3,174 research outputs found
The Error Probability of Generalized Perfect Codes via the Meta-Converse
We introduce a definition of perfect and quasiperfect codes for discrete symmetric channels based on the
packing and covering properties of generalized spheres whose
shape is tilted using an auxiliary probability measure. This
notion generalizes previous definitions of perfect and quasiperfect codes and encompasses maximum distance separable
codes. The error probability of these codes, whenever they exist,
is shown to coincide with the estimate provided by the metaconverse lower bound. We illustrate how the proposed definition
naturally extends to cover almost-lossless source-channel coding
and lossy compression.ER
Perfect and quasi-perfect codes for the Bosonic classical-quantum channel
We explore perfect and quasi-perfect codes for the Bosonic channel, where information is generated by a laser and conveyed in the form of coherent states. In particular, we consider the phase-modulation codebook for coherent states in a Bosonic channel. We show that these phase-modulation codes are quasi-perfect as long as the cardinality of the code is the same as the dimension of the coherent states. These codes feature the smallest error probability among all codes of the same cardinality and the same dimension of the channel Hilbert space. We study the performance of these codes in terms of error probability, incorporating the degradation caused by a depolarizing or an erasure quantum channel.This work was supported in part by the MCIN/AEI/ 10.13039/501100011033 under Grant PID2019-104958RB-C41 and Grant RED2018-102668-T, in part by the Departament de Recerca i Universitats de la Generalitat de Catalunya 10.13039/501100002809 under Grant 2017 SGR 578 and Grant QuantumCAT 001-P-001644, and in part by the European Regional Development Funds (ERDF) .Peer ReviewedPostprint (published version
Generalized perfect codes for symmetric classical-quantum channels
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain N-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.This work was supported in part by the European Research Council (ERC) under Grant 714161; in part by the Agencia Estatal de Investigación,
Ministerio de Ciencia e Innovación, the Spanish Government, under Grant RED2018-102668-T, Grant PID2019-104958RB-C41, and Grant PID2020-116683GB-C21; and in part by the Catalan Government, within the ERDF Program of Catalunya, under Grant 2017 SGR 578 AGAUR and Grant 001-P001644 QuantumCAT.Peer ReviewedPostprint (author's final draft
The Error Probability of Generalized Perfect Codes
This paper has been presented at : IEEE International Symposium on Information Theory 2018We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This new definition generalizes previous definitions and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to attain the meta-converse lower bound.This work has been funded in part by the European Research Council (ERC) under grants 714161 and 725411, by the Spanish Ministry of Economy and Competitiveness under Grants TEC2016-78434-C3 and IJCI-2015-27020, by
the National Science Foundation under Grant CCF-1513915 and by the Center for Science of Information, an NSF Science and Technology Center under Grant CCF-0939370
Improved Finite Blocklength Converses for Slepian-Wolf Coding via Linear Programming
A new finite blocklength converse for the Slepian- Wolf coding problem is
presented which significantly improves on the best known converse for this
problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of
the linear programming (LP) based framework for finite blocklength point-
to-point coding problems from [3] is employed. However, a direct application of
this framework demands a complicated analysis for the Slepian-Wolf problem. An
analytically simpler approach is presented wherein LP-based finite blocklength
converses for this problem are synthesized from point-to-point lossless source
coding problems with perfect side-information at the decoder. New finite
blocklength metaconverses for these point-to-point problems are derived by
employing the LP-based framework, and the new converse for Slepian-Wolf coding
is obtained by an appropriate combination of these converses.Comment: under review with the IEEE Transactions on Information Theor
Ultra-Reliable Short-Packet Communications: Fundamental Limits and Enabling Technologies
The paradigm shift from 4G to 5G communications, anticipated to enable ultra-reliable low-latency communications (URLLC), will enforce a radical change in the design of wireless communication systems. Unlike in 4G systems, where the main objective is to provide a large transmission rate, in URLLC, as implied by its name, the objective is to enable transmissions with low latency and, simultaneously, very high reliability. Since low latency implies the use of short data packets, the tension between blocklength and reliability is studied in URLLC.Several key enablers for URLLC communications have been designated in the literature. Of special importance are diversity-enabling technologies such as multiantenna systems and feedback protocols. Furthermore, it is not only important to introduce additional diversity by means of the above examples, one must also guarantee that thescarce number of channel uses are used in an optimal way. Therefore, it is imperative to develop design guidelines for how to enable reliable detection of incoming data, how to acquire channel-state information, and how to construct efficient short-packet channel codes. The development of such guidelines is at the heart of this thesis. This thesis focuses on the fundamental performance of URLLC-enabling technologies. Specifically, we provide converse (upper) bounds and achievability (lower) bounds on the maximum coding rate, based on finite-blocklength information theory, for systems that employ the key enablers outlined above. With focus on the wireless channel, modeled via a block-fading assumption, we are able to provide answers to questions like: howto optimally utilize spatial and frequency diversity, how far from optimal short-packet channel codes perform, how multiantenna systems should be designed to serve a given number of users, and how to design feedback schemes when the feedback link is noisy. In particular, this thesis is comprised out of four papers. In Paper A, we study the short-packet performance over the Rician block-fading channel. In particular, we present achievability bounds for pilot-assisted transmission with several different decoders that allow us to quantify the impact, on the achievable performance, of imposed pilots and mismatched decoding. Furthermore, we design short-packet channel codes that perform within 1 dB of our achievability bounds. Paper B studies multiuser massive multiple-input multiple-output systems with short packets. We provide an achievability bound on the average error probability over quasistatic spatially correlated Rayleigh-fading channels. The bound applies to arbitrary multiuser settings, pilot-assisted transmission, and mismatched decoding. This makes it suitable to assess the performance in the uplink/downlink for arbitrary linear signal processing. We show that several lessons learned from infinite-blocklength analyses carry over to the finite-blocklength regime. Furthermore, for the multicell setting with randomly placed users, pilot contamination should be avoided at all cost and minimum mean-squared error signal processing should be used to comply with the stringent requirements of URLLC.In Paper C, we consider sporadic transmissions where the task of the receiver is to both detect and decode an incoming packet. Two novel achievability bounds, and a novel converse bound are presented for joint detection-decoding strategies. It is shown that errors associated with detection deteriorates performance significantly for very short packet sizes. Numerical results also indicate that separate detection-decoding strategies are strictly suboptimal over block-fading channels.Finally, in Paper D, variable-length codes with noisy stop-feedback are studied via a novel achievability bound on the average service time and the average error probability. We use the bound to shed light on the resource allocation problem between the forward and the feedback channel. For URLLC applications, it is shown that enough resources must be assigned to the feedback link such that a NACK-to-ACK error becomes rarer than the target error probability. Furthermore, we illustrate that the variable-length stop-feedback scheme outperforms state-of-the-art fixed-length no-feedback bounds even when the stop-feedback bit is noisy
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
Minimum Energy to Send Bits Over Multiple-Antenna Fading Channels
This paper investigates the minimum energy required to transmit
information bits with a given reliability over a multiple-antenna Rayleigh
block-fading channel, with and without channel state information (CSI) at the
receiver. No feedback is assumed. It is well known that the ratio between the
minimum energy per bit and the noise level converges to dB as goes
to infinity, regardless of whether CSI is available at the receiver or not.
This paper shows that lack of CSI at the receiver causes a slowdown in the
speed of convergence to dB as compared to the case of
perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap
to dB is proportional to , whereas when perfect
CSI is available at the receiver, this gap is proportional to . In
both cases, the gap to dB is independent of the number of transmit
antennas and of the channel's coherence time. Numerically, we observe that,
when the receiver is equipped with a single antenna, to achieve an energy per
bit of dB in the no-CSI case, one needs to transmit at least information bits, whereas bits suffice for the case of
perfect CSI at the receiver
Converses for Secret Key Agreement and Secure Computing
We consider information theoretic secret key agreement and secure function
computation by multiple parties observing correlated data, with access to an
interactive public communication channel. Our main result is an upper bound on
the secret key length, which is derived using a reduction of binary hypothesis
testing to multiparty secret key agreement. Building on this basic result, we
derive new converses for multiparty secret key agreement. Furthermore, we
derive converse results for the oblivious transfer problem and the bit
commitment problem by relating them to secret key agreement. Finally, we derive
a necessary condition for the feasibility of secure computation by trusted
parties that seek to compute a function of their collective data, using an
interactive public communication that by itself does not give away the value of
the function. In many cases, we strengthen and improve upon previously known
converse bounds. Our results are single-shot and use only the given joint
distribution of the correlated observations. For the case when the correlated
observations consist of independent and identically distributed (in time)
sequences, we derive strong versions of previously known converses
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