General Bounds for Linear Code Conversion in the Merge Regime

Prof. Stanislav Kruglik

Technical University of Denmark (DTU)

Abstract:

Erasure codes are a core component of most existing large-scale distributed storage systems, ensuring reliability against node failures. Recent work has shown that adapting code parameters to changing node failure rates can lead to significant storage savings. The default approach is to re-encode the data under a new code, which consumes substantial system resources. Code conversion was introduced to reduce this cost. However, existing work has mainly focused on conversions within specific classes of codes. In this paper, we study scalar linear code conversion in the merge regime for arbitrary linear codes. We derive universal lower bounds on the write and read costs in terms of unchanged and read symbols. The bounds are refined using generalized Hamming weights, which capture support-growth properties of subcodes and can give sharper estimates than minimum-distance-only arguments. We show that the framework recovers known bounds for important special cases and can be strictly stronger when the final code has nontrivial jumps in its generalized Hamming weight hierarchy. Based on arxiv.org/abs/2606.27179 (under review at TCOM).

Biography:

Stanislav Kruglik is a tenure-track Assistant Professor in the Coding & Visual Communication Research Group at the Technical University of Denmark (DTU). Prior to joining DTU, he was a Research Fellow at Nanyang Technological University. He received his PhD in Theoretical Computer Science from the Moscow Institute of Physics and Technology in February 2022. His research interests span information theory and coding theory, with applications to distributed storage and data processing.