5G Low-Rate Polar Codes for Massive Machine-Type Communications

Kurzfassung

Massive machine-type communication is one of the key service categories of 5G, enabling connectivity for a very large number of devices that often transmit short packets under stringent reliability and complexity constraints. In this context, the design of efficient channel coding schemes operating at short blocklengths and low code rates is of particular interest. This work investigates the design and performance of polar codes, the coding scheme adopted for control channels in the 5G New Radio standard, over the binary erasure channel, focusing on the comparison of different code construction methods and the comparative evaluation of decoding strategies. Specifically, the study explores standard polar designs, Reed–Muler-like constructions, and density-evolution-based methods to determine their effectiveness in the finite-blocklength regime. Performance is assessed across a range of code rates by comparing maximum-likelihood decoding, used as the theoretical benchmark, with practical algorithms such as peeling, successive cancellation, and successive cancellation list decoding. A contribution of this work is the analysis of the decoding gap between list decoding and the optimal maximum-likelihood decoding as a function of the code rate. Numerical results show that this gap is non-monotonic: while list decoding closely approaches maximum-likelihood performance at extreme rates, very high or very low, it exhibits a peak in sub-optimality at medium rates, indicating that larger list sizes are required in this regime to approach the maximum-likelihood performance.