Optimal Instantly Decodable Network Codes for Multi-Sender Scenarios

Abstract

Instantly Decodable Network Codes (IDNCs) are of practical interest in many broadcast and multicast applications in both wired and wireless networks. They have low encoding and decoding complexities (simple XORing) and lower decoding delay. This work explores multi-sender multicast-broadcast scenarios and gives the theoretically optimal algorithm to find instantly decodable network codes. All the broadcast symbols are scheduled by a control node. At any particular instant of time, only one sender broadcasts coded symbols. No sender-to-sender communication is assumed. The optimality criterion is maximizing the number of users that are able to decode exactly one amongst the messages they desire, when a coded symbol is broadcasted. An IDNC graph is defined with the messages as vertices, and edges denoting the infeasibility of combining the messages to form an IDNC broadcast symbol. The solution consists of finding maximum independent sets in certain induced subgraphs of the IDNC graph. This problem is known to be NP-hard in the general case. Simulation results show the improvement in the average decoding delay experienced by the users and the total completion time compared to the uncoded ARQ re-transmissions in a broadcast erasure channel.