On the Probability of Partial Decoding in Sparse Network Coding

TL;DR

This paper derives analytical expressions for the probability of partial decoding in Sparse Network Coding, demonstrating potential improvements through sparsity tuning and providing insights into decoding performance.

Contribution

It introduces the first analytical model for partial decoding probability in SNC using Inclusion-Exclusion, and proposes a sparsity tuning scheme to enhance decoding success.

Findings

Analytical expressions predict partial decoding with 6% deviation.

Higher sparsity and smaller Galois fields improve partial decoding.

Sparsity tuning increases partial decoding probability by 16%.

Abstract

Sparse Network Coding (SNC) has been a promising network coding scheme as an improvement for Random Linear Network Coding (RLNC) in terms of the computational complexity. However, in this literature, there has been no analytical expressions for the probability of decoding a fraction of source messages after transmission of some coded packets. In this work, we looked into the problem of the probability of decoding a fraction of source messages, i.e., partial decoding, in the decoder for a system which uses SNC. We exploited the Principle of Inclusion and Exclusion to derive expressions of partial decoding probability. The presented model predicts the probability of partial decoding with an average deviation of 6%. Our results show that SNC has a great potential for recovering a fraction of the source message, especially in higher sparsity and lower Galois Field size. Moreover, to achieve a better probability of partial decoding throughout transmissions, we define a sparsity tuning scheme that significantly increases the probability of partial decoding. Our results show that this tuning scheme achieves a 16% improvement in terms of probability of decoding a fraction of source packets with respect to traditional SNC.