The semi-algebra low-density parity-check codes

In this paper, the construction of semi-algebra Low-density parity-check (LDPC) code with an arbitrary block length is presented. The encoding circuit is based on the original semi-algebra design and users can have the choice of using the matrix pattern and various code rates to design for different communication applications. Especially, a novel girth scheme named Adaptive Slope Group (ASG) is proposed for the semi-algebra code design with the large girth and maximum minimum distance. We can compare the performance of this novel semi-algebra LDPC code against the Shannon limit for several rates. The simulation results show our codes can perform a large coding gain at high SNRs with BPSK modulation over AWGN channels. However, column weight j is not random, only for j=2.