Related papers: Interpolation of Quantum Polar Codes and Quantum R…
This paper deals with two main issues regarding the short polar codes: the potential of FEC-assisted decoding and optimal code concatenation strategies under various design scenarios. Code concatenation and FEC-assisted decoding are…
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…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
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…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
The future of quantum repeater networking will require interoperability between various error correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
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…
In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
Polar molecules, with their rich internal structure, offer immense potential for fundamental physics, quantum technology, and controlled chemistry. However, their utilization is currently limited because of slow and imperfect state…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate…
In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a…
Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the computational cutoff…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…