Achieving Torn-Paper Channel Capacity with Successive Revelation

Abstract

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.