Decoding of Polar Codes with Future Constraints Over the Binary Erasure Channel

We address the suboptimality of successive cancellation (SC) decoding for polar codes, which is caused by treating as random variables all the future bits to be estimated later. For a target information bit, we define the frozen and parity bits located behind it as its future constraints (FCs). To incorporate FCs into the sequential decoding of the target bit, we propose two elementary techniques: an SC check (SCC) algorithm and an FC conversion rule enabling belief propagation (BP). Focusing on the binary erasure channel (BEC), we also present a tree search technique based on stack-based backjumping (SBJ) to efficiently solve dynamic constraint satisfaction problems (CSP) formulated by FCs. Numerical results show that the combination of BP and SCC decoding algorithms accompanied with the SBJ technique achieves excellent erasure recovery performance over the BEC, which is close to the dependence testing (DT) achievability bound.