One of the most important units of Low-Density Parity-Check (LDPC) decoders is the Check-Node Unit. Its main task is to find the first two minimum values among incoming variable-to-check messages and return check-to-variable messages. This block significantly affects the decoding performance, as well as the hardware implementation complexity. In this paper, we first propose a modification to the check-node update rule by introducing two optimal offset factors applied to the check-to-variable messages. Then, we present the Check-Node Unit hardware architecture which performs the proposed algorithm. The main objective of this work aims to improve further the decoding performance for 5th Generation (5G) LDPC codes. The simulation results show that the proposed algorithm achieves essential improvements in terms of error correction performance. More precisely, the error-floor does not appear within Bit-Error-Rate (BER) of 10^(-8), while the decoding gain increases up to 0.21 dB compared to the baseline Normalized Min-Sum, as well as several state-of-the-art LDPC-based Min-Sum decoders
