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Gerhard Kramer

Publications and source records attributed to Gerhard Kramer.

At least 37 records · Page 2Linked to original sources
arXiv2023

Successive Interference Cancellation for Bandlimited Channels with Direct Detection

The maximum information rates for bandlimited channels with direct detection are achieved with joint detection and decoding (JDD), but JDD is often too complex to implement. Two receiver structures are studied to reduce complexity: separate detection and decoding (SDD) and successive interference cancellation (SIC). For bipolar modulation, frequency-domain raised-cosine pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves rates close to those of JDD, thereby attaining significant energy gains over SDD and intensity modulation. Gibbs sampling further reduces the detector complexity and achieves rates close to those of the forward-backward algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high SNR. Simulations with polar codes, higher-order modulation, and multi-level coding confirm the predicted gains.

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arXiv2023

Stability of Bernstein's Theorem and Soft Doubling for Vector Gaussian Channels

The stability of Bernstein's characterization of Gaussian distributions is extended to vectors by utilizing characteristic functions. Stability is used to develop a soft doubling argument that establishes the optimality of Gaussian vectors for certain communications channels with additive Gaussian noise, including two-receiver broadcast channels. One novelty is that the argument does not require the existence of distributions that achieve capacity.

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arXiv2023

Information Rates for Channels with Fading, Side Information and Adaptive Codewords

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

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arXiv2023

Concatenated Forward Error Correction with KP4 and Single Parity Check Codes

Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation.

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arXiv2022

Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM

Downlink precoding is considered for multi-path multi-input single-output channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and data-aided channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.

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arXiv2022

Experiments on Bipolar Transmission with Direct Detection

Achievable information rates of bipolar 4- and 8-ary constellations are experimentally compared to those of intensity modulation (IM) when using an oversampled direct detection receiver. The bipolar constellations gain up to 1.8 dB over their IM counterparts.

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arXiv2022

Achievable Rates for Short-Reach Fiber-Optic Channels with Direct Detection

Spectrally efficient communication is studied for short-reach fiber-optic links with chromatic dispersion (CD) and receivers that employ direction-detection and oversampling. Achievable rates and symbol error probabilities are computed by using auxiliary channels that account for memory in the sampled symbol strings. Real-alphabet bipolar and complex-alphabet symmetric modulations are shown to achieve significant energy gains over classic intensity modulation. Moreover, frequency-domain raised-cosine (FD-RC) pulses outperform time-domain RC (TD-RC) pulses in terms of spectral efficiency for two scenarios. First, if one shares the spectrum with other users then inter-channel interference significantly reduces the TD-RC rates. Second, if there is a transmit filter to avoid interference then the detection complexity of FD-RC and TD-RC pulses is similar but FD-RC achieves higher rates.

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arXiv2021

Regular Perturbation and Achievable Rates of Space-Division Multiplexed Optical Channels

Regular perturbation is applied to space-division multiplexing (SDM) on optical fibers and motivates a correlated rotation-and-additive noise (CRAN) model. For S spatial modes, or 2S complex-alphabet channels, the model has 4S(S+1) hidden independent real Gauss-Markov processes, of which 2S model phase noise, 2S(2S-1) model spatial mode rotation, and 4S model additive noise. Achievable information rates of multi-carrier communication are computed by using particle filters. For S=2 spatial modes with strong coupling and a 1000 km link, joint processing of the spatial modes gains 0.5 bits/s/Hz/channel in rate and 1.4 dB in power with respect to separate processing of 2S complex-alphabet channels without considering CRAN.

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arXiv2021

Feedback Gains for Gaussian Massive Multiple-Access Channels

Feedback is shown to increase the sum-rate capacity of K-user Gaussian multiple-access channels by at most a factor of approximately 1.54, improving Thomas' doubling bound (1987). The new bound is the best possible in the sense that it can be approached as closely as desired for a massive number of users. Moreover, feedback provides unbounded power gain in K for a fixed transmit power per user.

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arXiv2021

Divergence Scaling for Distribution Matching

Distribution matchers for finite alphabets are shown to have informational divergences that grow logarithmically with the block length, generalizing a basic result for binary strings.

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arXiv2021

Mismatched Models to Lower Bound the Capacity of Dual-Polarization Optical Fiber Channels

Regular perturbation is applied to the Manakov equation and motivates a generalized correlated phase-and-additive noise model for wavelength-division multiplexing over dual-polarization optical fiber channels. The model includes three hidden Gauss-Markov processes: phase noise, polarization rotation, and additive noise. Particle filtering is used to compute lower bounds on the capacity of multi-carrier communication with frequency-dependent powers and delays. A gain of 0.17 bits/s/Hz/pol in spectral efficiency or 0.8 dB in power efficiency is achieved with respect to existing models at their peak data rate. Frequency-dependent delays also increase the spectral efficiency of single-polarization channels.

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arXiv2021

Polar-Coded Non-Coherent Communication

A polar-coded transmission (PCT) scheme with joint channel estimation and decoding is proposed for channels with unknown channel state information (CSI). The CSI is estimated via successive cancellation (SC) decoding and the constraints imposed by the frozen bits. SC list decoding with an outer code improves performance, including resolving a phase ambiguity when using quadrature phase-shift keying (QPSK) and Gray labeling. Simulations with 5G polar codes and QPSK show gains of up to $2$~dB at a frame error rate (FER) of $10^{-4}$ over pilot-assisted transmission for various non-coherent models. Moreover, PCT performs within a few tenths of a dB to a coherent receiver with perfect CSI. For Rayleigh block-fading channels, PCT outperforms an FER upper bound based on random coding and within one dB of a lower bound.

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arXiv2021

On Skew Convolutional and Trellis Codes

Two new classes of skew codes over a finite field $\F$ are proposed, called skew convolutional codes and skew trellis codes. These two classes are defined by, respectively, left or right sub-modules over the skew fields of fractions of skew polynomials over $\F$. The skew convolutional codes can be represented as periodic time-varying ordinary convolutional codes. The skew trellis codes are in general nonlinear over $\F$. Every code from both classes has a code trellis and can be decoded by Viterbi or BCJR algorithms.

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arXiv2020

Invertible Low-Divergence Coding

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best one-to-one encoders have I-divergences that grow logarithmically with the block length in general. To improve performance, an encoder is proposed that has an invertible one-to-many mapping and a low-rate resolution code. Two algorithms are developed to design the mapping by assigning strings in either a most-likely first or least-likely first order. Both algorithms give information rates approaching the entropy of the target distribution with exponentially decreasing I-divergence and with vanishing resolution rate in the block length.

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arXiv2020

Mismatched Models to Lower Bound the Capacity of Optical Fiber Channels

A correlated phase-and-additive-noise (CPAN) mismatched model is developed for wavelength division multiplexing over optical fiber channels governed by the nonlinear Schrödinger equation. Both the phase and additive noise processes of the CPAN model are Gauss-Markov whereas previous work uses Wiener phase noise and white additive noise. Second order statistics are derived and lower bounds on the capacity are computed by simulations. The CPAN model characterizes nonlinearities better than existing models in the sense that it achieves better information rates. For example, the model gains 0.35 dB in power at the peak data rate when using a single carrier per wavelength. For multiple carriers per wavelength, the model combined with frequency-dependent power allocation gains 0.14 bits/s/Hz in rate and 0.8 dB in power at the peak data rate.

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arXiv2020

Coding for Positive Rate in the Source Model Key Agreement Problem

A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of Rényi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information, and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables, which is of independent interest.

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arXiv2020

Stealth Communication with Vanishing Power over Binary Symmetric Channels

A framework for stealth communication with vanishing power (VP) is presented by studying binary symmetric channels. Coding theorems are proved by modifying Gallager's error exponents for VP and by applying resolvability exponents. The analysis unifies and generalizes existing rate bounds for covert and stealth communication.

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