The performance of low-density random linear fountain codes over higher order galois fields under maximum likelihood decoding

Digital fountain codes over higher order Galois fields exhibit a better performance than their binary counterparts under maximum likelyhood (ML) decoding when transmitted over a symbol erasure channel (SEC). Especially random linear fountain (RLF) codes exhibit an excellent performance, though at the expense of a high computational complexity for decoding due to their high density generator matrix. For practical applications, we propose RLF codes with a reduced density over higher order Galois fields. Although the reduction of the density results in an error floor at higher reception overheads, the level of this error floor can be well controlled by two parameters. For error floor levels that are tolerable in practical applications, a significant density reduction and thus a reduction of the computational complexity can be achieved. Furthermore, we derive a general upper bound on the symbol erasure rate for Luby Transform (LT) codes over Galois fields Fq of order q. Finally, we propose a method to enhance decoding of Fq-codes in the presence of bit erasures by using the binary images of the Fq-elements, such that not complete Fq-elements have to be discarded if their binary counterparts are impaired by bit erasures.