In this paper, we introduce a binary balanced tree (BBT) channel transformation that extends Arıkan's channel transformation to arbitrary block lengths. We prove that the proposed transformation induces channel polarization, thereby establishing that BBT polar codes achieve the capacity of binary-input memoryless symmetric (BMS) channels. To characterize the finite-length performance of BBT polar codes, we further develop an efficient method for estimating the weight spectrum by exploiting the hierarchical tree structure, and derive analytical upper and lower bounds on the frame error rate (FER) under maximum-likelihood (ML) decoding. For practical low-latency implementations, we propose interleaved BBT (IBBT) polar codes together with a belief-propagation (BP) decoding algorithm. Specifically, based on the normal-graph representation of BBT polar codes, interleavers are introduced between adjacent layers to modify the message-passing schedule. In addition, we propose to perform BP decoding on an IBBT sub-normal graph and replace partial BP processing modules with a posteriori probability (APP) calculation modules, thereby reducing the number of message-passing steps required per iteration. Numerical results demonstrate that the proposed interleaving strategy improves decoding convergence, while the sub-normal-graph-based BP decoding algorithm significantly reduces decoding latency while maintaining comparable error-rate performance.

翻译：本文提出了一种二叉树（BBT）信道变换方法，将Arıkan信道变换推广至任意分组长度。我们证明了该变换能够引发信道极化现象，从而确立BBT极化码可达到二进制输入无记忆对称（BMS）信道的容量。为刻画BBT极化码的有限长度性能，进一步利用层次树结构发展了一种高效的权重谱估计方法，并推导了最大似然（ML）译码下帧错误率（FER）的分析上下界。针对实际低延迟实现需求，我们提出了交织BBT（IBBT）极化码及其置信传播（BP）译码算法。具体而言，基于BBT极化码的正规图表示，在相邻层级间引入交织器以调整消息传递调度。此外，我们提出在IBBT子正规图上执行BP译码，并用后验概率（APP）计算模块替代部分BP处理模块，从而减少每次迭代所需的消息传递步骤数。数值结果表明，所提出的交织策略改进了译码收敛性，而基于子正规图的BP译码算法在保持相近误码率性能的同时显著降低了译码延迟。