Probability of Partially Decoding Network-Coded Messages

Jessica Claridge,Ioannis Chatzigeorgiou

doi:10.1109/lcomm.2017.2704110

Jessica Claridge, Ioannis Chatzigeorgiou

Open Access

https://doi.org/10.1109/lcomm.2017.2704110

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Abstract

In the literature there exists analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this work, we look into the probability that the receiver will decode at least a fraction of the source message, and present an exact solution to this problem for both non-systematic and systematic network coding. Based on the derived expressions, we investigate the potential of these two implementations of network coding for information-theoretic secure communication and progressive recovery of data.

Highlights

R ANDOM linear network coding (RNLC) is the process of constructing coded packets, which are random linear combinations of source packets over a finite field [1]
The results show that, if information-theoretic security is required, non-systematic RLNC over finite fields of size 8 or larger can be used to segment each message into a large number of source packets
If the objective of the system is to maximize the number of nodes that will recover at least a large part of a message, systematic RLNC over small finite fields can be used to divide data into source packets

Summary

INTRODUCTION

R ANDOM linear network coding (RNLC) is the process of constructing coded packets, which are random linear combinations of source packets over a finite field [1]. The fundamental problem that has motivated our work is the characterization of the probability of recovering some of the k source packets when n coded packets have been retrieved, where n can be smaller than, equal to or greater than k This idea was considered in [4] for random network communications over a matroid framework. This letter revisits the aforementioned problem and obtains an exact expression for the probability that a receiving node will recover at least x of the k source packets if n coded packets are collected, for x ≤ n.

SYSTEM MODEL AND PROBLEM FORMULATION

PROBABILITY ANALYSIS

RESULTS AND DISCUSSION

CONCLUSIONS