Cyclic codes for T-user adder channel over integer rings

Coding for the synchronous noiseless T-user real adder channel is considered by employing cyclic codes with symbols from an arbitrary finite integer ring. The code construction is based on the factorisation of xⁿ-1 over the unit ring of an appropriate extension of a finite integer ring. Any number of users in the system can be independently active and the maximum achievable sum rate is 1 (when all T users are active)