arXiv subjects

Gerhard Kramer

Publications and source records attributed to Gerhard Kramer.

At least 73 records · Page 4Linked to original sources

arXiv2017

Models and Information Rates for Wiener Phase Noise Channels

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. For an approximate discrete-time model of the multi-sample receiver, the capacity pre-log at high SNR is shown to be 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 still 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. 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.

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arXiv2017

Broadcast Channels with Privacy Leakage Constraints

The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate 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 rate 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 when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A Uniform Approximation Lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. 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.

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arXiv2017

Capacity Bounds on the Downlink of Symmetric, Multi-Relay, Single Receiver C-RAN Networks

The downlink of symmetric Cloud Radio Access Networks (C-RANs) with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton's coding which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow's technique to augment the system with an auxiliary random variable. The bounds are studied over scalar Gaussian C-RANs and are shown to meet and characterize the capacity for interesting regimes of operation.

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arXiv2017

Constructing Receiver Signal Points using Constrained Massive MIMO Arrays

A low cost solution for constructing receiver signal points is investigated that combines a large number of constrained radio frequency (RF) frontends with a limited number of full RF chains. The constrained RF front ends have low cost and are limited to on/off switching of antenna elements and a small number of phases. Severe degradations are typically observed for multi-user MIMO for these simple on/off antenna arrays. A few full RF frontends are shown to compensate for the signal errors of the high number of constrained RF frontends for various scenarios. An algorithm for such a hybrid RF (HRF) system is developed that achieves performance close to that of exhaustive search with respect to the mean square error of the constructed receiver signals for Rayleigh fading and the WINNER 2 Urban Macro channel model.

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arXiv2016

Duality of a Source Coding Problem and the Semi-Deterministic Broadcast Channel with Rate-Limited Cooperation

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.

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arXiv2015

Capacity Bounds for Discrete-Time, Amplitude-Constrained, Additive White Gaussian Noise Channels

The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bits of capacity for all signal-to-noise ratios (SNRs). The two-dimensional bound is within 0.15 bits of capacity provably up to 4.5 dB, and numerical evidence suggests a similar gap for all SNRs.

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arXiv2015

Capacity Bounds for Diamond Networks with an Orthogonal Broadcast Channel

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.

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arXiv2015

Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels

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.

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arXiv2015

Upper Bound on the Capacity of the Nonlinear Schrödinger Channel

It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schrödinger (NLS) equation is upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal P_0/σ^2(z)$, where $\mathcal P_0$ is the average input signal power and $σ^2(z)$ is the total noise power up to distance $z$. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dynamical system.

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arXiv2015

Lower Bound on the Capacity of Continuous-Time Wiener Phase Noise Channels

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.

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arXiv2015

Upper Bound on the Capacity of Discrete-Time Wiener Phase Noise Channels

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 $\text{SNR}^α$ for $0\le α\le 1$, then the capacity pre-log is at most $(1+α)/2$ at high SNR.

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arXiv2014

Phase Modulation for Discrete-time Wiener Phase Noise Channels with Oversampling at High SNR

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.

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arXiv2014

On Continuous-Time White Phase Noise Channels

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.

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arXiv2014

Information Networks with in-Block Memory

A class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks. The multi-user model is called an information network with in-block memory (NiBM). It is shown that block-fading channels, channels with state known causally at the encoder, and relay networks with delays are NiBMs. A cut-set bound is developed for NiBMs that unifies, strengthens, and generalizes existing cut bounds for discrete memoryless networks. The bound gives new finite-letter capacity expressions for several classes of networks including point-to-point channels, and certain multiaccess, broadcast, and relay channels. Cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action-dependent state available causally at the encoder and for relays without delay. Finally, quantize-forward network coding is shown to achieve rates within an additive gap of the new cut-set bound for linear, additive, Gaussian noise channels, symmetric power constraints, and a multicast session.

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arXiv2014

Impact of Spectrum Sharing on the Efficiency of Faster-Than-Nyquist Signaling

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.

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arXiv2014

Effective Secrecy: Reliability, Confusion and Stealth

A security measure called effective security is defined that includes strong secrecy and stealth communication. Effective secrecy ensures that a message cannot be deciphered and that the presence of meaningful communication is hidden. To measure stealth we use resolvability and relate this to binary hypothesis testing. Results are developed for wire-tap channels and broadcast channels with confidential messages.

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arXiv2014

Capacity Bounds for a Class of Diamond Networks

A class of diamond networks are studied where the broadcast component is modelled by two independent bit-pipes. New upper and low bounds are derived on the capacity which improve previous bounds. The upper bound is in the form of a max-min problem, where the maximization is over a coding distribution and the minimization is over an auxiliary channel. The proof technique generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981), and Kang and Liu for the Gaussian diamond network (2011). The bounds are evaluated for a Gaussian multiple access channel (MAC) and the binary adder MAC, and the capacity is found for interesting ranges of the bit-pipe capacities.

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arXiv2013

Short Message Noisy Network Coding with a Decode-Forward Option

Short message noisy network coding (SNNC) differs from long message noisy network coding (LNNC) in that one transmits many short messages in blocks rather than using one long message with repetitive encoding. Several properties of SNNC are developed. First, SNNC with backward decoding achieves the same rates as SNNC with offset encoding and sliding window decoding for memoryless networks where each node transmits a multicast message. The rates are the same as LNNC with joint decoding. Second, SNNC enables early decoding if the channel quality happens to be good. This leads to mixed strategies that unify the advantages of decode-forward and noisy network coding. Third, the best decoders sometimes treat other nodes' signals as noise and an iterative method is given to find the set of nodes that a given node should treat as noise sources.

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