|| Capacity of the Torn Paper Channel with Lost Pieces
||Aditya Narayan Ravi, University of Illinois Urbana-Champaign, United States; Alireza Vahid, University of Colorado, Denver, United States; Ilan Shomorony, University of Illinois Urbana-Champaign, United States|
||D4-S7-T2: Information Theory for Biology
||Friday, 16 July, 00:00 - 00:20
||Friday, 16 July, 00:20 - 00:40
We study the problem of transmitting a message over a channel that randomly breaks the message block into small fragments, deletes a subset of them, and shuffles the remaining fragments. We characterize the capacity of the binary torn-paper channel under arbitrary fragment length distribution and fragment deletion probabilities. We show that, for a message with block length n, discarding fragments shorter than log(n) does not affect the achievable rates, and that the capacity is given by a simple closed-form expression that can be understood as“coverage minus reordering-cost”.