Minimum distances of LDPC codes in 5G standard

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.