Codes for T-user asymmetric multiple-access channel with independent sources

An asymmetric multiple access channel (AMAC) is a multiple-access channel where a portion of the users can observe the messages of other users. We first propose three 2-user uniquely decodable (UD) codes for two-user AMAC, which are shown to achieve higher sum-rate than the previous 2-user codes. Then, we consider multiuser error correcting codes for T-user noisy AMAC. A theorem shows that given a T
_a
-user δ
_a
-decodable k-ary code A and a T
_d
-subset δa-decodable difference set D a priori, a larger error-correcting T-user code C is obtained by Hadamard matrices. For practical construction, we give 2-user difference sets based on the 2-user UD codes, and obtain multiuser correcting codes for multiuser AMAC. The proposed correcting codes have increasing sum-rate and error-correcting capability with an increasing code length.