2014
A, Pastore; Koch, Tobias; Fonollosa, Javier Rodriguez
A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information Artículo de revista
En: IEEE Transactions on Information Theory, vol. 60, no 7, pp. 4266–4285, 2014, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound
@article{Pastore2014a,
title = {A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information},
author = {Pastore A and Tobias Koch and Javier Rodriguez Fonollosa},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6832779 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60(7).pdf http://arxiv.org/pdf/1301.6120.pdf},
issn = {0018-9448},
year = {2014},
date = {2014-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {60},
number = {7},
pages = {4266--4285},
publisher = {IEEE},
abstract = {As shown by M\'{e}dard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat {H})) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat {H})) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying M\'{e}dard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than M\'{e}dard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat {H}) tends to zero as the SNR tends to infinity.},
keywords = {channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound},
pubstate = {published},
tppubtype = {article}
}
As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying Médard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity.
2013
Koch, Tobias; Lapidoth, Amos
At Low SNR, Asymmetric Quantizers are Better Artículo de revista
En: IEEE Transactions on Information Theory, vol. 59, no 9, pp. 5421–5445, 2013, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: 1-bit quantizer, asymmetric signaling constellation, asymmetric threshold quantizers, asymptotic power loss, Capacity per unit energy, channel capacity, discrete-time Gaussian channel, flash-signaling input distribution, Gaussian channel, Gaussian channels, low signal-to-noise ratio (SNR), quantisation (signal), quantization, Rayleigh channels, Rayleigh-fading channel, signal-to-noise ratio, SNR, spectral efficiency
@article{Koch2013,
title = {At Low SNR, Asymmetric Quantizers are Better},
author = {Tobias Koch and Amos Lapidoth},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6545291},
issn = {0018-9448},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {9},
pages = {5421--5445},
abstract = {We study the capacity of the discrete-time Gaussian channel when its output is quantized with a 1-bit quantizer. We focus on the low signal-to-noise ratio (SNR) regime, where communication at very low spectral efficiencies takes place. In this regime, a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2/$pi$, i.e., to cause an asymptotic power loss of approximately 2 dB. Here, it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. To avoid this power loss, flash-signaling input distributions are essential. Consequently, 1-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: at every fixed SNR, a threshold quantizer maximizes capacity among all 1-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case, a 1-bit output quantizer causes an unavoidable low-SNR asymptotic power loss. In the coherent case, however, this power loss is avoidable provided that we allow the quantizer to depend on the fading level.},
keywords = {1-bit quantizer, asymmetric signaling constellation, asymmetric threshold quantizers, asymptotic power loss, Capacity per unit energy, channel capacity, discrete-time Gaussian channel, flash-signaling input distribution, Gaussian channel, Gaussian channels, low signal-to-noise ratio (SNR), quantisation (signal), quantization, Rayleigh channels, Rayleigh-fading channel, signal-to-noise ratio, SNR, spectral efficiency},
pubstate = {published},
tppubtype = {article}
}
We study the capacity of the discrete-time Gaussian channel when its output is quantized with a 1-bit quantizer. We focus on the low signal-to-noise ratio (SNR) regime, where communication at very low spectral efficiencies takes place. In this regime, a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2/$pi$, i.e., to cause an asymptotic power loss of approximately 2 dB. Here, it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. To avoid this power loss, flash-signaling input distributions are essential. Consequently, 1-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: at every fixed SNR, a threshold quantizer maximizes capacity among all 1-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case, a 1-bit output quantizer causes an unavoidable low-SNR asymptotic power loss. In the coherent case, however, this power loss is avoidable provided that we allow the quantizer to depend on the fading level.
Bravo-Santos, Ángel M
Polar Codes for Gaussian Degraded Relay Channels Artículo de revista
En: IEEE Communications Letters, vol. 17, no 2, pp. 365–368, 2013, ISSN: 1089-7798.
Resumen | Enlaces | BibTeX | Etiquetas: channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors
@article{Bravo-Santos2013,
title = {Polar Codes for Gaussian Degraded Relay Channels},
author = {\'{A}ngel M Bravo-Santos},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6412681},
issn = {1089-7798},
year = {2013},
date = {2013-01-01},
journal = {IEEE Communications Letters},
volume = {17},
number = {2},
pages = {365--368},
publisher = {IEEE},
abstract = {In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.},
keywords = {channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors},
pubstate = {published},
tppubtype = {article}
}
In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.
Koch, Tobias; Kramer, Gerhard
On Noncoherent Fading Relay Channels at High Signal-to-Noise Ratio Artículo de revista
En: IEEE Transactions on Information Theory, vol. 59, no 4, pp. 2221–2241, 2013, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: channel capacity, Channel models, Fading, fading channels, MIMO communication, multiple-input single-output fading channel statis, noncoherent, noncoherent fading relay channel capacity, radio receiver, radio receivers, radio transmitter, radio transmitters, Receivers, relay channels, relay networks (telecommunication), Relays, Signal to noise ratio, signal-to-noise ratio, SNR, statistics, time selective, Transmitters, Upper bound
@article{Koch2013a,
title = {On Noncoherent Fading Relay Channels at High Signal-to-Noise Ratio},
author = {Tobias Koch and Gerhard Kramer},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6378474},
issn = {0018-9448},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {4},
pages = {2221--2241},
abstract = {The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate.},
keywords = {channel capacity, Channel models, Fading, fading channels, MIMO communication, multiple-input single-output fading channel statis, noncoherent, noncoherent fading relay channel capacity, radio receiver, radio receivers, radio transmitter, radio transmitters, Receivers, relay channels, relay networks (telecommunication), Relays, Signal to noise ratio, signal-to-noise ratio, SNR, statistics, time selective, Transmitters, Upper bound},
pubstate = {published},
tppubtype = {article}
}
The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate.
2012
Olmos, Pablo M; Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
On the Design of LDPC-Convolutional Ensembles Using the TEP Decoder Artículo de revista
En: IEEE Communications Letters, vol. 16, no 5, pp. 726–729, 2012, ISSN: 1089-7798.
Resumen | Enlaces | BibTeX | Etiquetas: belief propagation decoding, binary erasure channel, channel capacity, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, design, Error analysis, finite-length analysis, Iterative decoding, LDPC-convolutional ensemble design, LDPCC code decoding, low-density parity-check convolutional code, parity check codes, tree-expectation propagation decoder, tree-structured expectation propagation, window-sliding scheme
@article{Olmos2012b,
title = {On the Design of LDPC-Convolutional Ensembles Using the TEP Decoder},
author = {Pablo M Olmos and Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6168872},
issn = {1089-7798},
year = {2012},
date = {2012-01-01},
journal = {IEEE Communications Letters},
volume = {16},
number = {5},
pages = {726--729},
abstract = {Low-density parity-check convolutional (LDPCC) codes asymptotically achieve channel capacity under belief propagation (BP) decoding. In this paper, we decode LDPCC codes using the Tree-Expectation Propagation (TEP) decoder, recently proposed as an alternative decoding method to the BP algorithm for the binary erasure channel (BEC). We show that, for LDPCC codes, the TEP decoder improves the BP solution with a comparable complexity or, alternatively, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.},
keywords = {belief propagation decoding, binary erasure channel, channel capacity, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, design, Error analysis, finite-length analysis, Iterative decoding, LDPC-convolutional ensemble design, LDPCC code decoding, low-density parity-check convolutional code, parity check codes, tree-expectation propagation decoder, tree-structured expectation propagation, window-sliding scheme},
pubstate = {published},
tppubtype = {article}
}
Low-density parity-check convolutional (LDPCC) codes asymptotically achieve channel capacity under belief propagation (BP) decoding. In this paper, we decode LDPCC codes using the Tree-Expectation Propagation (TEP) decoder, recently proposed as an alternative decoding method to the BP algorithm for the binary erasure channel (BEC). We show that, for LDPCC codes, the TEP decoder improves the BP solution with a comparable complexity or, alternatively, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.
2010
Koch, Tobias; Lapidoth, Amos
Gaussian Fading Is the Worst Fading Artículo de revista
En: IEEE Transactions on Information Theory, vol. 56, no 3, pp. 1158–1165, 2010, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters
@article{Koch2010a,
title = {Gaussian Fading Is the Worst Fading},
author = {Tobias Koch and Amos Lapidoth},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429105},
issn = {0018-9448},
year = {2010},
date = {2010-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {56},
number = {3},
pages = {1158--1165},
abstract = {The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.},
keywords = {Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters},
pubstate = {published},
tppubtype = {article}
}
The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.
Koch, Tobias; Lapidoth, Amos
On Multipath Fading Channels at High SNR Artículo de revista
En: IEEE Transactions on Information Theory, vol. 56, no 12, pp. 5945–5957, 2010, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters
@article{Koch2010b,
title = {On Multipath Fading Channels at High SNR},
author = {Tobias Koch and Amos Lapidoth},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5625630},
issn = {0018-9448},
year = {2010},
date = {2010-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {56},
number = {12},
pages = {5945--5957},
abstract = {A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.},
keywords = {approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters},
pubstate = {published},
tppubtype = {article}
}
A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.
2009
Koch, Tobias; Lapidoth, Amos; Sotiriadis, Paul P
Channels That Heat Up Artículo de revista
En: IEEE Transactions on Information Theory, vol. 55, no 8, pp. 3594–3612, 2009, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: additive noise channel, Capacity per unit cost, channel capacity, channels with memory, cooling, electronic circuits, heat dissipation, heat sinks, high signal-to-noise ratio, high signal-to-noise ratio (SNR), intrinsic thermal noise, low transmit power, network analysis, noise variance, on-chip communication, thermal noise
@article{Koch2009,
title = {Channels That Heat Up},
author = {Tobias Koch and Amos Lapidoth and Paul P Sotiriadis},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5165190},
issn = {0018-9448},
year = {2009},
date = {2009-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {55},
number = {8},
pages = {3594--3612},
abstract = {This paper considers an additive noise channel where the time-A; noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity.},
keywords = {additive noise channel, Capacity per unit cost, channel capacity, channels with memory, cooling, electronic circuits, heat dissipation, heat sinks, high signal-to-noise ratio, high signal-to-noise ratio (SNR), intrinsic thermal noise, low transmit power, network analysis, noise variance, on-chip communication, thermal noise},
pubstate = {published},
tppubtype = {article}
}
This paper considers an additive noise channel where the time-A; noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity.