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In this paper, we propose a new polar coding scheme with molecular programming, which is capable of highly parallel implementation at a nano-scale without a need of electrical power sources. We designed chemical reaction networks (CRN) to…

In this paper, we introduce two novel methods to design outer polar codes for two previously proposed concatenated polar code architectures: augmented polar codes and local-global polar codes. These methods include a stopping set (SS)…

Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun {\em et al.} We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to…

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for…

We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…

An efficient algorithm for the construction of polar codes for higher-order modulation is presented based on information-theoretic principles. The bit reliabilities after successive demapping are estimated using the LM-rate, an achievable…

This paper investigates properties of concatenated polar codes and their potential applications. We start with reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated…

Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…

Arikan has shown that systematic polar codes (SPC) outperform nonsystematic polar codes (NSPC). However, the performance gain comes at the price of elevated encoding complexity, i.e., compared to NSPC, the available encoding methods for SPC…

J. Y. Hyun, et al. (Des. Codes Cryptogr., vol. 88, pp. 2475-2492, 2020) constructed some optimal and minimal binary linear codes generated by one or two order ideals in hierarchical posets of two levels. At the end of their paper, they left…

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…

A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan…

Motivated by the need for channel codes with low-complexity soft-decision decoding algorithms, we consider the recursive Plotkin concatenation of optimal low-rate and high-rate codes based on simplex codes and their duals. These component…

We propose a nonuniform quantized decoder for polar codes. The design metric of the quantizers is to minimize the distortion incurred by quantization. The quantizers are obtained via dynamic programming and the optimality of the quantizer…

Owing to their capacity-achieving performance and low encoding and decoding complexity, polar codes have drawn much research interests recently. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two common…

Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…

Channel polarization and Polar code are widely considered as major breakthroughs in coding theory because they have shown promising features for future wireless standards. The main drawbacks of Polar code are high-latency in decoding…

We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…

Precoded polar product codes are proposed, where selected component codes enable successive cancellation list decoding to generate bit-wise soft messages efficiently for iterative decoding while targeting optimized distance spectrum as…

This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…