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 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, 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 binary erasure channel (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，所有后续待估计的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，其级联编码方案还包含由先前已估计比特因果生成的奇偶校验比特（或动态冻结比特）。我们将位于目标译码比特之后的冻结比特和奇偶校验比特称为其未来约束（FCs）。尽管给定先前估计值时FCs取值具有确定性，但传统基于SC的译码器并未利用这一特性，导致无法达到最优性能。本文提出逐次消去校验（SCC）和置信传播SCC（BP-SCC）译码算法以在译码过程中利用FCs。我们进一步基于栈回溯跳转（SBJ）技术，设计了一种改进的树搜索方法用于求解由FCs构成的动态约束满足问题（CSPs）。在二进制删除信道（BEC）上的数值结果表明，BP-SCC算法与SBJ树搜索技术的组合可实现接近依赖性测试（DT）界的删除恢复性能，该界为有限码长可达性能边界。