Analysis and Optimization of Spinal Codes over the BSC: from the AoI Perspective

In the ultra-reliable low-latency communications (URLLC) and the prospective 6G communications, the optimization of the age of information (AoI) will enhance the performance in the real-time status update situations. Spinal codes is a new type of rateless codes which can achieve the channel capacity over both the additive white Gaussian noise (AWGN) channels and the binary symmetric channels (BSC), so minimizing the AoI of Spinal codes will significantly decrease the latency of the real-time status update system. In this paper, we firstly study the AoI of a specific code—Spinal codes, and derive the upper bound of the AoI of Spinal codes. We also prove that obtaining a fine-grained rate in the transmission pattern will decrease the AoI of Spinal codes. Then we formulate the optimizing problem and derive that the incremental-tail-transmission pattern of Spinal codes is the optimal pattern to minimize the AoI. Simulation results demonstrate that the upper bound of the AoI of Spinal codes is tighter when the channel condition is better and the incremental-tail-transmission pattern of Spinal codes is the optimal pattern to achieve the lowest AoI compared with the puncture-based pattern and the pass-to-pass pattern.