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

Abstract

NC (Network Coding) provides a new approach to packet retransmission problems in wireless networks, which are named as WPRTPs (Wireless Packet Retransmission Problems) in this paper. Some research has been conducted on P-WPRTPs (Perfect WPRTPs) where, for one receiver, a packet is either being requested by or already known to it. However, very few efforts are focused on IP-WPRTPs (Imperfect WPRTPs) where, for one receiver, a packet can be neither requested by nor already known to it. In this paper, we focus on IP-WPRTPs. Firstly, a WPRTP reduction theorem for simplifying WPRTPs is proposed and Z. Gao (B) 123 938 Z. Gao et al.proved. Then, the upper and lower bounds of the number of necessary packet transmissions in optimal NC-based solutions to IP-WPRTPs are analyzed. Next, a scheme named as IP-WPRTP-DC (Divide and Conquer based scheme for IP-WPRTPs) is proposed based on the WPRTP reduction theorem using a divide and conquer approach. Extensive simulations show that the IP-WPRTP-DC scheme is effective in saving the number of packet transmissions for solving IP-WPRTPs.

An enhanced XOR‐based scheme for wireless packet retransmission problem

“…Because ColorCliqueNC proposed in this paper combines the basic ideas in ColorNC and CliqueNC , we only provide a more detailed description about ColorNC and CliqueNC here. For a detailed description about other related works, interested readers can refer to and the references therein.…”

“…In recent years, some NC-based schemes have been proposed for WPRTP [1,[8][9][10][11]. The schemes in [1,8,9] search for solutions on Galois field (GF(2)), whereas the schemes in [10,11] work on larger fields.…”

“…In recent years, some NC-based schemes have been proposed for WPRTP [1,[8][9][10][11]. The schemes in [1,8,9] search for solutions on Galois field (GF(2)), whereas the schemes in [10,11] work on larger fields. The schemes in [8][9][10] are specially designed for P-WPRTP instances, whereas the schemes in [1,11] are suitable for all WPRTP instances.…”

“…The schemes in [1,8,9] search for solutions on Galois field (GF(2)), whereas the schemes in [10,11] work on larger fields. The schemes in [8][9][10] are specially designed for P-WPRTP instances, whereas the schemes in [1,11] are suitable for all WPRTP instances. As a summary, existing NC-based schemes for WPRTP are with high computational complexity resulting from computation on larger Galois fields (such as [10,11]), or the solutions on GF(2) found by them are less efficient (such as [1,8,9]).…”

“…The schemes in are specially designed for P‐WPRTP instances, whereas the schemes in are suitable for all WPRTP instances. As a summary, existing NC‐based schemes for WPRTP are with high computational complexity resulting from computation on larger Galois fields (such as ), or the solutions on GF(2) found by them are less efficient (such as ). Different from the NC‐based schemes, NoNC is a traditional non‐NC‐based scheme.…”