Extended LT decoder based on extra ripples

The ripple that was introduced to the decoder of LT codes plays a key role in the decoding process. Even Luby's degree distributions are defined so that this ripple maintains a reasonable size. For low block length which have many application in wireless, LT codes doesn't work properly so in this paper to extend the decodability of the LT codes for low block lengths, extra ripples are introduced to the decoder. Retaining the LT decoder's simplicity, it is possible to regenerate the main ripple and extend the decoding by means of these extra ripples. As the simulation and analytical results based on recursion of probability distributions show, lower error probabilities can be achieved. For the new decoder even the operational complexity is not increased that much due to the structure of LT codes. Even lower complexities in term of XOR operations can be achieved as the complexity of LT codes is mainly related to the number of edges in the decoding graph.