In this paper, the decoding of low-density parity-check (LDPC) codes is considered. A new algorithm, named $\lambda-$Min algorithm, for updating extrinsic information is proposed. The $\lambda-$Min algorithm offers different trade-off performance versus complexity between the belief propagation (BP) algorithm (optimal but complex) and the universal most powerful (UMP) BP-based algorithm (simple but leading to significant performance degradation in some cases). Hardware implementation of the $\lambda-$Min algorithm in a serial mode is also discussed. Reduction up to 75 \% of the extrinsic memory information can be obtained with high rate LDPC code without any significant degradation of the performance.