A New Kind of Nonbinary Uniquely Decodable Codes with Arbitrary Code Length for Multiple-Access Adder Channel

Abstract

A kind of multiuser k-ary codes for the multiple-access adder channel is proposed. Given any $T^{f}$-user and $T^{g}$-user k-ary uniquely decodable (UD) codes with code lengths f and g, respectively, a $(T^{f}\,+T^{g}\,+1)$-user k-ary UD code with code length $f+g$ is obtained. The proposed scheme has no restriction on the code structure, e.g., affine, and can be constructed from any arbitrary two UD codes. Moreover, a recursive construction of a kind of k-ary UD codes with arbitrary code length is given. The proposed codes have the higher code rate and the shorter code length than those of the previous codes for a fixed number of users.