Gerhard Kramer

Technische Universität München, München, Bavaria, Germany

Are you Gerhard Kramer?

Claim your profile

Publications (176)99.22 Total impact

  • Ziv Goldfeld · Gerhard Kramer · Haim H. Permuter · Paul Cuff
    [Show abstract] [Hide abstract]
    ABSTRACT: A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong-secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semi-deterministic and physically degraded BCs and the results are compared to those of the corresponding BCs without a secrecy constraint. Blackwell and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements.
    No preview · Article · Jan 2016
  • Shirin Saeedi Bidokhti · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all ranges of bit-pipe capacities.
    No preview · Article · Oct 2015
  • Z. Goldfeld · H.H. Permuter · G. Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: The semi-deterministic (SD) broadcast channel (BC) where the decoders cooperate via a one-sided link is considered and its capacity region is derived. The direct proof relies on an achievable region for the general BC that is tight for the SD scenario. This achievable region follows by a coding scheme that combines rate-splitting and binning with Marton and superposition coding. The SD-BC is shown to be operationally equivalent to a class of relay-BCs (RBCs) and the correspondence between their capacity regions is established. Furthermore, a dual source coding problem, referred to as the Wyner-Ahlswede-Körner (WAK) problem with one-sided encoder cooperation, is proposed. Transformation principles between the problems are presented and the optimal rate region for the AK problem is stated. The SD-BC capacity and the admissible region of the AK problem are shown to be dual to one another in the sense that the information measures defining the corner points of both regions coincide. Special cases of the two problems are inspected and shown to maintain duality.
    No preview · Article · Jun 2015
  • Ziv Goldfeld · Gerhard Kramer · Haim H. Permuter
    [Show abstract] [Hide abstract]
    ABSTRACT: The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived. Without leakage constraints the inner bound recovers Marton's region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios.
    No preview · Article · Apr 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schroedinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.
    Preview · Article · Mar 2015
  • Source
    Luca Barletta · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A continuous-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A lower bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. The capacity pre-log depends on the oversampling factor, and amplitude and phase modulation do not equally contribute to capacity at high SNR.
    Preview · Article · Mar 2015
  • Source
    Hassan Ghozlan · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: Discrete-time interference channel models are developed for information transmission over optical fiber using wavelength-division multiplexing. A set of coupled nonlinear Schroedinger equations forms the basis of the models. The first model is memoryless and captures the nonlinear phenomena of cross-phase modulation but ignores dispersion. For the case of two carriers, a new technique called interference focusing is proposed where each carrier achieves the capacity pre-log 1, thereby doubling the pre-log of 1/2 achieved by using conventional methods. For more than two carriers, interference focusing is also useful under certain conditions. The second model captures the nonlinear phenomena of cross-phase modulation in addition to dispersion due to group velocity mismatch. Moreover, the model captures the effect of filtering at the receivers. In a 3-user system, it is shown that all users can achieve the maximum pre-log factor 1 simultaneously by using interference focusing, a time-limited pulse and a bank of filters at the receivers.
    Preview · Article · Mar 2015
  • Source
    Hassan Ghozlan · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A waveform channel is considered where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise. A discrete-time channel model that takes into account the effect of filtering on the phase noise is developed. The model is based on a multi-sample receiver, i.e., an integrate-and-dump filter whose output is sampled at a rate higher than the signaling rate. It is shown that, at high signal-to-noise ratio (SNR), the multi-sample receiver achieves a rate that grows logarithmically with the SNR if the number of samples per symbol (oversampling factor) grows with the cubic root of the SNR. Moreover, the pre-log factor is at least 1/2 and can be achieved by amplitude modulation. Numerical simulations are used to compute lower bounds on the information rates achieved by the multi-sample receiver. The simulations show that oversampling is beneficial for both strong and weak phase noise at high SNR. In fact, the information rates are sometimes substantially larger than when using commonly-used approximate discrete-time models. Finally, for an approximate discrete-time model of the multi-sample receiver, the capacity pre-log at high SNR is at least 3/4 if the number of samples per symbol grows with the square root of the SNR. The analysis shows that phase modulation achieves a pre-log of at least 1/4 while amplitude modulation achieves a pre-log of 1/2. This is strictly greater than the capacity pre-log of the (approximate) discrete-time Wiener phase noise channel with only one sample per symbol, which is 1/2.
    Preview · Article · Mar 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schr\"odinger (NLS) equation is upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal{P}_0/\sigma^2(z)$, where $\mathcal{P}_0$ is the average input signal power and $\sigma^2(z)$ is the total noise power up to distance $z$. This implies that the capacity of this model of the single-user optical fiber channel is below the capacity of the corresponding additive white Gaussian noise channel. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dynamical system.
    Full-text · Article · Feb 2015
  • Source
    Ziv Goldfeld · Gerhard Kramer · Haim H Permuter
    [Show abstract] [Hide abstract]
    ABSTRACT: To be considered for an 2015 IEEE Jack Keil Wolf ISIT Student Paper Award. The broadcast channel (BC) with one confidential message and where the decoders cooperate via a one-sided link is considered. A pair of messages is transmitted, one message for each user. The message to the cooperative user is confidential and is kept secret from the cooperation-aided user. The secrecy level is measured by the equivocation rate. An inner bound on the secrecy-capacity region of the BC is derived. The inner bound is achieved by double-binning the codebook of the secret message. The inner bound is tight for the semi-deterministic (SD) and physically degraded (PD) cases. The secrecy results are compared to those of the corresponding BCs without a secrecy constraint. A cooperative Blackwell channel example illustrates the impact of secrecy on the rate regions.
    Full-text · Conference Paper · Jan 2015
  • Ziv Goldfeld · Haim H. Permuter · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: The semi-deterministic broadcast channel (BC) where the decoders may cooperate via a finite-capacity onesided link is considered. The capacity region is derived via a novel converse that uses a probabilistic construction of auxiliary random variables that depends on the distribution induced by the codebook. Achievability is established by providing a coding scheme that incorporates techniques such as rate-splitting and Marton coding with a Wyner-Ziv-like coding mechanism that optimally leverages the cooperation link. The BC is shown to be operationally equivalent to a certain class of relay-broadcast channels (RBCs) and the correspondence between their capacity regions is established.
    No preview · Conference Paper · Dec 2014
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A power spectral density based on the theory of weak wave turbulence is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems. This power spectrum, termed Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise (GN) model.
    Full-text · Article · Nov 2014
  • Source
    Luca Barletta · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. An upper bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. If the oversampling factor grows as $\text{SNR}^\alpha$ for $0\le \alpha \le 1$, then the capacity pre-log is at most $(1+\alpha)/2$ at high SNR.
    Preview · Article · Nov 2014
  • Ziv Goldfeld · Haim H. Permuter · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: The Ahlswede-Körner (AK) coordination problem with one-sided encoder cooperation is considered. Encoder co-operation refers to communication between the encoders via a finite-capacity one-sided link. For this setting, the coordination capacity region is derived. The optimal coding scheme leverages the link between the encoders to optimally handle the correlation between the sources. Moreover, the scheme incorporates several source coding techniques, such as Wyner-Ziv coding, binning and superposition coding. Furthermore, a dual semi-deterministic broadcast channel (BC) with one-sided cooperative decoders is considered. Transformation principles between the two problems are presented and an achievable rate region for the BC setting is derived. The region of the BC is shown to be dual to the optimal region of the AK problem in the sense that the information measures defining the corner points in both regions coincide. Although the optimality of the achievable region for the semi-deterministic BC setting is yet to be shown, the region is optimal in the fully-deterministic case.
    No preview · Conference Paper · Jun 2014
  • Source
    Ziv Goldfeld · Haim H. Permuter · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: The Wyner-Ahlswede-Körner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques, such as Wyner-Ziv (WZ) coding, binning and superposition coding. Furthermore, a semi-deterministic (SD) broadcast channel (BC) with one-sided decoder cooperation is considered. Duality principles relating the two problems are presented, and the capacity region for the SD-BC setting is derived. The direct part follows from an achievable region for a general BC that is tight for the SD scenario. A converse is established by using telescoping identities. The SD-BC is shown to be operationally equivalent to a class of relay-BCs (RBCs) and the correspondence between their capacity regions is established. The capacity region of the SD-BC is transformed into an equivalent region that is shown to be dual to the admissible region of the WAK problem in the sense that the information measures defining the corner points of both regions coincide. Achievability and converse proofs for the equivalent region are provided. For the converse, we use a probabilistic construction of auxiliary random variables that depends on the distribution induced by the codebook. Several examples illustrate the results.
    Preview · Article · May 2014
  • Source
    Hassan Ghozlan · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A discrete-time Wiener phase noise channel model is introduced in which multiple samples are available at the output for every input symbol. A lower bound on the capacity is developed. At high signal-to-noise ratio (SNR), if the number of samples per symbol grows with the square root of the SNR, the capacity pre-log is at least 3/4. This is strictly greater than the capacity pre-log of the Wiener phase noise channel with only one sample per symbol, which is 1/2. It is shown that amplitude modulation achieves a pre-log of 1/2 while phase modulation achieves a pre-log of at least 1/4.
    Preview · Article · May 2014
  • Shirin Saeedi Bidokhti · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: The problem of communicating over a multiple access channel with cooperative encoders is studied. A new upper bound is derived on the capacity which is motivated by the regime of operation where the relays start to cooperate. The proof technique is based on a wringing lemma by Dueck and Ahlswede which was used for the multiple description problem with no excess rate. Previous upper bounds are shown to be loose in general, and may be improved.
    No preview · Conference Paper · May 2014
  • Hassan Ghozlan · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A discrete-time Wiener phase noise channel model is introduced in which multiple samples are available at the output for every input symbol. A lower bound on the capacity is developed. At high signal-to-noise ratio (SNR), if the number of samples per symbol grows with the square root of the SNR, the capacity pre-log is at least 3/4. This is strictly greater than the capacity pre-log of the Wiener phase noise channel with only one sample per symbol, which is 1/2. It is shown that amplitude modulation achieves a pre-log of 1/2 while phase modulation achieves a pre-log of at least 1/4.
    No preview · Article · Apr 2014
  • Source
    Marwa El Hefnawy · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: Capacity computations are presented for Faster-Than-Nyquist (FTN) signaling in the presence of interference from neighboring frequency bands. It is shown that Shannon's sinc pulses maximize the spectral efficiency for a multi-access channel, where spectral efficiency is defined as the sum rate in bits per second per Hertz. Comparisons using root raised cosine pulses show that the spectral efficiency decreases monotonically with the roll-off factor. At high signal-to-noise ratio, these pulses have an additive gap to capacity that increases monotonically with the roll-off factor.
    Preview · Article · Jan 2014
  • Source
    Luca Barletta · Gerhard Kramer
    [Show abstract] [Hide abstract]
    ABSTRACT: A continuous-time model for the additive white Gaussian noise (AWGN) channel in the presence of white (memoryless) phase noise is proposed and discussed. It is shown that for linear modulation the output of the baud-sampled filter matched to the shaping waveform represents a sufficient statistic. The analysis shows that the phase noise channel has the same information rate as an AWGN channel but with a penalty on the average signal-to-noise ratio, the amount of penalty depending on the phase noise statistic.
    Preview · Article · Jan 2014

Publication Stats

7k Citations
99.22 Total Impact Points

Institutions

  • 2009-2015
    • Technische Universität München
      • • Institute for Advanced Study
      • • Department of Communications Engineering
      München, Bavaria, Germany
  • 2009-2010
    • University of Southern California
      • Department of Electrical Engineering
      Los Ángeles, California, United States
    • University of California, Los Angeles
      Los Ángeles, California, United States
  • 2007-2009
    • Alcatel Lucent
      Lutetia Parisorum, Île-de-France, France
    • Concordia University–Ann Arbor
      Ann Arbor, Michigan, United States
    • Stanford University
      • Department of Electrical Engineering
      Palo Alto, CA, United States
  • 2008
    • New Jersey Institute of Technology
      • Department of Electrical and Computer Engineering
      Newark, NJ, United States
    • Australian National University
      Canberra, Australian Capital Territory, Australia
    • Syracuse University
      • Department of Electrical Engineering and Computer Science
      Syracuse, NY, United States
  • 2004-2005
    • Rutgers, The State University of New Jersey
      • Department of Electrical and Computer Engineering
      New Brunswick, NJ, United States
  • 2002
    • École Polytechnique Fédérale de Lausanne
      Lausanne, Vaud, Switzerland