66 research outputs found
Memory effects can make the transmission capability of a communication channel uncomputable
Most communication channels are subjected to noise. One of the goals of
Information Theory is to add redundancy in the transmission of information so
that the information is transmitted reliably and the amount of information
transmitted through the channel is as large as possible. The maximum rate at
which reliable transmission is possible is called the capacity. If the channel
does not keep memory of its past, the capacity is given by a simple
optimization problem and can be efficiently computed. The situation of channels
with memory is less clear. Here we show that for channels with memory the
capacity cannot be computed to within precision 1/5. Our result holds even if
we consider one of the simplest families of such channels -information-stable
finite state machine channels-, restrict the input and output of the channel to
4 and 1 bit respectively and allow 6 bits of memory.Comment: Improved presentation and clarified claim
Efficient reconciliation with rate adaptive codes in quantum key distribution.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string ¿the key¿ known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals ¿the raw key¿ must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret- key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many com- munications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system
Improved construction of irregular progressive edge-growth Tanner graphs
The progressive edge-growth algorithm is a well-known procedure to construct
regular and irregular low-density parity-check codes. In this paper, we propose
a modification of the original algorithm that improves the performance of these
codes in the waterfall region when constructing codes complying with both,
check and symbol node degree distributions. The proposed algorithm is thus
interesting if a family of irregular codes with a complex check node degree
distribution is used.Comment: 3 pages, 3 figure
Untainted Puncturing for Irregular Low-Density Parity-Check Codes
Puncturing is a well-known coding technique widely used for constructing
rate-compatible codes. In this paper, we consider the problem of puncturing
low-density parity-check codes and propose a new algorithm for intentional
puncturing. The algorithm is based on the puncturing of untainted symbols, i.e.
nodes with no punctured symbols within their neighboring set. It is shown that
the algorithm proposed here performs better than previous proposals for a range
of coding rates and short proportions of punctured symbols.Comment: 4 pages, 3 figure
Blind Reconciliation
Information reconciliation is a crucial procedure in the classical
post-processing of quantum key distribution (QKD). Poor reconciliation
efficiency, revealing more information than strictly needed, may compromise the
maximum attainable distance, while poor performance of the algorithm limits the
practical throughput in a QKD device. Historically, reconciliation has been
mainly done using close to minimal information disclosure but heavily
interactive procedures, like Cascade, or using less efficient but also less
interactive -just one message is exchanged- procedures, like the ones based in
low-density parity-check (LDPC) codes. The price to pay in the LDPC case is
that good efficiency is only attained for very long codes and in a very narrow
range centered around the quantum bit error rate (QBER) that the code was
designed to reconcile, thus forcing to have several codes if a broad range of
QBER needs to be catered for. Real world implementations of these methods are
thus very demanding, either on computational or communication resources or
both, to the extent that the last generation of GHz clocked QKD systems are
finding a bottleneck in the classical part. In order to produce compact, high
performance and reliable QKD systems it would be highly desirable to remove
these problems. Here we analyse the use of short-length LDPC codes in the
information reconciliation context using a low interactivity, blind, protocol
that avoids an a priori error rate estimation. We demonstrate that 2x10^3 bits
length LDPC codes are suitable for blind reconciliation. Such codes are of high
interest in practice, since they can be used for hardware implementations with
very high throughput.Comment: 22 pages, 8 figure
Superadditivity of Private Information for Any Number of Uses of the Channel.
The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. Both quantities are given by the infinite regularization of the coherent and the private information, respectively, which makes their evaluation very difficult. Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses, thus demonstrating that the regularization is necessary. We prove this by showing that the coherent information is strictly larger than the private information of a smaller number of uses of the channel. This implies that even though the quantum capacity is upper bounded by the private capacity, the nonregularized quantities can be interleaved.SS acknowledges the support of Sidney Sussex College and European Union under project QALGO (Grant Agreement No. 600700). DE acknowledges financial support from the European CHIST-ERA project CQC (funded partially by MINECO grant PRI-PIMCHI-
2011-1071) and from Comunidad de Madrid (grant QUITEMAD+-CM, ref. S2013/ICE-2801). This work has been partially supported by STW, QuTech and by
the project HyQuNet (Grant No. TEC2012-35673), funded by Ministerio de Economia y Competitividad (MINECO), Spain. This work was made possible through
the support of grant #48322 from the John Templeton
Foundation.This is the author accepted manuscript. The final version of the article is available from APS at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.04050
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