Related papers: Polar decreasing monomial-Cartesian codes
We exploit the redundancy of the language-based source to help polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after…
The inherent nature of polar codes being channel specific makes it difficult to use them in a setting where the communication channel changes with time. In particular, to be able to use polar codes in a wireless scenario, varying…
A polar decomposition of mutual information between a complex-valued channel's input and output is proposed for a input whose amplitude and phase are independent of each other. The mutual information is symmetrically decomposed into three…
Minimum weight codewords play a crucial role in the error correction performance of a linear block code. In this work, we establish an explicit construction for these codewords of polar codes as a sum of the generator matrix rows, which can…
Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
An extension of polar codes is proposed, which allows some of the frozen symbols, called dynamic frozen symbols, to be data-dependent. A construction of polar codes with dynamic frozen symbols, being subcodes of extended BCH codes, is…
Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this…
We focus on the metric sorter unit of successive cancellation list decoders for polar codes, which lies on the critical path in all current hardware implementations of the decoder. We review existing metric sorter architectures and we…
Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra at short and moderate lengths. Recent algebraic results…
We construct a joint coordination-channel polar coding scheme for strong coordination of actions between two agents $\mathsf X$ and $\mathsf Y$, which communicate over a discrete memoryless channel (DMC) such that the joint distribution of…
Deep polar codes, employing multi-layered polar kernel pre-transforms in series, are recently introduced variants of pre-transformed polar codes. These codes have demonstrated the ability to reduce the number of minimum weight codewords,…
This paper focuses on low complexity successive cancellation list (SCL) decoding of polar codes. In particular, using the fact that splitting may be unnecessary when the reliability of decoding the unfrozen bit is sufficiently high, a novel…
A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are…
We study monomial ideals using the operation polarization to first turn them into square-free monomial ideals. We focus on monomial ideals whose polarization produce simplicial trees, and show that many of the properties of simplicial trees…
In this paper, we introduce a binary balanced tree (BBT) channel transformation that extends Ar{\i}kan's channel transformation to arbitrary block lengths. We prove that the proposed transformation induces channel polarization, thereby…
We show that the entire class of polar codes (up to a natural necessary condition) converge to capacity at block lengths polynomial in the gap to capacity, while simultaneously achieving failure probabilities that are exponentially small in…
In the low-energy high-energy-efficiency regime of classical optical communications---relevant to deep-space optical channels---there is a big gap between reliable communication rates achievable via conventional optical receivers and the…
A successive cancellation list (SCL) decoder with limited list size for polar codes can not be analyzed as a successive cancellation (SC) decoder, nor as a maximum likelihood (ML) decoder, due to the complicated decoding errors caused by…
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…