From the perspective of tree, we design a length-flexible coding scheme. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either active bits or frozen bits, and a parent node is related to its child nodes by a length-adaptive (U+V|V) operation. Both the encoding and the successive cancellation (SC)-based decoding can be implemented over the constructed coding tree. For code construction, we propose a signal-to-noise ratio (SNR)-dependent method and two SNR-independent methods, all of which evaluate the reliabilities of leaf nodes and then select the most reliable leaf nodes as the active nodes. Numerical results demonstrate that our proposed codes can have comparable performance to the 5G polar codes. To reduce the decoding latency, we propose a partitioned successive cancellation (PSC)-based decoding algorithm, which can be implemented over a sub-tree obtained by pruning the coding tree. Numerical results show that the PSC-based decoding can achieve similar performance to the conventional SC-based decoding.

翻译：从树的角度出发，我们设计了一种长度灵活的编码方案。对于任意码长，首先构建一棵平衡二叉树（BBT），其中根节点代表传输的码字，叶节点代表活跃比特或冻结比特，父节点通过长度自适应（U+V|V）操作与其子节点相关联。编码和基于连续消除（SC）的解码均可在此构建的编码树上实现。在码构造方面，我们提出了一种依赖于信噪比（SNR）的方法和两种与信噪比无关的方法，这些方法均评估叶节点的可靠性，并选择最可靠的叶节点作为活跃节点。数值结果表明，所提出的码性能可与5G极化码相媲美。为降低解码延迟，我们提出了一种基于分区连续消除（PSC）的解码算法，该算法可在通过修剪编码树得到的子树上实现。数值结果表明，基于PSC的解码可达到与传统基于SC的解码相似的性能。