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.

Network Coding Based Schemes for Imperfect Wireless Packet Retransmission Problems: A Divide and Conquer Approach

“…In computer science, a Galois Field is usually notated as GF(2 q ), which means that the number of elements of the Field is 2 q . In [3,[14][15][16], WPRTPs are studied using NC-based approaches, but most of these works are focused on solutions in Galois Field GF (2), where the coding and decoding calculations are both bitwise XOR operations (denoted as "⊕"). Since that finding optimal NC-based solutions on GF (2) to WPRTPs is a NP-Complete problem [3], the solutions found on GF(2) are usually not optimal, thus, in many cases, solutions with fewer packet transmissions may be highly appreciated.…”

“…In [16], using Galois Field GF(2 q ) where q > 1, optimal schemes for P-WPRTPs are studied, where the number of retransmitted packets in optimal valid NC-based solutions to P-WPRTPs is analyzed and proved. Then, based on RNC, a scheme that is optimal in the number of retransmitted packets is proposed for P-WPRTPs.…”

“…The Theorem about the number of retransmitted packets in optimal NC based solutions to P-WPRTPs in [16] is cited as the following Theorem 1.…”

“…Theorem 1 [16]: Given that the Galois Field GF(2 q ) to be used is not constrained, the number of retransmitted packets in an optimal valid NC-based solution to a P-WPRTP(P, R,…”

“…Then, we propose an optimal NC-based scheme for WPRTPs based on RNC. However, the solutions found by the scheme in [16] are only optimal for P-WPRTPs (Perfect Wireless Packet ReTransmission Problems) where, for one receiver, a packet can be neither requested by nor already known to it. All other WPRTPs are named as IP-WPRTPs (ImPerfect Wireless Packet ReTransmission Problems).…”