Browsing by Subject "PAC codes"

Now showing 1 - 9 of 9

Embargo
A Monte-Carlo based construction of polarization-adjusted convolutional (PAC) codes
(Elsevier BV, 2024-12-05) Moradi, Mohsen; Mozammel, Amir
This paper proposes a rate-profile construction method for polarization-adjusted convolutional (PAC) codes of any code length and rate, which is capable of preserving the trade-off between the error-correction performance and decoding complexity of PAC codes. The proposed method can improve the error-correction performance of PAC codes while guaranteeing a low mean sequential decoding complexity for signal-to-noise ratio (SNR) values beyond a target SNR value.
Open Access
A tree pruning technique for decoding complexity reduction of polar codes and PAC codes
(Institute of Electrical and Electronics Engineers , 2023-05-18) Moradi, Mohsen; Mozammel, Amir
Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without visible degradation in 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, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.
Open Access
Application of guessing to sequential decoding of polarization-adjusted convolutional (PAC) codes
(Institute of Electrical and Electronics Engineers Inc., 2023-08-16) Moradi, Mohsen
Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.
Open Access
Concatenated Reed-Solomon and Polarization-Adjusted Convolutional (PAC) Codes
(Institute of Electrical and Electronics Engineers (IEEE), 2022-08-24) Moradi, Mohsen; Mozammel, Amir
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of 10−5 , a concatenated scheme using RS and PAC codes has more than 0.25 dB coding gain over the NASA standard concatenation scheme, which uses RS and convolutional codes.
Open Access
Hardware implementation of Fano Decoder for polarization-adjusted convolutional (PAC) codes
(2022-06) Hokmabadi, Amir Mozammel
Polarization-adjusted convolutional (PAC) codes are a new class of error-correcting codes that have been shown to achieve near-optimum performance. By combining ideas from channel polarization and convolutional coding, PAC codes create an overall encoding transform that achieves a performance near the information-theoretic limits at short block lengths. In this thesis we propose a hardware implementation architecture for Fano decoding of PAC codes. First, we introduce a new variant of Fano algorithm for decoding PAC codes which is suitable for hardware implementation. Then we provide the hardware diagrams of the sub-blocks of the proposed PAC Fano decoder and an estimate of their hardware complexity and propagation delay. We also introduce a novel branch metric unit for sequential decoding of PAC codes which is capable of calculating the current and previous branch metric values online, without requiring any storage element or comparator. We evaluate the error-correction performance of the proposed decoder on FPGA and its hardware characteristics on ASIC with TSMC 28 nm 0.72 V library. We show that, for a block length of 128 and a message length of 64, the proposed decoder can be clocked at 500 MHz and achieve approximately 38.1 Mb/s information throughput at 3.5 dB signal-to-noise ratio with a power consumption of 3.85 mW.
Open Access
Hardware implementation of fano decoder for polarization-adjusted convolutional (PAC) codes
(IEEE, 2021-10-26) Mozammel, Amir
This brief proposes a hardware implementation architecture for Fano decoding of polarization-adjusted convolutional (PAC) codes. This architecture uses a novel branch metric unit specific to PAC codes. The proposed decoder is tested on FPGA, and its performance is evaluated on ASIC using TSMC 28 nm 0.72 V library. The decoder can be clocked at 500 MHz and reach an average information throughput of 38 Mb/s at 3.5 dB signal-to-noise ratio for a block length of 128 and a code rate of 1/2.
Open Access
On sequential decoding metric function of polarization-adjusted convolutional (PAC) codes
(IEEE, 2021-09-07) Moradi, Mohsen
In this paper, we present a sequential decoding metric function, which leads to significantly improved computational complexity while maintaining the superiority of polarizationadjusted 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.
Open Access
Polarization-adjusted convolutional (PAC) codes as a concatenation of inner cyclic and outer polar- and Reed-Muller-like codes
(Academic Press, 2023-10-23) Moradi, Mohsen
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this study, we show that PAC codes are equivalent to a new class of codes consisting of inner cyclic codes and outer polar- and Reed-Muller-like codes. We leverage the properties of cyclic codes to establish that PAC codes outperform polar- and Reed-Muller-like codes in terms of minimum distance.
Open Access
Systematic encoding and shortening of PAC codes
(MDPI AG, 2020-11) Arıkan, Erdal
Polarization adjusted convolutional (PAC) codes are a class of codes that combine channel polarization with convolutional coding. PAC codes are of interest for their high performance. This paper presents a systematic encoding and shortening method for PAC codes. Systematic encoding is important for lowering the bit-error rate (BER) of PAC codes. Shortening is important for adjusting the block length of PAC codes. It is shown that systematic encoding and shortening of PAC codes can be carried out in a unified framework.