Design of unequally error protecting low-density random linear fountain codes

Low-density random linear fountain (LDRLF) codes are a type of LT (Luby transform) codes with optimum erasure correction under maximum likelihood (ML) decoding given a certain density or average check node degree. The upper bound on the residual symbol erasure rate is very tight and can be used for the design of LDRLF codes instead of performing time-consuming simulations. Using LDRLF codes for unequal error protection (UEP), the excellent erasure correction performance is maintained as well as the tightness of the upper bounds for each importance class. Since the UEP upper bounds may be complex to compute, we provide an extremely good approximation thereof which is well suited to design UEP LDRLF codes. Furthermore, we provide a heuristic criterion that has to be fulfilled in order to yield good approximations.