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 γ 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.
In this letter, we compute the exact probability that a receiver obtains N linearly independent packets among K ≥ N received packets, when the sender s use s random linear network coding over a Galois Field of size q. Such condition maps to the receiver's capability to decode the original information, and its mathematical characterization helps to design the coding so to guarantee the correctness of the transmission. Our formulation represents an improvement over the current upper bound for the decoding probability, and provides theoretical grounding to simulative results in the literature.