Sparse Matrix Codes: Rate-Reliability Trade-offs for URLLC

In this paper, we present a new channel coding technique, namely sparse matrix codes (SMC), for URLLC applications with the goal of achieving higher reliability, and low decoding complexity. The main idea behind SMC is to map the message bits to a structured sparse matrix which is then multiplied by a spreading matrix and transmitted over the communication channel over time-or frequency resources. At the decoder, we recover the message from the channel output using a low-decoding complexity algorithm which is derived by leveraging and adapting tools from 2D compressed sensing. We perform various experiments to compare our approach with sparse vector code (SVC) and Polar codes for block error rate (BLER). From our experiments, we show that for a fixed code rate and reliability requirement (BLER), SMC operates at shorter blocklengths compared to Polar codes and SVC.