Role of the product λ′(0)ρ′(1) in determining ldpc code performance

The objective of this work is to analyze the importance of the product λ′ (0)ρ′ (1) in determining low density parity check (LDPC) code performance, as far as its influence on the weight distribution function and on the decoding thresholds. This analysis is based on the 2006 paper by Di et al., as far as the weight distribution function is concerned, and on the 2018 paper by Vatta et al., regarding the LDPC decoding thresholds. In particular, the first paper Di et al. analyzed the relation between the above mentioned product and the minimum weight of an ensemble of random LDPC codewords, whereas in the second some analytical upper bounds to the LDPC decoding thresholds were determined. In the present work, besides analyzing the performance of an ensemble of LDPC codes through the outcomes of Di et al.’s 2006 paper, we give the relation between one of the upper bounds found in Vatta et al.’s 2018 paper and the above mentioned product λ′ (0)ρ′ (1), thus showing its role in also determining an upper bound to LDPC decoding thresholds.