Age of Information With Product Coded $\text{IoT}$ Systems

In this paper, an Internet of things(IoTs) scenario with short packet coding is studied in which a large number of sensors transmit short packets to the edge server through a sink node using a product code. Two main requirements are considered in this scenario which focuses on lower AoI and higher reliability (lower packet error rate, PER). In previous works, short packets are usually encoded into a long packet to improve reliability, which leads to large AoI. In this paper, a product coded packet scheme is considered because the joint packet encoding scheme using product code can be decoded by two ways, decoding of each row/column component code and joint iterative decoding of all component codes. Both of them may lead to a successfully decoding which greatly improves the AoI performance under the same PER conditions. The expression of the average AoI in this IoT system is derived, and the theoretical and numerical results show the relationships between packet length, the number of sensors and AoI performance. Furthermore, the optimal number of jointly-coded packets to minimize the AoI performance also are discussed and illustrated.