The erasure correction performance of Luby transform (LT) code ensembles over higher order Galois fields is analysed under optimal, i.e. maximum likelihood (ML) erasure decoding. We provide the complete set of four bounds on the erasure probability after decoding on word as well as on symbol level. Especially the upper bounds are extremely close to the simulated residual erasure rates after decoding and can thus be used for code design instead of time-consuming simulations.
The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. 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 a MDS code and a linear random fountain code, both operating on the same finite field. Upper and lower bounds on the decoding failure probability under maximum-likelihood (ML) decoding are developed. It is shown how, for example, the concatenation of a (15, 10) Reed-Solomon (RS) code and a linear random fountain code over a finite field of order 16, F16, brings to a decoding failure probability 4 orders of magnitude lower than the one of a linear random fountain code for the same receiver overhead in a channel with a erasure probability of ǫ = 5 • 10 −2. It is illustrated how the performance of the novel scheme approaches that of an idealized fountain code for higher-order fields and moderate erasure probabilities. An efficient decoding algorithm is developed for the case of a (generalized) RS code.
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