Log-Logarithmic Time Pruned Polar Coding
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
- I. Duursma, Xiao Li, Hsin-Po Wang
- Computer ScienceSIAM Journal on applied algebra and geometry
- 16 June 2020
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.
Multilinear Algebra for Minimum Storage Regenerating Codes
- I. Duursma, Hsin-Po Wang
- Computer ScienceApplicable Algebra in Engineering, Communication…
- 30 June 2020
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.
Polar Codes’ Simplicity, Random Codes’ Durability
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 Code Moderate Deviation: Recovering the Scaling Exponent
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-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability
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.
Accelerating Polarization via Alphabet Extension
- I. Duursma, R. Gabrys, V. Guruswami, Ting Lin, Hsin-Po Wang
- Computer ScienceInternational Workshop and International Workshop…
- 10 July 2022
The main contribution is showing that the dynamic of TECs converges to an almost–one-parameter family of channels, which then leads to an upper bound of 3 .
Parity-Checked Strassen Algorithm
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.
Sub-4.7 Scaling Exponent of Polar Codes
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard, however, the per- formance of short-length polar code has rooms for improvement that could hinder its adoption by a wider class of applications.
Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels
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.