Multi-User UD k-Ary Codes Recursively Constructed from Short-Length Multiary Codes for Multiple-Access Adder Channel

A T -user UD k-ary codes for MAAC is proposed. First, a coding scheme for a T
^f+g
-user UD k-ary code with code length f + g is proposed that is constructed from a T
^f
-user UD k-ary code and a T
^g
-user UD (2k - 1)-ary difference set. In fact, the T
^g
-user UD (2k - 1)-ary difference set is associated with T
^g
-user UD (2k - 1)-ary code. Second, originally from the multi-user UD (2
ⁱ
(k - 1) + 1)-ary (i = 0, 1, 2,..., m) codes with unitary code length, by recursively employing the coding scheme, 2
^m+1
-user k-ary code with code length 2
^m
is obtained. Finally, by recursively employing the coding scheme, 2n-user UD k-ary code with arbitrary code length n from the codes with length 2
ⁱ
(i = 0, 1,..., ⌊log
₂
n⌋) is given. Since introducing the high-order multiary difference sets, the total rates of the proposed codes are higher those of conventional codes.