Probability of Partially Decoding Network-Coded Messages

TL;DR

This paper derives exact probabilities for partial decoding in network coding, enabling analysis of progressive data recovery and security features in systematic and non-systematic schemes.

Contribution

It provides the first exact analytical expressions for partial decoding probabilities in both systematic and non-systematic network coding schemes.

Findings

Exact probability formulas for partial decoding are derived.

Systematic coding shows potential for progressive data recovery.

Analysis indicates implications for secure communication.

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.