Efficient encoding of QC-LDPC codes related to cyclic MDS codes

Abstract

In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes which are related to cyclic maximum-distance separable (MDS) codes. The algorithm has linear time complexity, and it can be easily implemented by using polynomial multiplication and division circuits. We show that the division polynomials can be completely characterized by its zeros and that the sum of the numbers of the zeros is equal to the parity-length of the codes.

Overview of the FABULOUS EU Project: Final System Performance Assessment With Discrete Components

“…Such code is composed by a Reed Solomon RS(781,765) outer code and a concatenated QC-LDPC code as inner code. The resulting area occupation of both RS and LDPC FEC encoders is negligible with respect to DSP area occupation ( [17]);  a SRRC up-sampling filter, made of 128 complex taps;  a dual 600 MSps DAC. It is worth pointing out that the complexity of the US FEC resides mostly at the OLT, for the FEC decoding phase, where computational complexity is less of an issue compared to the ONU side since the overall cost can be shared by all users.…”