Average Bit Erasure Probability of Regular LDPC Code Ensembles under MAP Decoding over BEC

Takayuki Itsui, Kenta Kasai, Ryoji Ikegaya, Tomoharu Shibuya, Kohichi Sakaniwa

Abstract: The average bit erasure probability of a binary linear code ensemble under maximum <I>a-posteriori</I> probability (MAP) decoding over binary erasure channel (BEC) can be calculated with the average support weight distribution of the ensemble via the EXIT function and the shortened information function. In this paper, we formulate the relationship between the average bit erasure probability under MAP decoding over BEC and the average support weight distribution for a binary linear code ensemble. Then, we formulate the average support weight distribution and the average bit erasure probability under MAP decoding over BEC for regular LDPC code ensembles.