Construction algorithm for network error-correcting codes attaining the Singleton bound

TL;DR

This paper presents a deterministic algorithm for constructing optimal network error-correcting codes that meet the Singleton bound, with analysis of complexity and success probability.

Contribution

It introduces a centralized construction method for optimal network error-correcting codes based on existing algorithms, with complexity and probability estimates.

Findings

The algorithm attains the Singleton bound for network error correction.

Estimated time complexity and symbol size requirements are provided.

The probability of random encoding vectors yielding optimal codes is analyzed.

Abstract

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.