Simplified Multi-Level Quasi-Cyclic LDPC Codes for Low-Complexity Encoders

In this paper we propose a parity check matrix construction technique that simplifies the hardware encoders for Multi-Level-Quasi-Cyclic (ML-QC) LDPC codes. The proposed construction method is based on semi-random - ML-QC extension and appropriately selects shifting factors to reduce the density of the inverted matrix used in several encoding algorithms. The construction method derives low-complexity encoders with minimal degradation of error-correction performance, observable at low BER only. Furthermore a VLSI encoding architecture based on the suggested parity-check matrix (PCM) is also introduced. Experimental results show that the complexity of the proposed encoders depends on the density of the binary base matrix. A comparison with random QC codes reveals substantial complexity reduction without performance degradation for cases of practical interest. In fact a hardware complexity reduction by a factor of 7.5 is achieved, combined with the acceleration of the encoder, for certain cases.