Design of LT code degree distribution with profiled output ripple size

LT codes, a candidate for next-generation forward error correction (FEC) scheme, draws great attention due to its low encoding/decoding complexity and capacity-approaching properties. Especially for wireless applications in fast-changing environments, adaptive degree distribution is a possible solution to balance the trade-off between LT codes´ efficiency and robustness. A fast mapping from attributes in the decoding process to degree distribution is required for realizing adaptive degree distribution. This study presents a reverse mapping from the expected ripple size to degree distributions. The basic idea is to minimize the error between a predetermined curve μ(ρ) and the expected ripple size R(Ω(x),ρ) of a target degree distribution Ω(x), where ρ is the number of decoded input symbols. By converting the code degree design into a pure optimization problem, it is possible to design LT codes with constraints from performance requirements to complexity issues. Applying sequential quadratic programming, a ripple-based distribution (RBD) is presented as a feasible design example. Simulation results show that, as compared to robust Soliton distribution (RSD) and previous studies, RBD is able to reduce the transmission overhead as well as the encoding and decoding complexity by at least 31.2% and 25.4%, respectively.