Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOne way quantum repeaters with quantum Reed-Solomon codes
53
0
0.0
(
0
)
Added by
Sreraman Muralidharan
Publication date
2018
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of $d$-level systems for large dimension $d$. We study the performance of one-way quantum repeaters with these codes and obtain a significant improvement in key generation rate compared to previously investigated encoding schemes with quantum parity codes and quantum polynomial codes. We also compare the three generation of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.
rate research
Read More
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show that our construction yields several families of MDS codes. Further, for a large subclass of (MDS) twisted RS codes, we show that the new codes are not generalized RS codes. To achieve this, we use properties of Schur squares of codes as well as an explicit description of the dual of a large subclass of our codes. We conclude the paper with a description of a decoder, that performs very well in practice as shown by extensive simulation results.
In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of 3-dimensional MDS codes of length n=6,7,8,9.
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring their restriction to every line in the space to be a codeword of the RS code. In this paper, we investigate lifted RS codes and discuss their application to batch codes, a notion introduced in the context of private information retrieval and load-balancing in distributed storage systems. First, we improve the estimate of the code rate of lifted RS codes for lifting parameter $mge 3$ and large field size. Second, a new explicit construction of batch codes utilizing lifted RS codes is proposed. For some parameter regimes, our codes have a better trade-off between parameters than previously known batch codes.
Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length q+1. The classification of deep holes --received words with maximum possible error distance-- for PRS codes is an important and difficult problem. In this paper, we use algebraic methods to explicitly construct three classes of deep holes for PRS codes. We show that these three classes completely classify all deep holes of PRS codes with redundancy at most four. Previously, the deep hole classification was only known for PRS codes with redundancy at most three in work arXiv:1612.05447
Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols. Recently, certain Reed-Solomon codes were constructed which are MSR. However, the sub-packetization of these codes is exponentially large, growing like $n^{Omega(n)}$ in the constant-rate regime. In this work, we study the relaxed notion of $epsilon$-MSR codes, which incur a factor of $(1+epsilon)$ higher than the optimal repair bandwidth, in the context of Reed-Solomon codes. We give constructions of constant-rate $epsilon$-MSR Reed-Solomon codes with polynomial sub-packetization of $n^{O(1/epsilon)}$ and thereby giving an explicit tradeoff between the repair bandwidth and sub-packetization.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
