Related papers: A Randomized Construction of Polar Subcodes
In this paper, we present a deterministic algorithm to count the low-weight codewords of punctured and shortened pure and pre-transformed polar codes. The method first evaluates the weight properties of punctured/shortened polar cosets.…
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,…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…
It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's…
We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same as those in [Mori-Tanaka], yet we believe…
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…
Although power line communication (PLC) systems are available everywhere, unfortunately these systems are not suitable for information transmission due to the effects of the impulsive noise. Therefore, many previous studies on channel codes…
Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel…
In this paper, we propose a construction for multi-kernel polar codes based on the maximization of the minimum distance. Compared to the original construction based on density evolution, our new design shows particular advantages for short…
A hybrid automatic repeat request (HARQ) scheme based on a novel class of rate-compatible polar (\mbox{RCP}) codes are proposed. The RCP codes are constructed by performing punctures and repetitions on the conventional polar codes.…
Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have…
This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement learning techniques. The proposed method provides a novel technique…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
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…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
In this paper, we present an iterative construction of a polar code and develop properties of the dual of a polar code. Based on this approach, belief propagation of a polar code can be presented in the context of low-density parity check…
In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a…