Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of the algorithmic post-processing module based on linear codes, known as linear correctors. Our bound is based on the codes' weight distributions, and we prove that it holds even for the real-world noise sources that produce independent but not identically distributed bits. Additionally, we present a method for identifying the optimal linear corrector for a given input min-entropy rate that maximizes the throughput of the post-processed bits while simultaneously achieving the needed security level. Our findings show that for an output min-entropy rate of $0.999$, the extraction efficiency of the linear correctors with the new bound can be up to $130.56\%$ higher when compared to the old bound, with an average improvement of $41.2\%$ over the entire input min-entropy range. On the other hand, the required min-entropy of the raw bits for the individual correctors can be reduced by up to $61.62\%$.

翻译：对真实随机数生成器（TRNG）产生的原始比特进行后处理，当每比特熵不足以满足安全应用需求时总是必要的。本文推导了基于线性码的算法后处理模块（称为线性校正器）输出最小熵的紧致界。该界基于码的权重分布，且我们证明它对于产生独立但非同分布比特的现实噪声源同样成立。此外，我们提出了一种方法，用于在给定输入最小熵率下识别最优线性校正器，该方法能在最大化后处理比特吞吐量的同时达到所需安全级别。我们的结果表明，对于输出最小熵率为$0.999$的情况，采用新界的线性校正器相比旧界的提取效率最高可提升$130.56\%$，在整个输入最小熵范围内平均提升$41.2\%$。另一方面，各校正器所需原始比特的最小熵最高可降低$61.62\%$。