Minimum distances of LDPC codes in 5G standard
2026-07-06 • Information Theory
Information Theory
AI summaryⓘ
The authors studied a type of error-correcting code used in 5G networks called quasi-cyclic LDPC codes. They found specific ranges for the smallest number of errors these codes can detect for two particular code setups. They also introduced a new method to make the decoding process faster by simplifying some calculations. Overall, their work helps understand how well these codes perform and how to decode them more efficiently.
quasi-cyclic LDPC codes5G NR standardminimum distanceerror correctionearly terminationsyndrome calculationcirculant modular reductiondecoder complexity
Authors
V. R. Danilko, I. Yu. Mogilnykh, Ya. A. Tikhomolov
Abstract
We propose several approaches for bounding the minim\-um distances of the family of quasi-cyclic LDPC codes in the 5G NR standard. In particular, we show that the high-rate [9984, 8448] and the low-rate [25344, 8448] BG1 5G LDPC codes have minimum distances in the ranges {8..14} and {22..57}, respectively. Also we propose a new early termination approach based on circulant modular reduction, which significantly lowers syndrome calculation complexity for the LDPC decoder.