通过逐次揭示实现撕纸信道容量
Achieving Torn-Paper Channel Capacity with Successive Revelation
中文总结 AI 辅助
针对撕纸信道，提出逐次揭示方法将码字划分为交错轨道依次解码，可使有限轨道的可达速率与容量差距随轨道数增大而趋近于零，实现低于容量的任意速率下平均译码误差概率消失的确定性码。
中文摘要 AI 辅助
撕纸信道会沿二进制码字的内部边界独立切割，并将产生的定向片段作为无序多重集输出。我们考虑临界状态pN log N = α，此时信道容量为e^α。现有编码方案使用固定密度的导频来定位片段，在位置信息和有效载荷速率之间存在权衡。本文提出逐次揭示方法，该方法将码字划分为交错轨道并依次解码。每个已恢复的有效载荷轨道会成为后续阶段的额外位置参考，从而能定位更短的片段。我们确定了有限轨道可达速率，其与容量的差距为O(1/M)（M为轨道数）。因此，对于低于信道容量的每一个速率，有限数量的轨道可生成一系列确定性码，其平均译码误差概率趋近于零。
英文摘要
The torn-paper channel independently cuts a binary codeword at its internal boundaries and outputs the resulting oriented fragments as an unordered multiset. We consider the critical regime pN log N to alpha, in which the channel capacity is e to alpha. Existing coding schemes use a fixed-density pilot to localize fragments, creating a tradeoff between positional information and payload rate. This paper introduces successive revelation, which partitions the codeword into interleaved tracks and decodes them sequentially. Each recovered payload track becomes an additional positional reference for subsequent stages, allowing progressively shorter fragments to be localized. We establish a finite-track achievable rate whose gap to capacity is O 1 or M for M tracks. Consequently, for every rate below the channel capacity, a finite number of tracks yields a sequence of deterministic codes with vanishing average decoding error probability.
