Computing Algorithms for LDPC Coded Internet-of-Things

Low-density parity-check (LDPC) codes are widely employed in communication systems. We focus on the computing of messages at the sink node of internet-of-things (IoT). As opposed to decoding all the messages, we consider the case that the sink node is interested in computing a linear transformation of the messages. We assume that all the IoT devices are identical. We first present three representations of the considered systems, based on which three multistage computing algorithms are proposed, which are decoding-computing (DC) algorithm, computing-decoding (CD) algorithm, and computing-decoding-computing (CDC) algorithm. Secondly, we show that the considered system admits a compact normal graph representation, based on which a joint computing algorithm is proposed. Thirdly, we present numerical results to show the advantages of the proposed algorithms. Numerical results show that the optimality of the proposed algorithms depends on the channel conditions and the computing functions. Numerical results also show that the joint computing algorithm has the best performances for a variety of scenarios. Finally, we present a simulation-based optimization procedure to design finite-length LDPC codes for the joint computing algorithm.