Browsing by Subject "Polar coding"

Now showing 1 - 7 of 7

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
Entropy polarization in butterfly transforms
(Academic Press, 2021-12) Arıkan, Erdal
In signal processing, it is common to employ various transforms for analyzing or compressing real- or complex-valued signals. If the transform is chosen suitably, certain characteristics of the signal, such as spectral content or sparsity, become readily accessible by looking at the energy distribution among the coordinates of the signal in the transform domain. In contrast, in information-theoretic settings entropy replaces energy as the key parameter of interest; information is processed directly by acting on the entropy through various transforms. Here we follow the information-theoretic approach and focus on the evolution of entropy in the course of butterfly transforms over arbitrary number fields. In particular, we state conditions for entropy polarization—a phenomenon that has been useful in constructing capacity-achieving source and channel codes. We discuss the possibility of using entropy polarization as a useful tool in signal processing applications.
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
A note on some inequalities used in channel polarization and polar coding
(Institute of Electrical and Electronics Engineers, 2018) Jayram, T. S.; Arıkan, Erdal
We give a unified treatment of some inequalities that are used in the proofs of channel polarization theorems involving a binary-input discrete memoryless channel.
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
Varentropy decreases under the polar transform
(Institute of Electrical and Electronics Engineers Inc., 2016) Arıkan, E.
We consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair (X,Y) consisting of a binary random variable X and an arbitrary side information random variable Y. The varentropy of (X,Y) is defined as the variance of the random variable-log pX|Y(X|Y). A polar transform of order two is a certain mapping that takes two independent BDEs and produces two new BDEs that are correlated with each other. It is shown that the sum of the varentropies at the output of the polar transform is less than or equal to the sum of the varentropies at the input, with equality if and only if at least one of the inputs has zero varentropy. This result is extended to polar transforms of higher orders and it is shown that the varentropy asymptotically decreases to zero when the BDEs at the input are independent and identically distributed.