🤖 AI Summary
This study addresses the minimum distance—a critical error-correction performance metric—of quasi-cyclic LDPC codes specified in the 5G NR standard, focusing on both high- and low-rate base graph 1 (BG1) configurations. By integrating algebraic analysis, combinatorial bounding algorithms, and cyclic modulo reduction techniques, the work establishes tight upper and lower bounds on the minimum distance for specific code instances: [9984, 8448] codes exhibit a minimum distance between 8 and 14, while [25344, 8448] codes range from 22 to 57. Furthermore, the paper introduces a novel early-termination strategy based on cyclic modulo reduction, which substantially reduces the computational complexity of parity-check operations during decoding. This approach enhances decoding efficiency without compromising error-correction performance.
📝 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.