Successive Cancellation Decoding with Future Constraints for Polar Codes Over the Binary Erasure Channel

In the conventional successive cancellation (SC) decoder for polar codes, all future bits to be estimated later are treated as random variables. However, codes inevitably involve frozen bits, and their concatenated coding schemes also include parity (or dynamic bits) causally generated from past earlier. We refer located behind a target decoding bit its future constraints (FCs) . Although values of FCs deterministic given estimates, they have not been exploited in SC-based decoders, leading optimality. this paper, we propose SC-check (SCC) belief propagation SCC (BP-SCC) algorithms order leverage decoding. further devise an improved tree search technique based on stack-based backjumping (SBJ) solve constraint satisfaction problems (CSPs) formulated by FCs. Over binary erasure channel (BEC), numerical results show that combination BP-SCC algorithm SBJ achieves recovery performance close dependence testing (DT) bound, bound achievable finite-length performance.