Advances in Error-Correcting Codes and Information Theory

The field of error-correcting codes and information theory is seeing significant developments, with a focus on innovative methods for constructing and analyzing codes. Researchers are exploring new approaches to expand self-orthogonal codes, unified error analysis for synchronous and asynchronous systems, and block length gains for nanopore channels. Additionally, there is a growing interest in function-correcting codes with data protection, linear hull codes, and stitched polar codes. These advances have the potential to improve the reliability and efficiency of data transmission and storage systems. Noteworthy papers include:

  • Block Length Gain for Nanopore Channels, which extends the idea of Geno-Weaving to combat deletion errors and shows its advantages in reducing finite-length penalty.
  • Stitched Polar Codes, which introduces a novel generalization of regular polar codes that consistently outperforms them.

Sources

How to Expand a Self-orthogonal Code

Unified Error Analysis for Synchronous and Asynchronous Two-User Random Access

Block Length Gain for Nanopore Channels

On the Hamming Weight Functions of Linear Codes

Function-Correcting Codes With Data Protection

On Construction of Linear (Euclidean) Hull Codes over Finite Extensions Binary Fields

Theoretical and Empirical Analysis of Lehmer Codes to Search Permutation Spaces with Evolutionary Algorithms

Stitched Polar Codes

One-Shot Coding and Applications

Computer-aided Characterization of Fundamental Limits of Coded Caching with Linear Coding

Two-Step Decoding of Binary $2\times2$ Sum-Rank-Metric Codes

Dimension-counting bounds for equi-isoclinic subspaces

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