Analysis and Optimization of the HARQ-Based Spinal Coded Timely Status Update System

The age of information (AoI) is a new metric to measure the timeliness of various status update systems, and hybrid automatic repeat request (HARQ) transmission scheme is usually applied to ensure higher timeliness. However, little research considers encoding delay, propagation delay, decoding delay and feedback delay in the HARQ-based coded status update system. To the best of our knowledge, in this paper, the HARQ-based Spinal coded timely status update system with all the practical delay elements is considered for the first time. We derive the average AoI expression of the system and analyze the monotony of the AoI expression to give an average AoI upper bound. Then we optimize the HARQ transmission scheme to minimize the AoI. To decrease the complexity of the optimization algorithm, we separate it into two steps. First, we optimize the puncturing pattern of Spinal codes and propose a transmission scheme under incremental tail transmission puncturing (ITTP) pattern. Second, we optimize the number of symbols in each round under the ITTP transmission scheme, and propose the optimal transmission scheme under the coarse-grained ITTP pattern. Simulation results show that the proposed transmission scheme can significantly decrease the AoI compared to the baseline transmission schemes.