arXiv subjects

Gerhard Kramer

Publications and source records attributed to Gerhard Kramer.

At least 91 records · Page 5Linked to original sources

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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arXiv2013

Informational Divergence Approximations to Product Distributions

The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verdú on resolvability. The result also extends to cases where the source distribution is unknown but the entropy is known.

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arXiv2013

Multi-sample Receivers Increase 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 (AWGN). A discrete-time channel model is introduced that is based on a multi-sample receiver. Tight lower bounds on the information rates achieved by the multi-sample receiver are computed by means of numerical simulations. The results show that oversampling at the receiver is beneficial for both strong and weak phase noise at high signal-to-noise ratios. The results are compared with results obtained when using other discrete-time models.

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arXiv2013

Feasibility Conditions of Interference Alignment via Two Orthogonal Subcarriers

Conditions are derived on line-of-sight channels to ensure the feasibility of interference alignment. The conditions involve choosing only the spacing between two subcarriers of an orthogonal frequency division multiplexing (OFDM) scheme. The maximal degrees-of-freedom are achieved and even an upper bound on the sum-rate of interference alignment is approached arbitrarily closely.

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arXiv2013

On Wiener Phase Noise Channels at High Signal-to-Noise Ratio

Consider a waveform channel where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise (AWGN). 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 which, at high Signal-to-Noise Ratio (SNR), achieves a rate that grows logarithmically with the SNR if the number of samples per symbol grows with the square-root of the SNR. Moreover, the pre-log factor is at least 1/2 in this case.

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arXiv2012

On Noncoherent Fading Relay Channels at High Signal-to-Noise Ratio

The capacity of noncoherent 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.

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arXiv2012

A Two-Dimensional Signal Space for Intensity-Modulated Channels

A two-dimensional signal space for intensity- modulated channels is presented. Modulation formats using this signal space are designed to maximize the minimum distance between signal points while satisfying average and peak power constraints. The uncoded, high-signal-to-noise ratio, power and spectral efficiencies are compared to those of the best known formats. The new formats are simpler than existing subcarrier formats, and are superior if the bandwidth is measured as 90% in-band power. Existing subcarrier formats are better if the bandwidth is measured as 99% in-band power.

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arXiv2011

Interference Focusing for Simplified Optical Fiber Models with Dispersion

A discrete-time two-user interference channel model is developed that captures non-linear phenomena that arise in optical fiber communication employing wavelength-division multiplexing (WDM). The effect of non-linearity is that an amplitude variation on one carrier induces a phase variation on the other carrier. Moreover, the model captures the effect of group velocity mismatch that introduces memory in the channel. It is shown that both users can achieve the maximum pre-log factor of 1 simultaneously by using an interference focusing technique introduced in an earlier work.

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arXiv2011

Short-Message Quantize-Forward Network Coding

Recent work for single-relay channels shows that quantize-forward (QF) with long-message encoding achieves the same reliable rates as compress-forward (CF) with short-message encoding. It is shown that short-message QF with backward or pipelined (sliding-window) decoding also achieves the same rates. Similarly, for many relays and sources, short-message QF with backward decoding achieves the same rates as long-message QF. Several practical advantages of short-message encoding are pointed out, e.g., reduced delay and simpler modulation. Furthermore, short-message encoding lets relays use decode-forward (DF) if their channel quality is good, thereby enabling multiinput, multi-output (MIMO) gains that are not possible with long-message encoding. Finally, one may combine the advantages of long- and short-message encoding by hashing a long message to short messages.

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arXiv2011

Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.

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arXiv2010

Lossy Broadcasting in Two-Way Relay Networks with Common Reconstructions

The broadcast phase (downlink transmission) of the two-way relay network is studied in the source coding and joint source-channel coding settings. The rates needed for reliable communication are characterised for a number of special cases including: small distortions, deterministic distortion measures, and jointly Gaussian sources with quadratic distortion measures. The broadcast problem is also studied with common-reconstruction decoding constraints, and the rates needed for reliable communication are characterised for all discrete memoryless sources and per-letter distortion measures.

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arXiv2010

Capacity for Half-Duplex Line Networks with Two Sources

The focus is on noise-free half-duplex line networks with two sources where the first node and either the second node or the second-last node in the cascade act as sources. In both cases, we establish the capacity region of rates at which both sources can transmit independent information to a common sink. The achievability scheme presented for the first case is constructive while the achievability scheme for the second case is based on a random coding argument.

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arXiv2010

Interference Focusing for Mitigating Cross-Phase Modulation in a Simplified Optical Fiber Model

A memoryless interference network model is introduced that is based on non-linear phenomena observed when transmitting information over optical fiber using wavelength division multiplexing. The main characteristic of the model is that amplitude variations on one carrier wave are converted to phase variations on another carrier wave, i.e., the carriers interfere with each other through amplitude-to-phase conversion. 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. The technique requires neither channel time variations nor global channel state information. Generalizations to more than two carriers are outlined.

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arXiv2010

Analysis and Design of Binary Message-Passing Decoders

Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

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arXiv2009

MIMO Z-Interference Channels: Capacity Under Strong and Noisy Interference

The capacity regions of multiple-input multiple-output Gaussian Z-interference channels are established for the very strong interference and aligned strong interference cases. The sum-rate capacity of such channels is established under noisy interference. These results generalize known results for scalar Gaussian Z-interference channels.

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arXiv2009

Pipelined Encoding for Deterministic and Noisy Relay Networks

Recent coding strategies for deterministic and noisy relay networks are related to the pipelining of block Markov encoding. For deterministic networks, it is shown that pipelined encoding improves encoding delay, as opposed to end-to-end delay. For noisy networks, it is observed that decode-and-forward exhibits good rate scaling when the signal-to-noise ratio (SNR) increases.

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arXiv2009

Capacity Regions and Sum-Rate Capacities of Vector Gaussian Interference Channels

The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.

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arXiv2009

Noisy-interference Sum-rate Capacity of Parallel Gaussian Interference Channels

The sum-rate capacity of the parallel Gaussian interference channel is shown to be achieved by independent transmission across sub-channels and treating interference as noise in each sub-channel if the channel coefficients and power constraints satisfy a certain condition. The condition requires the interference to be weak, a situation commonly encountered in, e.g., digital subscriber line transmission. The optimal power allocation is characterized by using the concavity of sum-rate capacity as a function of the power constraints.

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