This paper was rejected by several journals during its submissions in the years of 2018-2020. Because the monograph [30] was published in 2018, and it covered most of the material presented in this paper, we decided to just post this paper on the website as an unpublished manuscript. Compared with the results published in [30], this paper gave a set of conditions, that is more general than those given in [30], for the convergence of the proposed MAC algorithm. [30] Y. Tang, F. Heydaryan, J. Luo, "Distributed Coding in A Multiple Access Environment," Foundations and Trends in Networking, Vol. 12, No. 4, pp. 260-412, Now Publishers, 2018.