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

翻译：在传统极化码逐次消去（SC）译码器中，所有后续待估计比特均被视为随机变量。然而，极化码不可避免地包含冻结比特，其级联编码方案中还存在由先前已估计比特因果生成的校验比特（或动态冻结比特）。我们将目标译码比特后方的冻结比特与校验比特称为其\textit{未来约束（FCs）}。尽管根据历史估计值可确定FCs的取值，但传统SC类译码器未利用这一特性，因此无法达到最优性能。本文针对二进制删除信道（BEC），提出SC校验（SCC）算法与置信传播SCC（BP-SCC）译码算法以利用FCs进行译码。我们进一步基于堆栈回溯（SBJ）技术设计了一种改进树搜索方法，用于求解由FCs构成的动态约束满足问题（CSPs）。在BEC上的数值结果表明，BP-SCC算法与SBJ树搜索技术的联合方案可实现接近依赖性检验（DT）界的擦除恢复性能，该界是可达有限长性能的理论界限。