Design, implementation and applications of low-complexity LDPC codes

Structured LDPC codes enable low-complexity decoding as well as efficient implementation of encoder reducing the complexity down to the order of the number of parity-check bits. Construction of structured LDPC codes is based on combinatorial approaches such as balanced-incomplete block-design (BIBD) and finite fields to design quasi-cyclic LDPC (QC-LDPC) codes. Well designed QC-LDPC codes can perform as well as randomly constructed LDPC codes with iterative decoding based on belief propagation in terms of bit-error probability. It has been shown that QC-LDPC codes can achieve lower error floor than randomly constructed LDPC codes. Within this work, the design of quasi-cyclic LDPC codes for a range of practical applications is discussed which includes construction of variable-rate large-block-length LDPC codes for DVB-S2 and DVB-T2 applications and adaptive short-block-length LDPC codes for HF applications. Moreover, efficient implementation of QC-LDPC decoder/encoder for FPGA devices which reduces memory requirements is presented.