Performance and computational analysis of polarization-adjusted convolutional (PAC) codes

Abstract

We study the performance of sequential decoding of polarization-adjusted con- volutional (PAC) codes. We present a metric function that employs bit-channel mutual information and cutoff rate values as the bias values and significantly re- duces the computational complexity while retaining the excellent error-correction performance of PAC codes. With the proposed metric function, the computa- tional complexity of sequential decoding of PAC codes is equivalent to that of conventional convolutional codes. Our results indicate that the upper bound on the sequential decoding compu- tational complexity of PAC codes follows a Pareto distribution. We also employ guessing technique to derive a lower bound on the computational complexity of sequential decoding of PAC codes. To reduce the PAC sequential decoder’s worst-case latency, we restrict the number of searches executed by the sequential decoder. We introduce an improvement to the successive-cancellation list (SCL) decod- ing for polarized channels that reduces the number of sorting operations without degrading the code’s error-correction performance. In an SCL decoding with an optimum metric function, we show that, on average, the correct branch’s bit- metric value must be equal to the bit-channel capacity. On the other hand, the average bit-metric value of a wrong branch can be at most 0. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. This enables the decoder to identify incorrect branches and exclude them from the list of metrics to be sorted. We employ a similar technique to the stack algorithm, resulting in a considerable reduction in the stack size. Additionally, we propose a technique for constructing a rate profile for PAC codes of arbitrary length and rate which is capable of balancing the error- correction performance and decoding complexity of PAC codes. For signal-to- noise ratio (SNR) values larger than a target SNR value, the proposed approach can significantly enhance the error-correction performance of PAC codes while retaining a low mean sequential decoding complexity. Finally, we examine the weight distribution of PAC codes with the goal of providing a new demonstration that PAC codes surpass polar codes in terms of weight distribution.