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.
Blasco and Liva have proposed a concatenated (15,10) RS code and RLNC @math generator matrix @cite_11 . Their results have shown that by concatenating the RLNC with an MDS code such RS code, the decoding failure probability can be reduced by a factor of upto four assuming that the channel erasure rate are from low-moderate. However their work assumes that coding is performed over a non-binary Galois field @math , and hence does not address the issue of high decoding computational complexity associated with non-binary coding coefficients.
@cite_11
2110464368
The performance of a novel fountain coding scheme based on maximum distance separable (MDS) codes constructed over Galois fields of order q>=2 is investigated. Upper and lower bounds on the decoding failure probability under maximum likelihood decoding are developed. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code, and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of an outer MDS code and an inner random linear fountain code, both operating on the same Galois field. A performance assessment is performed on the gain provided by MDS based fountain coding over linear random fountain coding in terms of decoding failure probability vs. overhead. It is shown how, for example, the concatenation of a (15,10) Reed-Solomon code and a linear random fountain code over F16 brings to a decoding failure probability 4 orders of magnitude lower than the linear random fountain code for the same overhead in a channel with a packet loss probability of epsilon=0.05. Moreover, it is illustrated how the performance of the concatenated fountain code approaches that of an idealized fountain code for higher-order Galois fields and moderate packet loss probabilities. The scheme introduced is of special interest for the distribution of data using small block sizes.