Generation of Innovative and Sparse Encoding Vectors for Broadcast Systems with Feedback

TL;DR

This paper investigates encoding vector generation in wireless broadcast systems with feedback, proving NP-completeness for binary fields and providing an efficient algorithm for larger fields, improving delay performance.

Contribution

It introduces an NP-completeness proof for binary fields and presents an efficient algorithm for generating innovative, sparse encoding vectors for larger fields.

Findings

NP-complete problem for binary finite fields

Always find an innovative, sparse vector when field size ≥ number of users

Improved delay performance in simulations

Abstract

In the application of linear network coding to wireless broadcasting with feedback, we prove that the problem of determining the existence of an innovative encoding vector is NP-complete when the finite field size is two. When the finite field size is larger than or equal to the number of users, it is shown that we can always find an encoding vector which is both innovative and sparse. The sparsity can be utilized in speeding up the decoding process. An efficient algorithm to generate innovative and sparse encoding vectors is developed. Simulations show that the delay performance of our scheme with binary finite field outperforms a number of existing schemes in terms of average and worst-case delay.