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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…
We propose a novel scheme for rate-compatible arbitrary-length polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of non-uniform channel polarization. The original polar…
Polar codes were recently introduced by Ar\i kan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code…
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…
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 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…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
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…
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…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such…
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…
To advance Polar code design for 6G applications, we develop a reinforcement learning-based universal sequence design framework that is extensible and adaptable to diverse channel conditions and decoding strategies. Crucially, our method…
The structure of polar codes inherently requires block lengths to be powers of two. In this paper, we investigate how different block lengths can be realized by coupling of several short-length polar codes. For this, we first analyze "code…
This paper revisits polar code design for a binary-input additive white Gaussian noise (BI-AWGN) channel when successive cancellation (SC) decoding is applied at the receiver. We focus on the reciprocal channel approximation (RCA), which is…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
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…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper…
We propose a new polar code construction framework (i.e., selecting the frozen bit positions) for the additive white Gaussian noise (AWGN) channel, tailored to a given decoding algorithm, rather than based on the (not necessarily optimal)…