Improved finite-length Luby-transform codes in the binary erasure channel

Fountain codes were introduced to provide high reliability and scalability and low complexities for networks such as the Internet. Luby-transform (LT) codes, which are the first realisation of Fountain codes, achieve the capacity of the binary erasure channel (BEC) asymptotically and universally. Most previous work on single-layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as a Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, the author's focus is on designing better codes for the BEC at practical lengths. Their left degree shaping provides codes outperforming LT codes and all other competing schemes in the literature. At a bit error rate of 10−7 and packet length k = 256, their scheme provides a realised rate of 0.6 which is 23.5% higher than that of Sorensen et al.’s decreasing-ripple-size scheme.