@article{Bravo-Santos2013,
title = {Polar Codes for Gaussian Degraded Relay Channels},
author = {Ángel M Bravo-Santos},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6412681},
issn = {1089-7798},
year = {2013},
date = {2013-01-01},
journal = {IEEE Communications Letters},
volume = {17},
number = {2},
pages = {365--368},
publisher = {IEEE},
abstract = {In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.},
keywords = {channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors},
pubstate = {published},
tppubtype = {article}
}

In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.

@inproceedings{Zhong2012a,
title = {Efficient Gaussian Inference Algorithms for Phase Imaging},
author = {Jingshan Zhong and Justin Dauwels and Manuel A Vazquez and Laura Waller},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6287959},
issn = {1520-6149},
year = {2012},
date = {2012-01-01},
booktitle = {2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages = {617--620},
publisher = {IEEE},
address = {Kyoto},
abstract = {Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images.},
keywords = {biomedical optical imaging, complex optical field, computational complexity, defocus distances, Fourier domain, Gaussian inference algorithms, image sequences, inference mechanisms, intensity image sequence, iterative Kalman smoothing, iterative methods, Kalman filter, Kalman filters, Kalman recursions, linear model, Manganese, Mathematical model, medical image processing, Noise, noisy intensity image, nonlinear observation model, Optical imaging, Optical sensors, Phase imaging, phase inference algorithms, smoothing methods},
pubstate = {published},
tppubtype = {inproceedings}
}

Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images.