Capacity of the Erasure Shuffling Channel

Seiyun Shin, Reinhard Heckel, Ilan Shomorony

Abstract: Motivated by DNA-based data storage, we study the erasure shuffling channel. This channel takes as input multiple strings, which are passed through an erasure channel and then shuffled out of order. We show that the capacity of this channel, for a large set of channel parameters, is given by the capacity of the binary erasure channel, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BEC</sub> , minus a term that captures the loss of ordering information due to shuffling.