### 2014

Ostman, Johan; Yang, Wei; Durisi, Giuseppe; Koch, Tobias

Diversity Versus Multiplexing at Finite Blocklength Inproceedings

In: 2014 11th International Symposium on Wireless Communications Systems (ISWCS), pp. 702–706, IEEE, Barcelona, 2014, ISBN: 978-1-4799-5863-4.

Abstract | Links | BibTeX | Tags: Antennas, Channel Coding, channel selectivity, Coherence, delay-sensitive ultra-reliable communication links, diversity reception, diversity-exploiting schemes, diversity-multiplexing tradeoff, Fading, finite blocklength analysis, maximum channel coding rate, multiple-antenna block-memoryless Rayleigh-fading, Multiplexing, nonasymptotic bounds, packet size, radio links, Rayleigh channels, Time-frequency analysis, Transmitters, Upper bound

@inproceedings{Ostman2014,

title = {Diversity Versus Multiplexing at Finite Blocklength},

author = {Johan Ostman and Wei Yang and Giuseppe Durisi and Tobias Koch},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6933444},

isbn = {978-1-4799-5863-4},

year = {2014},

date = {2014-01-01},

booktitle = {2014 11th International Symposium on Wireless Communications Systems (ISWCS)},

pages = {702--706},

publisher = {IEEE},

address = {Barcelona},

abstract = {A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels. The bounds in this paper allow one to numerically assess for which packet size, number of antennas, and degree of channel selectivity, diversity-exploiting schemes are close to optimal, and when instead the available spatial degrees of freedom should be used to provide spatial multiplexing. This finite blocklength view on the diversity-multiplexing tradeoff provides insights on the design of delay-sensitive ultra-reliable communication links.},

keywords = {Antennas, Channel Coding, channel selectivity, Coherence, delay-sensitive ultra-reliable communication links, diversity reception, diversity-exploiting schemes, diversity-multiplexing tradeoff, Fading, finite blocklength analysis, maximum channel coding rate, multiple-antenna block-memoryless Rayleigh-fading, Multiplexing, nonasymptotic bounds, packet size, radio links, Rayleigh channels, Time-frequency analysis, Transmitters, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2013

Alvarado, Alex; Brannstrom, Fredrik; Agrell, Erik; Koch, Tobias

High-SNR Asymptotics of Mutual Information for Discrete Constellations Inproceedings

In: 2013 IEEE International Symposium on Information Theory, pp. 2274–2278, IEEE, Istanbul, 2013, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: AWGN channels, discrete constellations, Entropy, Fading, Gaussian Q-function, high-SNR asymptotics, IP networks, least mean squares methods, minimum mean-square error, MMSE, Mutual information, scalar additive white Gaussian noise channel, Signal to noise ratio, signal-to-noise ratio, Upper bound

@inproceedings{Alvarado2013b,

title = {High-SNR Asymptotics of Mutual Information for Discrete Constellations},

author = {Alex Alvarado and Fredrik Brannstrom and Erik Agrell and Tobias Koch},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6620631},

issn = {2157-8095},

year = {2013},

date = {2013-01-01},

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

pages = {2274--2278},

publisher = {IEEE},

address = {Istanbul},

abstract = {The asymptotic behavior of the mutual information (MI) at high signal-to-noise ratio (SNR) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Asymptotics of the minimum mean-square error (MMSE) are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated.},

keywords = {AWGN channels, discrete constellations, Entropy, Fading, Gaussian Q-function, high-SNR asymptotics, IP networks, least mean squares methods, minimum mean-square error, MMSE, Mutual information, scalar additive white Gaussian noise channel, Signal to noise ratio, signal-to-noise ratio, Upper bound},

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}

}

Durisi, Giuseppe; Koch, Tobias; Polyanskiy, Yury

Diversity Versus Channel Knowledge at Finite Block-Length Inproceedings

In: 2012 IEEE Information Theory Workshop, pp. 572–576, IEEE, Lausanne, 2012, ISBN: 978-1-4673-0223-4.

Abstract | Links | BibTeX | Tags: Approximation methods, block error probability, channel coherence time, Channel estimation, channel knowledge, Coherence, diversity, diversity reception, error statistics, Fading, finite block-length, maximal achievable rate, noncoherent setting, Rayleigh block-fading channels, Rayleigh channels, Receivers, Signal to noise ratio, Upper bound

@inproceedings{Durisi2012,

title = {Diversity Versus Channel Knowledge at Finite Block-Length},

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

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6404740},

isbn = {978-1-4673-0223-4},

year = {2012},

date = {2012-01-01},

booktitle = {2012 IEEE Information Theory Workshop},

pages = {572--576},

publisher = {IEEE},

address = {Lausanne},

abstract = {We study the maximal achievable rate R*(n, ∈) for a given block-length n and block error probability o over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, R*(n, ∈) is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel.},

keywords = {Approximation methods, block error probability, channel coherence time, Channel estimation, channel knowledge, Coherence, diversity, diversity reception, error statistics, Fading, finite block-length, maximal achievable rate, noncoherent setting, Rayleigh block-fading channels, Rayleigh channels, Receivers, Signal to noise ratio, 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}

}

Campo, Adria Tauste; Vazquez-Vilar, Gonzalo; i Fabregas, Albert Guillen; Koch, Tobias; Martinez, Alfonso

Achieving Csiszár's Source-Channel Coding Exponent with Product Distributions Inproceedings

In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 1548–1552, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095.

Abstract | Links | BibTeX | Tags: average probability of error, Channel Coding, code construction, codewords, Csiszár's source-channel coding, Decoding, Encoding, error probability, error statistics, Joints, Manganese, product distributions, random codes, random-coding upper bound, source coding, source messages, Upper bound

@inproceedings{Campo2012a,

title = {Achieving Csiszár's Source-Channel Coding Exponent with Product Distributions},

author = {Adria Tauste Campo and Gonzalo Vazquez-Vilar and Albert Guillen i Fabregas and Tobias Koch and Alfonso Martinez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283524},

issn = {2157-8095},

year = {2012},

date = {2012-01-01},

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

pages = {1548--1552},

publisher = {IEEE},

address = {Cambridge, MA},

abstract = {We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszár's error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.},

keywords = {average probability of error, Channel Coding, code construction, codewords, Csiszár's source-channel coding, Decoding, Encoding, error probability, error statistics, Joints, Manganese, product distributions, random codes, random-coding upper bound, source coding, source messages, Upper bound},

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}

}

Goparaju, S; Calderbank, A R; Carson, W R; Rodrigues, Miguel R D; Perez-Cruz, Fernando

When to Add Another Dimension when Communicating over MIMO Channels Inproceedings

In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3100–3103, IEEE, Prague, 2011, ISSN: 1520-6149.

Abstract | Links | BibTeX | Tags: divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound

@inproceedings{Goparaju2011,

title = {When to Add Another Dimension when Communicating over MIMO Channels},

author = {S Goparaju and A R Calderbank and W R Carson and Miguel R D Rodrigues and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5946351},

issn = {1520-6149},

year = {2011},

date = {2011-01-01},

booktitle = {2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},

pages = {3100--3103},

publisher = {IEEE},

address = {Prague},

abstract = {This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit.},

keywords = {divide and conquer approach, divide and conquer methods, error probability, error rate, error statistics, Gaussian channels, Lattices, Manganese, MIMO, MIMO channel, MIMO communication, multiple input multiple output Gaussian channel, Mutual information, optimal power allocation, power allocation, power constraint, receive filter, Resource management, Signal to noise ratio, signal-to-noise ratio, transmit filter, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2010

Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando

Tree-Structure Expectation Propagation for Decoding LDPC Codes over Binary Erasure Channels Inproceedings

In: 2010 IEEE International Symposium on Information Theory, pp. 799–803, IEEE, Austin, TX, 2010, ISBN: 978-1-4244-7892-7.

Abstract | Links | BibTeX | Tags: belief propagation, binary erasure channels, Bipartite graph, BP decoder, Capacity planning, Channel Coding, codeword, computational complexity, Decoding, Finishing, graph theory, H infinity control, LDPC code decoding, LDPC Tanner graph, Maxwell decoder, parity check codes, Performance analysis, tree structure expectation propagation, trees (mathematics), Upper bound

@inproceedings{Olmos2010,

title = {Tree-Structure Expectation Propagation for Decoding LDPC Codes over Binary Erasure Channels},

author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5513636},

isbn = {978-1-4244-7892-7},

year = {2010},

date = {2010-01-01},

booktitle = {2010 IEEE International Symposium on Information Theory},

pages = {799--803},

publisher = {IEEE},

address = {Austin, TX},

abstract = {Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal distribution constraints in some check nodes of the LDPC Tanner graph. These additional constraints allow decoding the received codeword when the BP decoder gets stuck. In this paper, we first present the new decoding algorithm, whose complexity is identical to the BP decoder, and we then prove that it is able to decode codewords with a larger fraction of erasures, as the block size tends to infinity. The proposed algorithm can be also understood as a simplification of the Maxwell decoder, but without its computational complexity. We also illustrate that the new algorithm outperforms the BP decoder for finite block-size codes.},

keywords = {belief propagation, binary erasure channels, Bipartite graph, BP decoder, Capacity planning, Channel Coding, codeword, computational complexity, Decoding, Finishing, graph theory, H infinity control, LDPC code decoding, LDPC Tanner graph, Maxwell decoder, parity check codes, Performance analysis, tree structure expectation propagation, trees (mathematics), Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2009

Martino, Luca; Miguez, Joaquin

A Novel Rejection Sampling Scheme for Posterior Probability Distributions Inproceedings

In: 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2921–2924, IEEE, Taipei, 2009, ISSN: 1520-6149.

Abstract | Links | BibTeX | Tags: Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound

@inproceedings{Martino2009,

title = {A Novel Rejection Sampling Scheme for Posterior Probability Distributions},

author = {Luca Martino and Joaquin Miguez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4960235},

issn = {1520-6149},

year = {2009},

date = {2009-01-01},

booktitle = {2009 IEEE International Conference on Acoustics, Speech and Signal Processing},

pages = {2921--2924},

publisher = {IEEE},

address = {Taipei},

abstract = {Rejection sampling (RS) is a well-known method to draw from arbitrary target probability distributions, which has important applications by itself or as a building block for more sophisticated Monte Carlo techniques. The main limitation to the use of RS is the need to find an adequate upper bound for the ratio of the target probability density function (pdf) over the proposal pdf from which the samples are generated. There are no general methods to analytically find this bound, except in the particular case in which the target pdf is log-concave. In this paper we adopt a Bayesian view of the problem and propose a general RS scheme to draw from the posterior pdf of a signal of interest using its prior density as a proposal function. The method enables the analytical calculation of the bound and can be applied to a large class of target densities. We illustrate its use with a simple numerical example.},

keywords = {Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}