Minimum Required Information to Achieve a Performance Target in a Network With Memoryless States

The performance of networks is greatly affected by the available network state information, such as network topology, channel state, and traffic information. Previous research on network performance analysis is based on the assumption that complete and precise network state information is available. However, in reality, precise information is difficult to obtain, and it requires a large amount of bandwidth resource to maintain accurate information. In this paper, we study networks with memoryless states and address the following question: Given the true network state and a performance measure, what is the minimum information required to achieve a given network performance? We propose a general information-theoretic framework, which can be applied to memoryless network and network protocol, to study the effect of information on network performance. We find that the minimum required information is equal to the mutual information between the true network state and the decision of the controller. To illustrate our approach, we use the framework to determine the lower bound on the channel state information in wireless networks, and then find the coding rate to achieve optimal net data rate. We also study the lower bound on the traffic information required in a distributed network, propose an encoding scheme for exchanging the state information, and then study the gap between the performance of the proposed scheme and the theoretical bound.