A Class of LDPC Erasure Distributions with Closed-Form Threshold Expression

— In this paper, a family of low-density parity-check (LDPC) degree distributions, whose decoding threshold on the binary erasure channel (BEC) admits a simple closed form, is presented. These degree distributions are a subset of the check regular distributions (i.e. all the check nodes have the same degree), and are referred to as p-positive distributions. It is given proof that the threshold for a p-positive distribution is simply expressed by [λ (0)ρ (1)]−1 . Besides this closed form threshold expression, the p-positive distributions exhibit three additional properties. First, for given code rate, check degree and maximum variable degree, they are in some cases characterized by a threshold which is extremely close to that of the best known check regular distributions, under the same set of constraints. Second, the threshold optimization problem within the p-positive class can be solved in some cases with analytic methods, without using any numerical optimization tool. Third, t...

• Type: Conference
• Year: 2007
• Where: ICC
• Authors: Enrico Paolini, Marco Chiani
• Keywords: Check Regular Distributions, Communications, Degree Distributions, ICC 2007, P-positive Distributions