Optimal channel utilization with limited feedback

A channel with multiplicity feedback in case of collision returns the exact number of stations simultaneously transmitting. In this model, circle minus((d log(n/d))/ log d) time rounds are sufficient and necessary to identify d transmitting stations out of n. In contrast, in the ternary feedback model the time complexity is 6(d log(n/d)). Generalizing, we can define a feedback interval [x, y], where 0 <= x <= y <= d, such that the channel returns the exact number of transmitting stations only if this number is within that interval. For a feedback interval centered in d/2 we show that it is possible to get the same optimal time complexity for the channel with multiplicity feedback even if the interval has only size O(root d log d). On the other hand, if we further reduce the size to O(root d/log d) , then we show that no protocol having time complexity circle minus((d log(n/d))/(log d)) is possible. (C) 2021 Elsevier Inc. All rights reserved.