### 2014

Yang, Wei; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury

Dispersion of Quasi-Static MIMO Fading Channels via Stokes' Theorem Inproceedings

In: 2014 IEEE International Symposium on Information Theory, pp. 2072–2076, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4.

Abstract | Links | BibTeX | Tags: channel capacity, differential form integration, Dispersion, Fading, fading channels, fading distribution, integration, Manifolds, Measurement, MIMO, MIMO communication, quasistatic MIMO fading channels dispersion, quasistatic multiple-input multiple-output fading, radio transmitters, Random variables, Stoke Theorem, transmitter

@inproceedings{Yang2014b,

title = {Dispersion of Quasi-Static MIMO Fading Channels via Stokes' Theorem},

author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875198},

isbn = {978-1-4799-5186-4},

year = {2014},

date = {2014-01-01},

booktitle = {2014 IEEE International Symposium on Information Theory},

pages = {2072--2076},

publisher = {IEEE},

address = {Honolulu},

abstract = {This paper analyzes the channel dispersion of quasi-static multiple-input multiple-output fading channels with no channel state information at the transmitter. We show that the channel dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary.},

keywords = {channel capacity, differential form integration, Dispersion, Fading, fading channels, fading distribution, integration, Manifolds, Measurement, MIMO, MIMO communication, quasistatic MIMO fading channels dispersion, quasistatic multiple-input multiple-output fading, radio transmitters, Random variables, Stoke Theorem, transmitter},

pubstate = {published},

tppubtype = {inproceedings}

}

Koch, Tobias

On the Dither-Quantized Gaussian Channel at Low SNR Inproceedings

In: 2014 IEEE International Symposium on Information Theory, pp. 186–190, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4.

Abstract | Links | BibTeX | Tags: Additive noise, channel capacity, dither quantized Gaussian channel, Entropy, Gaussian channels, low signal-to-noise-ratio, low-SNR asymptotic capacity, peak power constraint, peak-and-average-power-limited Gaussian channel, Quantization (signal), Signal to noise ratio

@inproceedings{Koch2014,

title = {On the Dither-Quantized Gaussian Channel at Low SNR},

author = {Tobias Koch},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6874820},

isbn = {978-1-4799-5186-4},

year = {2014},

date = {2014-01-01},

booktitle = {2014 IEEE International Symposium on Information Theory},

pages = {186--190},

publisher = {IEEE},

address = {Honolulu},

abstract = {We study the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $Delta$. We focus on the low signal-to-noise-ratio (SNR) regime, where communication at low spectral efficiencies takes place. We show that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of $Delta$. We further derive an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios and evaluate it in the low- and high-resolution limit. We demonstrate that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity.},

keywords = {Additive noise, channel capacity, dither quantized Gaussian channel, Entropy, Gaussian channels, low signal-to-noise-ratio, low-SNR asymptotic capacity, peak power constraint, peak-and-average-power-limited Gaussian channel, Quantization (signal), Signal to noise ratio},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2013

Yang, Wei; Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury

Quasi-Static SIMO Fading Channels at Finite Blocklength Inproceedings

In: 2013 IEEE International Symposium on Information Theory, pp. 1531–1535, IEEE, Istanbul, 2013, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion

@inproceedings{Yang2013a,

title = {Quasi-Static SIMO Fading Channels at Finite Blocklength},

author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620483},

issn = {2157-8095},

year = {2013},

date = {2013-01-01},

booktitle = {2013 IEEE International Symposium on Information Theory},

pages = {1531--1535},

publisher = {IEEE},

address = {Istanbul},

abstract = {We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The result follows from computationally and analytically tractable converse and achievability bounds. Through numerical evaluation, we verify that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases. In the example of a particular 1×2 SIMO Rician channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity.},

keywords = {achievability bounds, AWGN channel, AWGN channels, channel capacity, channel dispersion, channel gains, Dispersion, error probability, error statistics, Fading, fading channels, fading realizations, fast convergence, finite blocklength, maximal achievable rate, numerical evaluation, outage capacity, quasistatic SIMO fading channels, Random variables, Receivers, SIMO Rician channel, single-input multiple-output, Transmitters, zero dispersion},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2012

Koch, Tobias; Martinez, Alfonso; i Fabregas, Albert Guillen

The Capacity Loss of Dense Constellations Inproceedings

In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 572–576, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: capacity loss, channel capacity, Constellation diagram, dense constellations, Entropy, general complex-valued additive-noise channels, high signal-to-noise ratio, loss 1.53 dB, power loss, Quadrature amplitude modulation, Random variables, signal constellations, Signal processing, Signal to noise ratio, square signal constellations, Upper bound

@inproceedings{Koch2012,

title = {The Capacity Loss of Dense Constellations},

author = {Tobias Koch and Alfonso Martinez and Albert Guillen i Fabregas},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283482},

issn = {2157-8095},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE International Symposium on Information Theory Proceedings},

pages = {572--576},

publisher = {IEEE},

address = {Cambridge, MA},

abstract = {We determine the loss in capacity incurred by using signal constellations with a bounded support over general complex-valued additive-noise channels for suitably high signal-to-noise ratio. Our expression for the capacity loss recovers the power loss of 1.53 dB for square signal constellations.},

keywords = {capacity loss, channel capacity, Constellation diagram, dense constellations, Entropy, general complex-valued additive-noise channels, high signal-to-noise ratio, loss 1.53 dB, power loss, Quadrature amplitude modulation, Random variables, signal constellations, Signal processing, Signal to noise ratio, square signal constellations, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

Pastore, Adriano; Koch, Tobias; Fonollosa, Javier Rodriguez

Improved Capacity Lower Bounds for Fading Channels with Imperfect CSI Using Rate Splitting Inproceedings

In: 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, pp. 1–5, IEEE, Eilat, 2012, ISBN: 978-1-4673-4681-8.

Abstract | Links | BibTeX | Tags: channel capacity, channel capacity lower bounds, conditional entropy, Decoding, Entropy, Fading, fading channels, Gaussian channel, Gaussian channels, Gaussian random variable, imperfect channel-state information, imperfect CSI, independent Gaussian variables, linear minimum mean-square error, mean square error methods, Medard lower bound, Mutual information, Random variables, rate splitting approach, Resource management, Upper bound, wireless communications

@inproceedings{Pastore2012,

title = {Improved Capacity Lower Bounds for Fading Channels with Imperfect CSI Using Rate Splitting},

author = {Adriano Pastore and Tobias Koch and Javier Rodriguez Fonollosa},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6377031},

isbn = {978-1-4673-4681-8},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel},

pages = {1--5},

publisher = {IEEE},

address = {Eilat},

abstract = {As shown by Medard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. Theory, May 2000), the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input X, and by upper-bounding the conditional entropy h(XY, Ĥ), conditioned on the channel output Y and the CSI Ĥ, by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, by using a rate-splitting approach, this lower bound can be sharpened: we show that by expressing the Gaussian input X as as the sum of two independent Gaussian variables X(1) and X(2), and by applying Medard's lower bound first to analyze the mutual information between X(1) and Y conditioned on Ĥ while treating X(2) as noise, and by applying the lower bound then to analyze the mutual information between X(2) and Y conditioned on (X(1), Ĥ), we obtain a lower bound on the capacity that is larger than Medard's lower bound.},

keywords = {channel capacity, channel capacity lower bounds, conditional entropy, Decoding, Entropy, Fading, fading channels, Gaussian channel, Gaussian channels, Gaussian random variable, imperfect channel-state information, imperfect CSI, independent Gaussian variables, linear minimum mean-square error, mean square error methods, Medard lower bound, Mutual information, Random variables, rate splitting approach, Resource management, Upper bound, wireless communications},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2011

Ruiz, Francisco J R; Perez-Cruz, Fernando

Zero-Error Codes for the Noisy-Typewriter Channel Inproceedings

In: 2011 IEEE Information Theory Workshop, pp. 495–497, IEEE, Paraty, 2011, ISBN: 978-1-4577-0437-6.

Abstract | Links | BibTeX | Tags: channel capacity, Channel Coding, Equations, Linear code, Noise measurement, noisy-typewriter channel, nontrivial codes, nonzero zero-error rate, odd-letter noisy-typewriter channels, Upper bound, Vectors, zero-error capacity, zero-error codes

@inproceedings{Ruiz2011,

title = {Zero-Error Codes for the Noisy-Typewriter Channel},

author = {Francisco J R Ruiz and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6089510},

isbn = {978-1-4577-0437-6},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE Information Theory Workshop},

pages = {495--497},

publisher = {IEEE},

address = {Paraty},

abstract = {In this paper, we propose nontrivial codes that achieve a non-zero zero-error rate for several odd-letter noisy-typewriter channels. Some of these codes (specifically, those which are defined for a number of letters of the channel of the form 2n + 1) achieve the best-known lower bound on the zero-error capacity. We build the codes using linear codes over rings, as we do not require the multiplicative inverse to build the codes.},

keywords = {channel capacity, Channel Coding, Equations, Linear code, Noise measurement, noisy-typewriter channel, nontrivial codes, nonzero zero-error rate, odd-letter noisy-typewriter channels, Upper bound, Vectors, zero-error capacity, zero-error codes},

pubstate = {published},

tppubtype = {inproceedings}

}

Koch, Tobias; Lapidoth, Amos

Asymmetric Quantizers are Better at Low SNR Inproceedings

In: 2011 IEEE International Symposium on Information Theory Proceedings, pp. 2592–2596, IEEE, St. Petersburg, 2011, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: asymmetric one-bit quantizer, asymmetric signal constellations, channel capacity, Channel Coding, Constellation diagram, Decoding, discrete-time average-power-limited Gaussian chann, Gaussian channels, quantization, Signal to noise ratio, signal-to-noise ratio, SNR, spread spectrum communication, spread-spectrum communications, ultra wideband communication, ultrawideband communications, Upper bound

@inproceedings{Koch2011,

title = {Asymmetric Quantizers are Better at Low SNR},

author = {Tobias Koch and Amos Lapidoth},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6034037},

issn = {2157-8095},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE International Symposium on Information Theory Proceedings},

pages = {2592--2596},

publisher = {IEEE},

address = {St. Petersburg},

abstract = {We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/$pi$, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.},

keywords = {asymmetric one-bit quantizer, asymmetric signal constellations, channel capacity, Channel Coding, Constellation diagram, Decoding, discrete-time average-power-limited Gaussian chann, Gaussian channels, quantization, Signal to noise ratio, signal-to-noise ratio, SNR, spread spectrum communication, spread-spectrum communications, ultra wideband communication, ultrawideband communications, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2010

Koch, Tobias; Lapidoth, Amos

Increased Capacity per Unit-Cost by Oversampling Inproceedings

In: 2010 IEEE 26-th Convention of Electrical and Electronics Engineers in Israel, pp. 000684–000688, IEEE, Eliat, 2010, ISBN: 978-1-4244-8681-6.

Abstract | Links | BibTeX | Tags: AWGN, AWGN channels, bandlimited Gaussian channel, channel capacity, Gaussian channels, increased capacity per unit cost, Information rates, one bit output quantizer, oversampling, quantisation (signal), quantization, sampling rate recovery, signal sampling

@inproceedings{Koch2010,

title = {Increased Capacity per Unit-Cost by Oversampling},

author = {Tobias Koch and Amos Lapidoth},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5662127},

isbn = {978-1-4244-8681-6},

year = {2010},

date = {2010-01-01},

booktitle = {2010 IEEE 26-th Convention of Electrical and Electronics Engineers in Israel},

pages = {000684--000688},

publisher = {IEEE},

address = {Eliat},

abstract = {It is demonstrated that doubling the sampling rate recovers some of the loss in capacity incurred on the bandlimited Gaussian channel with a one-bit output quantizer.},

keywords = {AWGN, AWGN channels, bandlimited Gaussian channel, channel capacity, Gaussian channels, increased capacity per unit cost, Information rates, one bit output quantizer, oversampling, quantisation (signal), quantization, sampling rate recovery, signal sampling},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2008

Koch, Tobias; Lapidoth, Amos

On Multipath Fading Channels at High SNR Inproceedings

In: 2008 IEEE International Symposium on Information Theory, pp. 1572–1576, IEEE, Toronto, 2008, ISBN: 978-1-4244-2256-2.

Abstract | Links | BibTeX | Tags: channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters

@inproceedings{Koch2008,

title = {On Multipath Fading Channels at High SNR},

author = {Tobias Koch and Amos Lapidoth},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4595252},

isbn = {978-1-4244-2256-2},

year = {2008},

date = {2008-01-01},

booktitle = {2008 IEEE International Symposium on Information Theory},

pages = {1572--1576},

publisher = {IEEE},

address = {Toronto},

abstract = {This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1.},

keywords = {channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters},

pubstate = {published},

tppubtype = {inproceedings}

}

Koch, Tobias; Lapidoth, Amos

Multipath Channels of Unbounded Capacity Inproceedings

In: 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, pp. 640–644, IEEE, Eilat, 2008, ISBN: 978-1-4244-2481-8.

Abstract | Links | BibTeX | Tags: channel capacity, discrete-time capacity, Entropy, Fading, fading channels, Frequency, H infinity control, Information rates, multipath channels, multipath fading channels, noncoherent, noncoherent capacity, path gains decay, Signal to noise ratio, statistics, Transmitters, unbounded capacity

@inproceedings{Koch2008b,

title = {Multipath Channels of Unbounded Capacity},

author = {Tobias Koch and Amos Lapidoth},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4736611},

isbn = {978-1-4244-2481-8},

year = {2008},

date = {2008-01-01},

booktitle = {2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel},

pages = {640--644},

publisher = {IEEE},

address = {Eilat},

abstract = {The capacity of discrete-time, noncoherent, multipath fading channels is considered. It is shown that if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the transmit power.},

keywords = {channel capacity, discrete-time capacity, Entropy, Fading, fading channels, Frequency, H infinity control, Information rates, multipath channels, multipath fading channels, noncoherent, noncoherent capacity, path gains decay, Signal to noise ratio, statistics, Transmitters, unbounded capacity},

pubstate = {published},

tppubtype = {inproceedings}

}