arXiv subjects

Gerald Matz

Publications and source records attributed to Gerald Matz.

17 recordsLinked to original sources

arXiv2017

Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing

Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple vectors with identical support and accounts for correlations in the signal of interest and in the noise. In this paper, we show how to reduce the complexity of vector BAMP via a simple joint decorrelation diagonalization) transform of the signal and noise vectors, which also facilitates the subsequent performance analysis. We prove that BAMP and the corresponding state evolution (SE) are equivariant with respect to the joint decorrelation transform and preserve diagonality of the residual noise covariance for the Bernoulli-Gauss (BG) prior. We use these results to analyze the dynamics and the mean squared error (MSE) performance of BAMP via the replica method, and thereby understand the impact of signal correlation and number of jointly sparse signals.

cs.IT↗

arXiv2017

Sampling and Reconstruction in Distinct Subspaces Using Oblique Projections

We study reconstruction operators on a Hilbert space that are exact on a given reconstruction subspace. Among those the reconstruction operator obtained by the least squares fit has the smallest operator norm, and therefore is most stable with respect to noisy measurements. We then construct the operator with the smallest possible quasi-optimality constant, which is the most stable with respect to a systematic error appearing before the sampling process (model uncertainty). We describe how to vary continuously between the two reconstruction methods, so that we can trade stability for quasi-optimality. As an application we study the reconstruction of a compactly supported function from nonuniform samples of its Fourier transform.

math.NA↗

arXiv2017

A 588 Gbps LDPC Decoder Based on Finite-Alphabet Message Passing

An ultra-high throughput low-density parity check (LDPC) decoder with an unrolled full-parallel architecture is proposed, which achieves the highest decoding throughput compared to previously reported LDPC decoders in the literature. The decoder benefits from a serial message-transfer approach between the decoding stages to alleviate the well-known routing congestion problem in parallel LDPC decoders. Furthermore, a finite-alphabet message passing algorithm is employed to replace the variable node update rule of the standard min-sum decoder with look-up tables, which are designed in a way that maximizes the mutual information between decoding messages. The proposed algorithm results in an architecture with reduced bit-width messages, leading to a significantly higher decoding throughput and to a lower area as compared to a min-sum decoder when serial message-transfer is used. The architecture is placed and routed for the standard min-sum reference decoder and for the proposed finite-alphabet decoder using a custom pseudo-hierarchical backend design strategy to further alleviate routing congestions and to handle the large design. Post-layout results show that the finite-alphabet decoder with the serial message-transfer architecture achieves a throughput as large as 588 Gbps with an area of 16.2 mm$^2$ and dissipates an average power of 22.7 pJ per decoded bit in a 28 nm FD-SOI library. Compared to the reference min-sum decoder, this corresponds to 3.1 times smaller area and 2 times better energy efficiency.

cs.AR↗

arXiv2016

Dictator Functions Maximize Mutual Information

Let $(\mathbf X, \mathbf Y)$ denote $n$ independent, identically distributed copies of two arbitrarily correlated Rademacher random variables $(X, Y)$. We prove that the inequality $I(f(\mathbf X); g(\mathbf Y)) \le I(X; Y)$ holds for any two Boolean functions: $f,g \colon \{-1,1\}^n \to \{-1,1\}$ ($I(\cdot; \cdot)$ denotes mutual information). We further show that equality in general is achieved only by the dictator functions $f(\mathbf x)=\pm g(\mathbf x)=\pm x_i$, $i \in \{1,2,\dots,n\}$.

cs.IT↗

arXiv2016

Distributed Information-Theoretic Clustering

We study a novel multi-terminal source coding setup motivated by the biclustering problem. Two separate encoders observe two i.i.d. sequences $X^n$ and $Y^n$, respectively. The goal is to find rate-limited encodings $f(x^n)$ and $g(z^n)$ that maximize the mutual information $I(f(X^n); g(Y^n))/n$. We discuss connections of this problem with hypothesis testing against independence, pattern recognition, and the information bottleneck method. Improving previous cardinality bounds for the inner and outer bounds allows us to thoroughly study the special case of a binary symmetric source and to quantify the gap between the inner and the outer bound in this special case. Furthermore, we investigate a multiple description (MD) extension of the Chief Operating Officer (CEO) problem with mutual information constraint. Surprisingly, this MD-CEO problem permits a tight single-letter characterization of the achievable region.

cs.IT↗

arXiv2015

Quantized Message Passing for LDPC Codes

We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic criterion. We show that even with message resolutions as low as 3 bits, the proposed algorithm can achieve better error rates than a floating-point min-sum decoder. Moreover, we study in detail the effect of different decoder design parameters, like the design SNR and the LUT tree structure on the performance of our decoder, and we propose some complexity reduction techniques, such as LUT re-use and message alphabet downsizing.

cs.IT↗

arXiv2015

An Approach to Complex Bayesian-optimal Approximate Message Passing

In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and imaginary parts of the unknown. By introducing a latent activity variable, BOSSAMP separates the tasks of activity detection and value estimation to overcome the problem of detecting different supports in the real and imaginary parts. We complement the recovery algorithm by two novel support detection schemes that utilize the updated auxiliary variables of BOSSAMP. Simulations show the superiority of our proposed method against approximate message passing (AMP) and its Bayesian-optimal sibling (BAMP), both in mean squared error and support detection performance.

cs.IT↗

arXiv2015

A Fully-Unrolled LDPC Decoder Based on Quantized Message Passing

In this paper, we propose a finite alphabet message passing algorithm for LDPC codes that replaces the standard min-sum variable node update rule by a mapping based on generic look-up tables. This mapping is designed in a way that maximizes the mutual information between the decoder messages and the codeword bits. We show that our decoder can deliver the same error rate performance as the conventional decoder with a much smaller message bit-width. Finally, we use the proposed algorithm to design a fully unrolled LDPC decoder hardware architecture.

cs.IT↗

arXiv2014

Spatially-Coupled LDPC Codes for Decode-and-Forward Relaying of Two Correlated Sources over the BEC

We present a decode-and-forward transmission scheme based on spatially-coupled low-density parity-check (SC-LDPC) codes for a network consisting of two (possibly correlated) sources, one relay, and one destination. The links between the nodes are modeled as binary erasure channels. Joint source-channel coding with joint channel decoding is used to exploit the correlation. The relay performs network coding. We derive analytical bounds on the achievable rates for the binary erasure time-division multiple-access relay channel with correlated sources. We then design bilayer SC-LDPC codes and analyze their asymptotic performance for this scenario. We prove analytically that the proposed coding scheme achieves the theoretical limit for symmetric channel conditions and uncorrelated sources. Using density evolution, we furthermore demonstrate that our scheme approaches the theoretical limit also for non-symmetric channel conditions and when the sources are correlated, and we observe the threshold saturation effect that is typical for spatially-coupled systems. Finally, we give simulation results for large block lengths, which validate the DE analysis.

cs.IT↗

arXiv2013

Interference Alignment via Message-Passing

We introduce an iterative solution to the problem of interference alignment (IA) over MIMO channels based on a message-passing formulation. We propose a parameterization of the messages that enables the computation of IA precoders by a min-sum algorithm over continuous variable spaces -- under this parameterization, suitable approximations of the messages can be computed in closed-form. We show that the iterative leakage minimization algorithm of Cadambe et al. is a special case of our message-passing algorithm, obtained for a particular schedule. Finally, we show that the proposed algorithm compares favorably to iterative leakage minimization in terms of convergence speed, and discuss a distributed implementation.

cs.IT↗

arXiv2013

Energy-Neutral Source-Channel Coding with Battery and Memory Size Constraints

We study energy management policies for the compression and transmission of source data collected by an energy-harvesting sensor node with a finite energy buffer (e.g., rechargeable battery) and a finite data buffer (memory) between source encoder and channel encoder. The sensor node can adapt the source and channel coding rates depending on the observation and channel states. In such a system, the absence of precise information about the amount of energy available in the future is a key challenge. We provide analytical bounds and scaling laws for the average distortion that depend on the size of the energy and data buffers. We furthermore design a resource allocation policy that achieves almost optimal distortion scaling. Our results demonstrate that the energy leakage of state of art energy management policies can be avoided by jointly controlling the source and channel coding rates.

cs.IT↗

arXiv2013

Time-Frequency Foundations of Communications

In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book chapters on the topic are available (see, e.g., [2]-[4] and references therein), the goal of this paper is to present the fundamental aspects in a coherent and easily accessible manner. Specifically, we establish the role of TF methods in communications across a range of subject areas including TF dispersive channels, orthogonal frequency division multiplexing (OFDM), information-theoretic limits, and system identification and channel estimation. Furthermore, we present fundamental results that are stated in the literature for the continuous-time case in simple linear algebra terms.

cs.IT↗

arXiv2009

Outage Behavior of Discrete Memoryless Channels (DMCs) Under Channel Estimation Errors

Communication systems are usually designed by assuming perfect channel state information (CSI). However, in many practical scenarios, only a noisy estimate of the channel is available, which may strongly differ from the true channel. This imperfect CSI scenario is addressed by introducing the notion of estimation-induced outage (EIO) capacity. We derive a single-letter characterization of the maximal EIO rate and prove an associated coding theorem and its strong converse for discrete memoryless channels (DMCs). The transmitter and the receiver rely on the channel estimate and the statistics of the estimate to construct codes that guarantee reliable communication with a certain outage probability. This ensures that in the non-outage case the transmission meets the target rate with small error probability, irrespective of the quality of the channel estimate. Applications of the EIO capacity to a single-antenna (non-ergodic) Ricean fading channel are considered. The EIO capacity for this case is compared to the EIO rates of a communication system in which the receiver decodes by using a mismatched ML decoder. The effects of rate-limited feedback to provide the transmitter with quantized CSI are also investigated.

cs.IT↗

arXiv2009

Quantization for Soft-Output Demodulators in Bit-Interleaved Coded Modulation Systems

We study quantization of log-likelihood ratios (LLR) in bit-interleaved coded modulation (BICM) systems in terms of an equivalent discrete channel. We propose to design the quantizer such that the quantizer outputs become equiprobable. We investigate semi-analytically and numerically the ergodic and outage capacity over single- and multiple-antenna channels for different quantizers. Finally, we show bit error rate simulations for BICM systems with LLR quantization using a rate 1/2 low-density parity-check code.

cs.IT↗

arXiv2009

Performance Assessment of MIMO-BICM Demodulators based on System Capacity

We provide a comprehensive performance comparison of soft-output and hard-output demodulators in the context of non-iterative multiple-input multiple-output bit-interleaved coded modulation (MIMO-BICM). Coded bit error rate (BER), widely used in literature for demodulator comparison, has the drawback of depending strongly on the error correcting code being used. This motivates us to propose a code-independent performance measure in terms of system capacity, i.e., mutual information of the equivalent modulation channel that comprises modulator, wireless channel, and demodulator. We present extensive numerical results for ergodic and quasi-static fading channels under perfect and imperfect channel state information. These results reveal that the performance ranking of MIMO demodulators is rate-dependent. Furthermore, they provide new insights regarding MIMO-BICM system design, i.e., the choice of antenna configuration, symbol constellation, and demodulator for a given target rate.

cs.IT↗

arXiv2008

Perturbation-based Distributed Beamforming for Wireless Relay Networks

This paper deals with distributed beamforming techniques for wireless networks with half-duplex amplify-and-forward relays. Existing schemes optimize the beamforming weights based on the assumption that channel state information (CSI) is available at the relays. We propose to use adaptive beamforming based on deterministic perturbations and limited feedback (1-bit) from the destination to the relays in order to avoid CSI at the relays. Two scalable perturbation schemes are considered and practical implementation aspects are addressed. Simulation results confirm that the proposed techniques closely approach optimum performance and have satisfactory tracking properties in time-varying environments.

cs.IT↗

arXiv2007

Outage Behavior of Discrete Memoryless Channels Under Channel Estimation Errors

Classically, communication systems are designed assuming perfect channel state information at the receiver and/or transmitter. However, in many practical situations, only an estimate of the channel is available that differs from the true channel. We address this channel mismatch scenario by using the notion of estimation-induced outage capacity, for which we provide an associated coding theorem and its strong converse, assuming a discrete memoryless channel. We illustrate our ideas via numerical simulations for transmissions over Ricean fading channels under a quality of service (QoS) constraint using rate-limited feedback channel and maximum likelihood (ML) channel estimation. Our results provide intuitive insights on the impact of the channel estimate and the channel characteristics (SNR, Ricean K-factor, training sequence length, feedback rate, etc.) on the mean outage capacity.

cs.IT↗