二元删除信道容量精确到百分之一比特以内
Binary Deletion Channel Capacity to Within One Hundredth of a Bit
- Microsoft Research（微软研究院）
- University of Wisconsin（威斯康星大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对二元删除信道容量未知问题，提出计算机辅助近似方法，误差低于0.0095比特，通过有限不等式与解析比较给出显式上下界，并验证结果。
中文摘要 AI 辅助
尽管在可达速率和逆界方面进行了数十年的研究，二元删除信道的精确容量仍然未知。我们建立了一个计算机辅助近似，其误差低于每传输比特$0.0095$比特，且对所有删除概率一致成立。在删除概率均匀加权下，平均认证误差界低于$0.006522$。该估计是显式下界和上界的中点。对于逆界，将平稳信源约化与覆盖所有允许输入配置的有限不等式相结合。两种构造控制有限窗口之外的未观测输入：一种使用公共外部幸存序列并界定被省略的删除模式，另一种则抵消熵项以使外部概率线性进入。对于下界，有限状态输入将输出熵估计与兼容删除掩码的选定不相交计数相结合；独立游程输入则保留关于输出游程边界的额外不确定性。有向数值检查确立了有限不等式。随后，删除概率之间的解析比较将逐点界扩展到整个参数范围。下端点提供渐近编码意义下容量$0.019$比特以内的速率。我们给出了推导过程、记录的计算成本以及验证结果所需的完整数值输入和程序。
英文摘要
The exact capacity of the binary deletion channel remains unknown despite decades of work on achievable rates and converse bounds. We establish a computer-assisted approximation whose error is below $0.0095$ bits per transmitted bit, uniformly over all deletion probabilities. The mean certified error bound, with uniform weighting of deletion probability, is below $0.006522$. The estimate is the midpoint of explicit lower and upper bounds. For the converse, a stationary-source reduction is combined with finite inequalities covering every allowed input configuration. Two constructions control the unobserved input beyond a finite window: one uses a common outside survivor sequence and bounds omitted deletion patterns, while the other cancels an entropy term to make outside probabilities enter linearly. For the lower bound, finite-state inputs combine output-entropy estimates with selected disjoint counts of compatible deletion masks; independent-run inputs retain additional uncertainty about output-run boundaries. Directed numerical checks establish the finite inequalities. An analytic comparison between deletion probabilities then extends the pointwise bounds over the entire parameter range. The lower endpoint supplies rates within $0.019$ bits of capacity in the asymptotic coding sense. We give the derivations, recorded computational costs, and complete numerical inputs and programs needed to verify the result.
