Random network coding‐based optimal scheme for perfect wireless packet retransmission problems

Abstract

Solving wireless packet retransmission problems (WPRTPs) using network coding (NC) approach is increasingly attracting research efforts. However, existing researches are almost all focused on solutions in Galois field GF(2), and consequently, the solutions found by these schemes are usually less optimal. In this paper, we focus on optimal NC‐based scheme for perfect WPRTPs (P‐WPRTPs) where, with respect to each receiver, a packet is either requested by or already known to it. The number of retransmitted packets in optimal NC‐based solutions to P‐WPRTPs is firstly analyzed and proved. Then, random network coding‐based optimal scheme (RNCOPT) is proposed for P‐WRPTPs. RNCOPT is optimal in the sense that it guarantees to obtain a valid solution with minimum number of packet retransmissions. Furthermore, in RNCOPT, each coding vector is generated using a publicly known pseudorandom function with a randomly selected seed. The seed, instead of the coding vector, is used as decoding information to be retransmitted together with the coded packet. Thus, packet overhead of RNCOPT is reduced further. Extensive simulations show that RNCOPT distinctively outperforms some previous typical schemes for P‐WPRTPs in saving the number of retransmitted packets. Copyright © 2011 John Wiley & Sons, Ltd. This paper studied Perfect Wireless Packet ReTransmission Problems (P‐WPRTPs) where, with respect to each receiver, a packet is either requested by or already known to it. The number of retransmitted packets in optimal NC‐based solutions to P‐WPRTPs was analyzed and proved. Then, random network coding‐based optimal scheme (RNCOPT) is proposed for P‐WPRTPs. RNCOPT is optimal in the sense that it guarantees to obtain a valid solution with minimum number of packet retransmissions.