Abstract
We introduce fair-density parity-check (FDPC) codes targeting high-rate applications. In particular, we start with a base parity-check matrix, where the number of rows scales with the square root of the block length. We propose a deterministic combinatorial method for picking the base matrix. Then we extend this by obtaining permuted versions of the base matrix and stacking them on top of each other leading to codes of smaller dimension (but still at the high-rate regime). We discuss methods to explicitly characterize and bound the weight distribution of the new codes and utilize them to derive union-type approximate upper bounds on their error probability under Maximum Likelihood (ML) decoding. We further propose a combination of weighted min-sum message-passing (MP) decoding algorithm together with a new progressive list (PL) decoding component, referred to as the MP-PL decoder, to decode FDPC codes. Simulation results are shown for various high-rate FDPC codes in moderate-to-large block length regimes. We numerically demonstrate that they beat other state-of-the-art codes for various ranges of parameters in the high-rate regime, with the lower-complexity and lower-latency MP-PL decoder.