Integer programming‐based non‐uniform window decoding schedules for spatially coupled low‐density parity‐check codes

Abstract

Abstract Spatially coupled low‐density parity‐check (SC‐LDPC) codes generally use a window decoding scheme, which is known to yield a near‐optimal decoding, compared to full block decoding. Recently, a non‐uniform schedule has been proposed to eliminate unnecessary updates of variable nodes within a window: this schedule is generated based on the behaviour of variable node updates analysed by density evolution. Here, the authors present a new non‐uniform schedule based on integer programming, whereby the objective functions and constraints are derived from a protograph‐based extrinsic information transfer chart. Our design is more flexible than the previous design, because the integer programming‐based design allows reduction of update numbers and performance losses through the constraints function, whereas the previous design requires observation of variable node update behaviour. The authors report the performance of their designs of non‐uniform schedules in additive white Gaussian noise (AWGN) and inter‐symbol interference (ISI) channels. Particularly, in the ISI channel, the authors’ non‐uniform schedules are designed with cooperative decoding between a Bahl‐Cocke‐Jelinek‐Raviv (BCJR) detector and an SC‐LDPC decoder.