Related papers: Magic state distillation with punctured polar code…
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…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
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…
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…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…
Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…
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, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under…
A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations…
This work presents a polar coding scheme for fading channels, focusing primarily on fading binary symmetric and additive exponential noise channels. For fading binary symmetric channels, a hierarchical coding scheme is presented, utilizing…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
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…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
In this paper we show a polar coding scheme for the deletion channel with a probability of error that decays roughly like $2^{-\sqrt{\Lambda}}$, where $\Lambda$ is the length of the codeword. That is, the same decay rate as that of seminal…
This paper presents a puncturing technique based on the channel polarization index for the design of rate-compatible polar codes in the fifth generation (5G) of wireless systems. The proposed strategy consists of two steps: we first…
Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…
Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…