New quasi-cyclic LDPC codes with girth at least eight based on Sidon sequences

A new family of quasi-cyclic low-density parity-check (LDPC) codes of girth at least eight is explicitly constructed from Sidon sequences. These codes can be encoded using simple shift-registers. Furthermore, for short to moderate lengths these quasi-cyclic codes perform close to random progressive edge-growth (PEG) LDPC codes in terms of bit-error probability and block-error probability, collectively.