Fly-PRAC: Packet Recovery for Random Linear Network Coding

TL;DR

Fly-PRAC exploits algebraic relations between a group of coded packets to estimate their corrupted parts and recovers them without decoding them, and can recover coded packets at the intermediate node without decoding them.

Abstract

Network Coding (NC) is a compelling solution for increasing network efficiency. However, it discards corrupted packets and cannot achieve optimal performance in noisy communications. Since most of the information in corrupted packets is error-free, discarding them is not the best strategy. Several packet recovery techniques such as PRAC and S-PRAC were proposed to exploit corrupted packets. Yet, they are slow and only practical when the packet size is small and communication channels are not very noisy. We propose a packet recovery scheme called Fly-PRAC to address these issues. Fly-PRAC exploits algebraic relations between a group of coded packets to estimate their corrupted parts and recovers them. Unlike previous schemes, Fly-PRAC can recover coded packets at the intermediate node without decoding them. We have compared Fly-PRAC against S-PRAC. Results show when the bit error rate (ε) is 10^-4, Fly-PRAC outperforms S-PRAC by two folds for a payload of 900B. In two-hop communication with ε = 10^-4 and a payload size of 500B, by enabling the recovery in the intermediate node, Fly-PRAC reduces transmissions by 16%. In a Sparse Network Coding (SNC) scenario, with two non-zero elements in the coefficient vectors and a payload of 800B, there is a reduction by 31% on average for decoding delay.

Figures (12)

• Figure 1: Format of a coded packet.
• Figure 2: An overview of the error location estimation process. In this example, three packets are sent, one of which has a coefficient vector that is linearly dependent on the other two. Here, $c$ and $s'$ are referring to coefficients, and coded symbols, respectively. Furthermore, the red color refers to an erroneous symbol, and $e$ refers to a non-zero value which shows the location of the erroneous column. For simplification, each coded packet contains one segment with two coded symbols. One of these elements becomes corrupted during transmission.
• Figure 3: The comparison of the expected number of inconsistent columns for different $R$ (colored) with (red) in a channel with $\epsilon$ =$10^{-3}$, where $g=100$, $l=50$, and field size is $GF(2^{8})$.
• Figure 4: The figure shows the probability of false-positive events during the estimation process for an arbitrary column of $R$ packets for different bit error rates.
• Figure 5: The figure shows the comparison of the probability of false-positive events resulting from \ref{['eq:pfpe']} and from simulation results for different $\epsilon$ and $R=20$.