Kutupsal ve polarizayson ayarlı evrişimli (PAC) kodlarının performans ve hesaplama analizi

We study the performance of sequential decoding of polarization-adjusted convolutional (PAC) codes. We present a metric function that employs bit-channel mutual information and cutoff rate values as the bias values and significantly reduces the computational complexity while retaining the excellent error-correction performance of PAC codes. With the proposed metric function, the computational 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 computational 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) decoding 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.