On the capacity of generalized write-once memory with state transitions described by an arbitrary directed acyclic graph

The generalized write-once memory introduced by Bat and Shamir is a q-ary information storage medium. Each storage cell is expected to store one of q symbols, and the legal state transitions are described by an arbitrary directed acyclic graph. This memory model can be understood as a generalization of the binary write-once memory which was introduced by Rivest and Shamir. During the process of updating information, the contents of a cell, can be changed from a 0-state to a 1-state but not vice versa. We study the problem of reusing a generalized write-once memory for T successive cycles (generations). We determine the zero-error capacity region and the maximum total number of information bits stored in the memory for T consecutive cycles for the situation where the encoder knows and the decoder does not know the previous state of the memory. These results extend the results of Wolf, Wyner, Ziv, and Korner for the binary write-once memory.