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.
Cruces have derived the exact decoding probability of decoding the codewords once a receiver has received @math , @math , codewords @cite_7 . Based on this result they derived the expected number of excess codewords a receiver needs to receive before performing decoding.
@cite_7
2137266817 2087879325 2613932151 2083594366
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. We study the Tardos' probabilistic fingerprinting scheme and show that its codeword length may be shortened by a factor of approximately 4. We achieve this by retracing Tardos' analysis of the scheme and extracting from it all constants that were arbitrarily selected. We replace those constants with parameters and derive a set of inequalities that those parameters must satisfy so that the desired security properties of the scheme still hold. Then we look for a solution of those inequalities in which the parameter that governs the codeword length is minimal. A further reduction in the codeword length is achieved by decoupling the error probability of falsely accusing innocent users from the error probability of missing all colluding pirates. Finally, we simulate the Tardos scheme and show that, in practice, one may use codewords that are shorter than those in the original Tardos scheme by a factor of at least 16. In the literature, there exist analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this letter, we look into the probability that the receiver will decode at least a fraction of the source message, and present an exact solution to this problem for both non-systematic and systematic network coding. Based on the derived expressions, we investigate the potential of these two implementations of network coding for information-theoretic secure communication and progressive recovery of data. We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1 (k221n2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotics, numerical solutions to the game for small k are also presented.