work establishes a multilinear algebra foundation to assemble $(n, k, d, \alpha, \beta, M)$-ERRCs for all meaningful tuples, and ties the $\alpha/M$-versus-$\beta/M $ trade-off with cascade codes, the best known construction for this trade-offs.
Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels
TLDR
A pruned variant of polar coding is reinvented for all binary erasure channels for small $\varepsilon>0$ codes with block length, code rate, error probability, and encoding and decoding time complexity.
Parity-Checked Strassen Algorithm
TLDR
To multiply astronomic matrices using parallel workers subject to straggling, this work recommends interleaving checksums with some fast matrix multiplication algorithms, and proposes probability-wise favorable configurations whose numbers of workers are close to, if not less than, the thresholds of other codes.
Multilinear Algebra for Minimum Storage Regenerating Codes
  • I. Duursma, Hsin-Po Wang
  • Computer Science, Mathematics
    Applicable Algebra in Engineering, Communication…
  • 30 June 2020
TLDR
In this work, various ways to re-express the infamous product-matrix construction using skew-symmetric matrices, polynomials, symmetric algebras, and exterior alge bras are explored.