Multi-User UD k-Ary Codes Recursively Constructed from Short-Length Multiary Codes for Multiple-Access Adder Channel
Shan Lu, Wei Guo Hou, Jun Cheng, Hiroshi Kamabe · 2019
A T -user UD k-ary codes for MAAC is proposed. First, a coding scheme for a Tf+g-user UD k-ary code with code length f + g is proposed that is constructed from a Tf-user UD k-ary code and a Tg-user UD (2k - 1)-ary difference set. In fact, the Tg-user UD (2k - 1)-ary difference set is associated with Tg-user UD (2k - 1)-ary code. Second, originally from the multi-user UD (2i(k - 1) + 1)-ary (i = 0, 1, 2,..., m) codes with unitary code length, by recursively employing the coding scheme, 2m+1-user k-ary code with code length 2mis obtained. Finally, by recursively employing the coding scheme, 2n-user UD k-ary code with arbitrary code length n from the codes with length 2i(i = 0, 1,..., ⌊log2n⌋) is given. Since introducing the high-order multiary difference sets, the total rates of the proposed codes are higher those of conventional codes.