Random Linear Fountain Code with Improved Decoding Success Probability

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.Comment: This paper appears in: Communications (APCC), 2016 22nd Asia-Pacific Conference o

Fountain Codes under Maximum Likelihood Decoding

This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are presented to characterize the decoding complexity. Next an upper bound to the probability of decoding failure of Raptor codes under ML decoding is provided. Then, the distance properties of an ensemble of fixed-rate Raptor codes with linear random outer codes are analyzed. Finally, a novel class of fountain codes is presented, which consists of a parallel concatenation of a block code with a linear random fountain code.Comment: PhD Thesi