Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound
2026-03-25 • Information Theory
Information Theory
AI summaryⓘ
The authors create a new type of error-correcting code by combining two existing code families called Hsu-Anastasopoulos and MacKay-Neal codes. They show that these codes maintain good performance in terms of how many errors they can detect and correct, even when the code complexity is kept fixed. To support their results, they use both mathematical proofs and computer-assisted calculations, especially for certain specific cases. Their work helps ensure reliable communication with a balance between code length and error correction capability.
Calderbank-Shor-Steane codesnested codescoding raterelative linear distanceGilbert-Varshamov boundHsu-Anastasopoulos codesMacKay-Neal codeserror-correcting codescomputer-assisted proof
Authors
Kenta Kasai
Abstract
We construct nested Calderbank-Shor-Steane code pairs with non-vanishing coding rate from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove relative linear distance with high probability. Moreover, for several finite degree settings, we prove Gilbert-Varshamov distance by a rigorous computer-assisted proof.