Network error correction with limited feedback capacity

We consider the problem of characterizing network capacity in the presence of adversarial errors on network links, focusing in particular on the effect of low-capacity feedback links across network cuts. In [1], the authors gave cut-set bound for unequal links capacity network and achievable strategy for coding, decoding and detection ,which only cover the network with large enough feedback across the network, allowing intermediate nodes reliably transporting part of code by some proper code back to supper source. However when feedback has small capacity, the strategy will be failed , the intuition is that you cannot have a simple code on low capacity feedback. We analysis thoroughly the behavior of adversary on small capacity of feedback link, which turns out that it’s more complex than large-capacity feedback, and give corresponding strategies. We give a new outer bound as well as a new achievable strategy, and show a family of networks where the inner and outer bounds coincide.