Goal‐oriented design of optimal degree distribution for LT codes

Abstract

Goal-oriented Luby transform (LT) codes are required in different scenarios. Based on the random walk model, analysis of ripple size evolution provides an effective method to design LT codes. However, the ripple addition in each step depends on both the number of symbols released in the current step and the ripple size in the last step, leading to distortion. Therefore, the authors propose a random walk algorithm with barrier (RWA-B) to model the ripple addition directly. To evaluate the performance of ripple size evolution, they utilise generalised degree distribution algorithm to generate corresponding degree distribution. Through analysing the relationship between the performance of generated ripple size evolution and the parameters of RWA-B, they design an iterator greedy algorithm to search the optimal ripple size evolution for desired goals. As a result, they compare three goal-oriented degree distributions with others through numerical simulations. In binary erasure channel, both the memory usage oriented and block error rate (BER) oriented degree distributions outperform others with lowest average overhead, and the overhead oriented degree distribution outperforms others in terms of average overhead and average degree. In additive white Gaussian noise channel, the BER-oriented degree distribution outperforms others in terms of BER and average overhead.