Analysis of LT Codes over Finite Fields under Optimal Erasure Decoding

The erasure correction performance of Luby transform (LT) code ensembles over higher order Galois fields is analysed under optimal, \ie 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.