Luby Transform Code - Optimization of LT Codes

Optimization of LT Codes

There is only one parameter that can be used to optimize a straight LT code: the degree distribution function (described as a pseudorandom number generator for the degree d in the LT encoding section above). In practice the other "random" numbers (the list of indices { i₁, i₂, …, i_d } ) are invariably taken from a uniform distribution on

Luby himself discussed the "ideal soliton distribution" defined by

This degree distribution theoretically minimizes the expected number of redundant code words that will be sent before the decoding process can be completed. However the ideal soliton distribution does not work well in practice because any fluctuation around the expected behavior makes it likely that at some step in the decoding process there will be no available packet of (reduced) degree 1 so decoding will fail. Furthermore, some of the original blocks will not be xor-ed into any of the transmission packets. Therefore, in practice, a modified distribution, the "robust soliton distribution", is substituted for the ideal distribution. The effect of the modification is, generally, to produce more packets of very small degree (around 1) and fewer packets of degree greater than 1, except for a spike of packets at a fairly large quantity chosen to ensure that all original blocks will be included in some packet.