Browsing by Subject "Weight distribution"
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Item Open Access On polarization adjusted convolutional codes over fading and additive white Gaussian noise channels(Bilkent University, 2022-05) Seyedmasoumian Charandabi, Seyed SadraUltra-reliable and low-latency communications (URLLC), which focuses on delay sensitive applications and services, is one of the three main pillars of 5G New Radio (NR) network architecture. URLLC's physical layer design is challenging since it must meet two contradictory requirements: ultra-low latency and ultra-high reliability. Short packets are used to minimize latency but at the cost of a significant loss of coding gain. Alternatively, system bandwidth can be increased, which is not always practical, particularly for some URLLC applications in industrial control that use unlicensed spectrum. In order to improve reliability, we must utilize robust channel codes in conjunction with retransmission techniques. Therefore, the construction of block codes with short blocklengths (e.g., a thousand or less information bits) is receiving significant attention with emerging wireless communications applications. In this thesis, we review existing channel coding bounds with short blocklengths for both additive white Gaussian noise (AWGN) and block fading channels. Furthermore, we investigate the performances of tail-biting convolutional, polar, and polarization adjusted convolutional (PAC) codes. With the motivation of reducing the decoding complexity of PAC decoders, we implement an alternative sequential decoding algorithm, namely, creeper algorithm, and describe a simplified list decoding approach. We also conduct an investigation on the performance of PAC codes and channel coding limits for block fading channels. Furthermore, we derive a method for computing approximate weight distribution of PAC codes, which can be used for an accurate performance bound; and, employing this approximation, we design PAC codes utilizing simulated annealing for optimization of the rate profiles. The results show that the newly designed PAC code rate profiles offer superior performance.Item Open Access Performance and computational analysis of polarization-adjusted convolutional (PAC) codes(Bilkent University, 2022-06) Moradi, MohsenWe 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.