# Random Linear Fountain Code with Improved Decoding Success Probability

## TL;DR

This paper proposes a novel coding scheme for random linear fountain codes over GF(2) that significantly reduces transmission redundancy and improves decoding success probability in delay-sensitive applications like multimedia streaming.

## Contribution

It introduces a new code construction and a receiver feedback mechanism to lower redundancy and enhance decoding success for small packet lengths.

## Key findings

- Reduces expected redundancy by a factor of three.
- Increases decoding success probability for small packet lengths.
- Effective in delay-intolerant multimedia streaming applications.

## Abstract

In this paper we study the problem of increasing the decoding success probability of random linear fountain code over GF(2) for small packet lengths used in delay-intolerant applications such as multimedia streaming. Such code over GF(2) are attractive as they have lower decoding complexity than codes over larger field size, but suffer from high transmission redundancy. In our proposed coding scheme we construct a codeword which is not a linear combination of any codewords previously transmitted to mitigate such transmission redundancy. We then note the observation that the probability of receiving a linearly dependent codeword is highest when the receiver has received k-1 linearly independent codewords. We propose using the BlockACK frame so that the codeword received after k-1 linearly independent codeword is always linearly independent, this reduces the expected redundancy by a factor of three.