On LT Codes with Decreasing Ripple Size

In the orignal work on LT codes by Luby, the ripple size during decoding was designed to be approximately constant. In fact, the Ideal Soliton and the Robust Soliton distributions were designed to yield an approximately unit ripple size and a fixed ripple size greater than one, respectively. In this work, the redundancy within an LT code is characterized, and it is found that a decreasing ripple size during decoding is beneficial. Furthermore, a new design of LT codes with decreasig ripple size is proposed, and it is shown that this design significantly decreases the average amount of redundancy in comparison to existing designs.