Related papers: Compound Polar Codes
Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…
In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source $P_{X,Z}$ there exists a slightly modified polar code - having the same rate, the…
With the evolution from 5G to 6G, ultra-reliable low-latency communication (URLLC) faces increasingly stringent performance requirements. Lower latency constraints demand shorter channel coding lengths, which can severely degrade decoding…
It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the…
Polar codes have emerged as the most favorable channel codes for their unique capacity-achieving property. To date, numerous works have been reported for efficient design of polar codes decoder. However, these prior efforts focused on…
Concatenating the state-of-the-art codes at moderate rates with repetition codes has emerged as a practical solution deployed in various standards for ultra-low-power devices such as in Internet-of-Things (IoT) networks. In this paper, we…
Similar to existing codes, puncturing and shortening are two general ways to obtain an arbitrary code length and code rate for polar codes. When some of the coded bits are punctured or shortened, it is equivalent to a situation in which the…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
Polar codes are designed for parallel binary-input additive white Gaussian noise (BiAWGN) channels with an average power constraint. The two main design choices are: the mapping between codeword bits and channels of different quality, and…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
Polar codes are widely used in modern communication systems due to their capacity-achieving properties. This paper investigates the importance of coded bits in the decoding process of polar codes and aims to determine which bits contribute…
Long polar codes can achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. However, for polar codes with short and moderate code length,…
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…
We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances…
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding…
Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive…