Distinguishable codeword sets for shared memory

In data processing, a transmitter
T
andreceiver
R
communicate via a random-access memory
m
that they share with a set
U
of other users.
T
selects a codeword
c
from a set
C
known to
R
and stores
c
in some of the cells of
m
, not necessarily adjacent to one another.
U
does not change the values
T
has stored but fills in the values stored in the other cells of
m
.
C
is said to be distinguishable if
R
can always find which codeword
T
stored in
m
no matter what
U
stores in the other cells and to be locally distinguishable if
R
can do so reading only the values written by
T
not by
U
. Necessary and sufficient conditions for distinguishability and local distinguishability are given. Generalizations of the Kraft inequality to this setting follow and give lower bounds to the numbers of cells occupied by the members of a distinguishable set of codewords and to the numbers of cells in
m
that
R
must access to distinguish among them. Upper bounds to numbers of necessary accesses are also given.