Efficient Encoding Algorithm of Binary and Non-Binary LDPC Codes Using Block Triangulation

Abstract

We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal submatrices by row and column permutations in the preprocessing stage. This algorithm determines the parity part of a codeword by block back-substitution to reduce the encoding complexity in the encoding stage. Numerical experiments show that this algorithm has a lower encoding complexity than existing encoding algorithms. Moreover, we show that this algorithm encodes the non-binary cycle codes in linear time.