The four cases of write unidirectional memory codes over arbitrary alphabets (optical storage)

The capacity region for W(write) U(unidirectional) M(memory) codes over an alphabet of size q for three of the cases as defined by G. Simonyi (1989) are derived. These are the cases where either the encoder, the decoder, or both know the old state of the WUM code. For the case where neither user knows the old state, an achievable rate region is derived. Also proved is a partial converse, showing that the achievable rate region may be equal to the capacity region. If one takes q=2, then the results obtained reduce to the known results for the binary WUM code.