On Sequential Decoding Metric Function of Polarization-Adjusted Convolutional (PAC) Codes

In this paper, we present a sequential decoding metric function, which leads to significantly improved computational complexity while maintaining the superiority of polarization-adjusted convolutional (PAC) codes’ error-correction performance. With the proposed metric function, the PAC codes’ decoding computational complexity is comparable to the computational complexity of sequential decoding of conventional convolutional codes (CCs). Moreover, simulation results show an improvement in the error-correction performance of low rate PAC codes when using the proposed metric function. Simulation results also show that using the proposed metric, the upper bound on the PAC codes’ computational complexity has a Pareto distribution. To reduce the worst-case latency of PAC sequential decoder, we limit the number of searches performed by sequential decoder. The results show that for PAC codes of length 128, search-limited sequential decoding can achieve an error-correction performance close to the error-correction performance of polar codes with successive cancellation list decoding with list size 64 and CRC length 11 with considerably less computational complexity.