Linear Permutation Polynomial Codes

Quasi-cyclic low-density parity-check (QC-LDPC) codes are one of the most important code classes of LDPC codes. They have two drawbacks: lack of randomness and limited girth lead to a degraded decoding performance in the waterfall and error floor regions, respectively. To tackle these problems, we present a new class of LDPC codes, named linear permutation polynomial (LPP) codes, whose parity-check matrix consists of permutation matrices based on LPPs. The girth of regular QC-LDPC codes is upper bounded by 12, while LPP codes break this limit. We demonstrate that LPP codes have error performance almost equivalent to random ones.