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1. Mutual Information as a Function of Matrix SNR for Linear Gaussian Channels

   Reeves, Galen; Pfister, Henry D.; Dytso, Alex (July 2018, IEEE International Symposium on Information Theory)

   This paper focuses on the mutual information and minimum mean-squared error (MMSE) as a function a matrix- valued signal-to-noise ratio (SNR) for a linear Gaussian channel with arbitrary input distribution. As shown by Lamarca, the mutual-information is a concave function of a positive semi- definite matrix, which we call the matrix SNR. This implies that the mapping from the matrix SNR to the MMSE matrix is decreasing monotone. Building upon these functional properties, we start to construct a unifying framework that provides a bridge between classical information-theoretic inequalities, such as the entropy power inequality, and interpolation techniques used in statistical physics and random matrix theory. This framework provides new insight into the structure of phase transitions in coding theory and compressed sensing. In particular, it is shown that the parallel combination of linear channels with freely-independent matrices can be characterized succinctly via free convolution. 

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2. Block Soft Decision Feedback Turbo Equalization for Orthogonal Signal-Division Multiplexing Underwater Acoustic Communications

   https://doi.org/10.23919/OCEANS40490.2019.8962719  

   Qin, Xiangzhao; Qu, Fengzhong; Zheng, Y. Rosa (October 2019, OCEANS 2019 MTS/IEEE SEATTLE)

   Orthogonal signal-division multiplexing (OSDM) is one of the generalized modulation schemes that bring the gap between orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE). By performing encoding upon subvectors of each interleaved block, it enjoys a flexible resource management with low peak-to-average power ratio (PAPR). Meanwhile, the OSDM induces the intervector interference (IVI) inherently, which requires a more powerful equalizer. By deriving the input and output system model, this paper proposes a time domain soft decision feedback equalizer (SDFE) on per vector equalization with successful soft interference cancellation (SSIC). In addition, this paper takes the whole OSDM block to perform the channel encoding rather than on each vector of the OSDM. Simulation and experimental results demonstrate that the proposed SDFE with SSIC structure outperforms the conventional minimum mean square error (MMSE) equalizer and the block encoding (BE) scheme outperforms the vector encoding (VE) scheme, because theoretically the longer the encoded bit stream is, the more stable and more confident the maximum a posteriori probability (MAP) decoder will be. 

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3. Block Soft Decision Feedback Turbo Equalization for Orthogonal Signal-Division Multiplexing Underwater Acoustic Communications

   Xiangzhao Qin, Fengzhong Qu (September 2019, MTS/IEEE Oceans)

   Orthogonal signal-division multiplexing (OSDM) is one of the generalized modulation schemes that bring the gap between orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE). By performing encoding upon subvectors of each interleaved block, it enjoys a flexible resource management with low peakto- average power ratio (PAPR). Meanwhile, the OSDM induces the intervector interference (IVI) inherently, which requires a more powerful equalizer. By deriving the input and output system model, this paper proposes a time domain soft decision feedback equalizer (SDFE) on per vector equalization with successful soft interference cancellation (SSIC). In addition, this paper takes the whole OSDM block to perform the channel encoding rather than on each vector of the OSDM. Simulation and experimental results demonstrate that the proposed SDFE with SSIC structure outperforms the conventional minimum mean square error (MMSE) equalizer and the block encoding (BE) scheme outperforms the vector encoding (VE) scheme, because theoretically the longer the encoded bit stream is, the more stable and more confident the maximum a posteriori probability (MAP) decoder will be. 

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4. Optimally-tuned nonparametric linear equalization for massive MU-MIMO systems

   https://doi.org/10.1109/ISIT.2017.8006903  

   Ghods, Ramina; Jeon, Charles; Mirza, Gulnar; Maleki, Arian; Studer, Christoph (June 2017, IEEE International Symposium on Information Theory (ISIT))

   This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum mean-square error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show that NOPE achieves the same performance as that of the L-MMSE equalizer in the large-antenna limit, and we demonstrate its efficacy in realistic, finite-dimensional systems. From a practical perspective, NOPE is computationally efficient and avoids dedicated training that is typically required for parameter estimation. 

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5. All-or-Nothing Phenomena: From Single-Letter to High Dimensions

   https://doi.org/10.1109/CAMSAP45676.2019.9022473  

   Reeves, Galen; Xu, Jiaming; Zadik, Ilias (December 2019, 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP))

   We consider the problem of estimating a $$p$$ -dimensional vector $$\beta$$ from $$n$$ observations $$Y=X\beta+W$$ , where $$\beta_{j}\mathop{\sim}^{\mathrm{i.i.d}.}\pi$$ for a real-valued distribution $$\pi$$ with zero mean and unit variance’ $$X_{ij}\mathop{\sim}^{\mathrm{i.i.d}.}\mathcal{N}(0,1)$$ , and $$W_{i}\mathop{\sim}^{\mathrm{i.i.d}.}\mathcal{N}(0,\ \sigma^{2})$$ . In the asymptotic regime where $$n/p\rightarrow\delta$$ and $$p/\sigma^{2}\rightarrow$$ snr for two fixed constants $$\delta,\ \mathsf{snr}\in(0,\ \infty)$$ as $$p\rightarrow\infty$$ , the limiting (normalized) minimum mean-squared error (MMSE) has been characterized by a single-letter (additive Gaussian scalar) channel. In this paper, we show that if the MMSE function of the single-letter channel converges to a step function, then the limiting MMSE of estimating $$\beta$$ converges to a step function which jumps from 1 to 0 at a critical threshold. Moreover, we establish that the limiting mean-squared error of the (MSE-optimal) approximate message passing algorithm also converges to a step function with a larger threshold, providing evidence for the presence of a computational-statistical gap between the two thresholds. 

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