# On Error Decoding of Locally Repairable and Partial MDS Codes

## TL;DR

This paper studies the effectiveness of interleaved decoding for locally repairable and partial MDS codes, showing that it can significantly improve decoding success probabilities and radius under certain conditions.

## Contribution

It provides new insights into the success probability of interleaved decoding for LRCs and demonstrates potential radius improvements for PMDS codes as code length increases.

## Key findings

- Interleaved decoding success probability approaches 1 for certain LRCs.
- Decoding radius of PMDS codes can exceed minimum distance with high probability.
- Performance improves as code length tends to infinity.

## Abstract

We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that there is a wide range of parameters for which interleaved decoding can increase their decoding radius beyond the minimum distance with the probability of successful decoding approaching $1$, when the code length goes to infinity.