Algorithms for \(q\)-ary error-correcting codes with limited magnitude and feedback (Q2214047)

In this paper, the authors consider wraparound channels with limited magnitude and noiseless feedback. They completely determine the capacity error function for all \(q\)-ary wraparound channels with a magnitude of level \(r\). All of the presented algorithms use partial noiseless feedback. Furthermore, a special case of the problem is equivalent to Shannon's zero-error problem. In Section 2, the authors give some definitions and general results about \(Q\)-ary codes with feedback. In Section 3, the considered special \(g\)-ary channel is presented by a bipartite graph. Here, some theorems related to the capacity error function are presented and proved. The authors give a successful algorithm that attains defined bounds. In Section 4, the algorithm is generalized. The algorithms have the property that the sender does not need to get the received symbol of the receiver immediately. In this case, such an algorithm is called an algorithm using partial noiseless feedback. As a conclusion, the paper contains an interesting valuable results and should be considered by all the researchers in the related scientific areas.