Distance verification for LDPC codes
Ilya Dumer, Alexey A. Kovalev, Leonid P. Pryadko
TL;DR
This paper develops new algorithms for verifying the distance of LDPC codes, providing complexity bounds tied to erasure thresholds that significantly improve upon previous estimates for linear codes.
Contribution
It re-designs generic distance verification algorithms specifically for LDPC codes and derives new exponential complexity bounds based on erasure-correcting thresholds.
Findings
New complexity bounds for LDPC code distance verification
Exponential reduction in complexity estimates compared to prior work
Bounds expressed in terms of erasure-correcting thresholds
Abstract
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are known for distance verification in other ensembles of linear codes. Our goal is to re-design the existing generic algorithms of distance verification and derive their complexity for LDPC codes. We obtain new complexity bounds with provable performance expressed in terms of the erasure-correcting thresholds of long LDPC codes. These bounds exponentially reduce complexity estimates known for linear codes.
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