Performance analysis of implement-oriented capacity-achieving LDPC codes on erasure channel and its encoder design

This paper is concerned with threshold performance analysis of implement-oriented low-density parity check (LDPC) ensemble on binary erasure channel and design of its H-matrix structure and encoder hardware architecture. We construct a class of the special LDPC ensemble which has capacity-achieving degree distribution pair for infinity length code over the binary erasure channel (BEC). Its special characteristic different from the other LDPC ensembles is that the coefficient lambda₁ of its degree distribution pair equal 1 instead of 0. Its H-matrix is constructed by combining zigzag matrix and partitioned permutation matrices. This paper completed a design from capacity-achieving sequence to algebraic structural H-matrix, and the H-matrix can directly be used to design low complexity recursive encoding circuit.