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Hypernetworks were recently shown to improve the performance of message passing algorithms for decoding error correcting codes. In this work, we demonstrate how hypernetworks can be applied to decode polar codes by employing a new…
Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed…
In this paper, we propose a Polar coding scheme for parallel Gaussian channels. The encoder knows the sum rate of the parallel channels but does not know the rate of any channel. By using the nesting property of Polar code, we design a…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the…
Polar codes are a new family of error correction codes for which efficient hardware architectures have to be defined for the encoder and the decoder. Polar codes are decoded using the successive cancellation decoding algorithm that includes…
We propose a method to increase the capacity achieved by uniform prior in discrete memoryless channels (DMC) with high input cardinality. It consists in appropriately reducing the input set. Different design criteria of the input subset are…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.
In this paper, we propose \textit{selectively precoded polar (SPP) code}, built on top of Arikan's capacity achieving polar codes. We provide the encoding and decoding scheme for SPP code. Simulation results show that for a target frame…
We show that the mismatched capacity of binary discrete memoryless channels can be improved by channel combining and splitting via Ar{\i}kan's polar transformations. We also show that the improvement is possible even if the transformed…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
We consider lossy source compression of a binary symmetric source using polar codes and the low-complexity successive encoding algorithm. It was recently shown by Arikan that polar codes achieve the capacity of arbitrary symmetric…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error…
Polar codes based on $2\times2$ non-binary kernels are discussed in this work. The kernel over $\text{GF}(q)$ is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.