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Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique,…
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar…
A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows…
Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the analysis and construction of polar codes involve the complex iterative-calculation. In…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. In this paper, two types of partial orders (PO) of polar codes are…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
We consider the problem of efficiently constructing polar codes over binary memoryless symmetric (BMS) channels. The complexity of designing polar codes via an exact evaluation of the polarized channels to find which ones are "good" appears…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
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 definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and…
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
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…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…
In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…
Polar codes were originally specified for codelengths that are powers of two. In many applications, it is desired to have a code that is not restricted to such lengths. Two common strategies of modifying the length of a code are shortening…
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…