Towards systematic Luby transform codes: Optimisation design over binary erasure channel

Abstract

In this Letter, the authors introduce optimisation design technique of systematic Luby transform (SLT) codes over binary erasure channel (BEC). SLT codes are more efficient than Luby transform (LT) codes since the former ones can recover source symbols more quickly. There was some work about designing degree distribution in LT codes and it was shown that erasure probability barely impact performances of LT codes. Using degree distributions designed for LT codes directly in SLT codes does not provide satisfied performances. For the first time, they introduce erasure probability as a parameter to establish a linear programming model in SLT codes. By applying And–or Tree analysis, they propose the asymptotic analysis formulae of SLT codes over BEC. To achieve the goal of recovering source symbols as soon as possible, the authors’ objective of optimisation is to minimise overhead. Simulations are offered to validate the performance of their optimisation result. Besides, their degree distribution outperforms other distributions with respect to bit error ratio.