Physical unclonable functions (PUFs) involve challenging practical applications of error-correcting codes (ECCs), requiring extremely low failure rates on the order of $10^{-6}$ and below despite raw input bit error rates as high as 22%. These requirements call for an efficient ultra-low rate code design. In this work, we propose a novel coding scheme tailored for PUFs based on Polar codes and a low-complexity version of automorphism ensemble decoding (AED). Notably, our serial AED scheme reuses a single successive cancellation (SC) decoder across multiple decoding attempts. By introducing cascaded and recursive interleavers, we efficiently scale the number of AED candidates without requiring expensive large multiplexers. An aggressive quantization strategy of only 3 bits per message further reduces the area requirements of the underlying SC decoder. The resulting coding scheme achieves the same block error rate of $10^{-6}$ as our baseline based on Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes while requiring 1.75x fewer codeword bits to encode the same K = 312 payload bits. This reduction translates directly into 1.75x less helper data storage and, consequently, a smaller overall chip area.

翻译：物理不可克隆函数（PUFs）对纠错码（ECCs）提出了极具挑战性的实际应用要求：尽管原始输入比特错误率高达22%，仍需实现低至$10^{-6}$量级及以下的极低失效率。这些要求催生了高效超低码率编码设计的必要性。本研究提出一种基于极化码的新型编码方案，专为PUFs定制，并采用低复杂度版本的自同构集成解码（AED）算法。值得注意的是，我们的串行AED方案通过在多次解码尝试中复用单个连续消除（SC）解码器，显著降低了硬件开销。通过引入级联与递归交织器，我们实现了AED候选规模的扩展，同时避免了昂贵的大型多路复用器需求。采用每消息仅3比特的激进量化策略，进一步降低了底层SC解码器的面积需求。实验结果表明，该编码方案在保持与基于Bose-Ray-Chaudhuri-Hocquenghem（BCH）码的基线方案相同$10^{-6}$误块率的同时，对相同K = 312有效载荷比特进行编码所需的码字比特数减少了1.75倍。这一缩减直接转化为1.75倍的辅助数据存储量降低，最终实现整体芯片面积的减小。