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.
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.
This paper proposes a rate-profile construction method for polarization-adjusted convolutional (PAC) codes of any code length and rate, which is capable of maintaining trade-off between the error-correction performance and decoding complexity of PAC code. 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.
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose systematic PAC codes. Thanks to the systematic property, improvement in the bit-error rate of up to 0.2 dB is observed, while preserving the frame-error rate performance. Moreover, a genetic-algorithm based construction method targeted to approach the theoretical bound is provided. It is then shown that using the proposed construction method systematic and non-…
Polarization-adjusted convolutional (PAC) codes combine the polar and convolutional transformations to enhance the distance properties of polar codes. They offer a performance very close to the finite length information-theoretic bounds for short block lengths. In this paper, we develop a method of computing the weight distribution of PAC codes in an approximate form by employing a probabilistic technique. We demonstrate that the results well match the exact weight distributions for small codes that can be computed using a brute-force algorithm. We also present a way employing the results (alo…
A latest coding scheme named polarization-adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near-bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable latency. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. We define four types of constituent nodes and provide fast list decoding algorithms for each of them. Simulation results present that fast list decoding with three types of constituent nodes…
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 computational 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 computational cutoff rate in sequential decoding of pre-transformed polar codes polarizes. The polarization of the computational cutoff rate …
Sun Yat-sen University（中山大学）；Guangdong Province Key Laboratory of Information Security Technology（广东省信息安全技术重点实验室）；Huawei Technologies Co., Ltd.（华为技术有限公司）
Performance and complexity of sequential decoding of polarization-adjusted convolutional (PAC) codes is studied. In particular, a performance and computational complexity comparison of PAC codes with 5G polar codes and convolutional codes is given. A method for bounding the complexity of sequential decoding of PAC codes is proposed.
Decoding Golay Codes and their Related Lattices: A PAC Code Perspective
College of Computer Science and Software Engineering, Shenzhen Univeristy（深圳大学计算机科学与软件工程学院）；Guangzhou Institute of Technology, Xidian University（西安电子科技大学广州研究院）；College of Cyber Security, Jinan University（暨南大学网络空间安全学院）
Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a precoding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results in the literature show that this concatenation improves the weight distribution of polar codes which justifies the superior error correction performance of PAC codes relative to polar codes. In this work, we explicitl…
Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near) maximum likelihood (ML) decoders such as sequential decoders and sphere decoders. However, PAC codes cannot be decoded by sphere decoding. The reason is twofold: 1) Sphere decoding of polar codes is performed from the last bit - due to the lower rectangular shape of the polar transform. Whereas the shape of PAC codes generator matrix is no longer triangular. …
Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results show that this concatenation improves the Hamming distance properties of polar codes. In this work, we implement the parallel list Viterbi algorithm (LVA) and show how the error correction performance moves from the …
In this paper, we present an optimal metric function on average, which leads to a significantly low decoding computation while maintaining the superiority of the polarization-adjusted convolutional (PAC) codes' error-correction performance. With our proposed metric function, the PAC codes' decoding computation is comparable to the conventional convolutional codes (CC) sequential decoding. Moreover, simulation results show an improvement in the low-rate PAC codes' error-correction performance when using our proposed metric function. We prove that choosing the polarized cutoff rate as the metric…
The polarization-adjusted convolutional (PAC) codes concatenate the polar transform and the convolutional transform to improve the decoding performance of the finite-length polar codes, where the rate-profile is used to construct the PAC codes by setting the positions of frozen bits. However, the optimal rateprofile method of PAC codes is still unknown. In this paper, an optimized rate-profile algorithm of PAC codes is proposed. First, we propose the normalized compression factor (NCF) to quantify the transmission efficiency of useful information, showing that the distribution of useful inform…
Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short block lengths is far from optimal. Arikan has recently presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. Such PAC codes provide dramatic improvement in performance as compared to both standard successive-cancellation decoding as well as CRC-aided list decoding. Arikan's PAC codes are based primarily upon the following ideas: replacing CRC precoding wit…
