19 research outputs found
Block-fading channels at finite blocklength
This tutorial paper deals with the problem of characterizing the maximal achievable rate R(n; ϵ )at a given blocklength n and error probability ϵ over block-fading channels. We review recent results that establish tight bounds on R(n; ϵ )and characterize its asymptotic behavior. Comparison between the theoretical results and the data rates achievable with the coding scheme used in LTE-Advanced are reported
Coherent multiple-antenna block-fading channels at finite blocklength
In this paper we consider a channel model that is often used to describe the
mobile wireless scenario: multiple-antenna additive white Gaussian noise
channels subject to random (fading) gain with full channel state information at
the receiver. Dynamics of the fading process are approximated by a
piecewise-constant process (frequency non-selective isotropic block fading).
This work addresses the finite blocklength fundamental limits of this channel
model. Specifically, we give a formula for the channel dispersion -- a quantity
governing the delay required to achieve capacity. Multiplicative nature of the
fading disturbance leads to a number of interesting technical difficulties that
required us to enhance traditional methods for finding channel dispersion.
Alas, one difficulty remains: the converse (impossibility) part of our result
holds under an extra constraint on the growth of the peak-power with
blocklength.
Our results demonstrate, for example, that while capacities of and antenna configurations coincide (under fixed received
power), the coding delay can be quite sensitive to this switch. For example, at
the received SNR of dB the system achieves capacity with
codes of length (delay) which is only of the length required for the
system. Another interesting implication is that for the MISO
channel, the dispersion-optimal coding schemes require employing orthogonal
designs such as Alamouti's scheme -- a surprising observation considering the
fact that Alamouti's scheme was designed for reducing demodulation errors, not
improving coding rate. Finding these dispersion-optimal coding schemes
naturally gives a criteria for producing orthogonal design-like inputs in
dimensions where orthogonal designs do not exist
On Single-Antenna Rayleigh Block-Fading Channels at Finite Blocklength
This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.The work of A. Lancho and T. Koch was supported in part by the Spanish Ministerio de Economia y Competitividad under Grant TEC2013-41718-R and Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU), in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under Grant 714161, and in part by the Comunidad de Madrid under Grant S2103/ICE-2845. The work of A. Lancho further was supported by an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274. The work of T. Koch further was supported in part by the Spanish Ministerio de EconomÃa y Competitividad under Grant RYC-2014-16332 and in part by the 7th European Union Framework Programme under Grant 333680. The work of G. Durisi was supported by the Swedish Research Council under Grant 2012-4571 and Grant 2016-03293
Block-Fading Channels with Delayed CSIT at Finite Blocklength
In many wireless systems, the channel state information at the transmitter
(CSIT) can not be learned until after a transmission has taken place and is
thereby outdated. In this paper, we study the benefits of delayed CSIT on a
block-fading channel at finite blocklength. First, the achievable rates of a
family of codes that allows the number of codewords to expand during
transmission, based on delayed CSIT, are characterized. A fixed-length and a
variable-length characterization of the rates are provided using the dependency
testing bound and the variable-length setting introduced by Polyanskiy et al.
Next, a communication protocol based on codes with expandable message space is
put forth, and numerically, it is shown that higher rates are achievable
compared to coding strategies that do not benefit from delayed CSIT.Comment: Extended version of a paper submitted to ISIT'1
A high-SNR normal approximation for single-antenna Rayleigh block-fading channels
Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.A. Lancho and T. Koch have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de EconomÃa y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), from an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274 and from the Comunidad de Madrid under Grant S2103/ICE-2845. G. Durisi has been supported by the Swedish Research Council under Grants 2012-4571 and 2016-03293
Closed-form Approximation for Performance Bound of Finite Blocklength Massive MIMO Transmission
Ultra-reliable low latency communications (uRLLC) is adopted in the fifth
generation (5G) mobile networks to better support mission-critical applications
that demand high level of reliability and low latency. With the aid of
well-established multiple-input multiple-output (MIMO) information theory,
uRLLC in the future 6G is expected to provide enhanced capability towards
extreme connectivity. Since the latency constraint can be represented
equivalently by blocklength, channel coding theory at finite block-length plays
an important role in the theoretic analysis of uRLLC. On the basis of
Polyanskiy's and Yang's asymptotic results, we first derive the exact
close-form expressions for the expectation and variance of channel dispersion.
Then, the bound of average maximal achievable rate is given for massive MIMO
systems in ideal independent and identically distributed fading channels. This
is the study to reveal the underlying connections among the fundamental
parameters in MIMO transmissions in a concise and complete close-form formula.
Most importantly, the inversely proportional law observed therein implies that
the latency can be further reduced at expense of spatial degrees of freedom
Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback
We present an upper bound on the error probability achievable using
variable-length stop feedback codes, for a fixed size of the information
payload and a given constraint on the maximum latency and the average service
time. Differently from the bound proposed in Polyanskiy et al. (2011), which
pertains to the scenario in which the stop signal is sent over a noiseless
feedback channel, our bound applies to the practically relevant setup in which
the feedback link is noisy. By numerically evaluating our bound, we illustrate
that, for fixed latency and reliability constraints, noise in the feedback link
can cause a significant increase in the minimum average service time, to the
extent that fixed-length codes without feedback may be preferable in some
scenarios.Comment: Submitted to a Transactions on Wireless Communication