Related papers: Polar codes for the m-user multiple access channel…
We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters…
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…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
This paper presents a coding scheme for an insertion deletion substitution channel. We extend a previous scheme for the deletion channel where polar codes are modified by adding "guard bands" between segments. In the new scheme, each guard…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM…
Polar codes have become one of the most favorable capacity achieving error correction codes (ECC) along with their simple encoding method. However, among the very few prior successive cancellation (SC) polar decoder designs, the required…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and the multilevel coding (MLC) approach for $2^m$-ary digital pulse-amplitude modulation (PAM). The conceptual equivalence of polar…
Among error-correcting codes, polar codes are the first to provably achieve channel capacity with an explicit construction. In this work, we present software implementations of a polar decoder that leverage the capabilities of modern…
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…
Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used…
We study polarization for nonbinary channels with input alphabet of size q=2^r,r=2,3,... Using Arikan's polarizing kernel H_2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with…
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…
In this letter, we propose parallel SC (Successive Cancellation) decoder and parallel SC-List decoder for polar codes. The parallel decoder is composed of M=2^m(m>=1) component decoders working in parallel and each component decoder decodes…
In 2008 Arikan proposed polar coding [arXiv:0807.3917] which we summarize as follows: (a) From the root channel $W$ synthesize recursively a series of channels $W_N^{(1)},\dotsc,W_N^{(N)}$. (b) Select sophisticatedly a subset $A$ of…
Different polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding and/or layered secrecy. In this setting, the transmitter wishes to send…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
It is shown that for any binary-input discrete memoryless channel $W$ with symmetric capacity $I(W)$ and any rate $R <I(W)$, the probability of block decoding error for polar coding under successive cancellation decoding satisfies $P_e \le…