A. Korhan Tanc

Design of LDPC Codes for Two-Way Relay Systems with Physical-Layer Network Coding

This letter presents low-density parity-check (LDPC) code design for two-way relay (TWR) systems employing physical-layer network coding (PLNC). We focus on relay decoding, and propose an empirical density evolution method for estimating the decoding threshold of the LDPC code ensemble. We utilize the proposed method in conjunction with a random walk optimization procedure to obtain good LDPC code degree distributions. Numerical results demonstrate that the specifically designed LDPC codes can attain improvements of about 0.3 dB over off-the-shelf LDPC codes (designed for point-to-point additive white Gaussian noise channels), i.e., it is new code designs are essential to optimize the performance of TWR systems.

Implementing the Han-Kobayashi Scheme Using Low Density Parity Check Codes Over Gaussian Interference Channels

We focus on Gaussian interference channels (GICs) and study the Han-Kobayashi coding strategy for the two-user case with the objective of designing implementable (explicit) channel codes. Specifically, low-density parity-check codes are adopted for use over the channel, their benefits are studied, and suitable codes are designed. Iterative joint decoding is used at the receivers, where independent and identically distributed channel adapters are used to prove that log-likelihood-ratios exchanged among the nodes of the Tanner graph enjoy symmetry when BPSK or QPSK with Gray coding is employed. This property is exploited in the proposed code optimization algorithm adopting a random perturbation technique. Code optimization and convergence threshold computations are carried out for different GICs employing finite constellations by tracking the average mutual information. Furthermore, stability conditions for the admissible degree distributions under strong and weak interference levels are determined. Via examples, it is observed that the optimized codes using BPSK or QPSK with Gray coding operate close to the capacity boundary for strong interference. For the case of weak interference, it is shown that nontrivial rate pairs are achievable via the newly designed codes, which are not possible by single user codes with time sharing. Performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions, where, for one instance, the results are compared with those of some structured designs.

LDPC Code Design for the Two-User Gaussian Multiple Access Channel

We study code design for two-user Gaussian multiple access channels (GMACs) under fixed channel gains and under quasi-static fading. We employ low-density parity-check (LDPC) codes with BPSK modulation and utilize an iterative joint decoder. Adopting a belief propagation (BP) algorithm, we derive the PDF of the log-likelihood-ratios (LLRs) fed to the component LDPC decoders. Via examples, it is illustrated that the characterized PDF resembles a Gaussian mixture (GM) distribution, which is exploited in predicting the decoding performance of LDPC codes over GMACs. Based on the GM assumption, we propose variants of existing analysis methods, named modified density evolution (DE) and modified extrinsic information transfer (EXIT). We derive a stability condition on the degree distributions of the LDPC code ensembles and utilize it in the code optimization. Under fixed channel gains, the newly optimized codes are shown to perform close to the capacity region boundary outperforming the existing designs and the off-the-shelf point-to-point (P2P) codes. Under quasi-static fading, optimized codes exhibit consistent improvements upon the P2P codes as well. Finite block length simulations of specific codes picked from the designed ensembles are also carried out and it is shown that optimized codes perform close to the outage limits.

Transform learning MRI with global wavelet regularization

Sparse regularization of the reconstructed image in a transform domain has led to state of the art algorithms for magnetic resonance imaging (MRI) reconstruction. Recently, new methods have been proposed which perform sparse regularization on patches extracted from the image. These patch level regularization methods utilize synthesis dictionaries or analysis transforms learned from the patch sets. In this work we jointly enforce a global wavelet domain sparsity constraint together with a patch level, learned analysis sparsity prior. Simulations indicate that this joint regularization culminates in MRI reconstruction performance exceeding the performance of methods which apply either of these terms alone.

Sparsity regularized recursive total least-squares

This paper introduces a new family of recursive total least-squares (RTLS) algorithms for identification of sparse systems with noisy input vector. We regularize the RTLS cost function by adding a sparsifying term and utilize subgradient analysis. We present ? 1 norm and approximate ? 0 norm regularized RTLS algorithms, and we elaborate on the selection of algorithm parameters. Simulation results show that the presented algorithms outperform the existing RLS and RTLS algorithms significantly in terms of mean square deviation (MSD). Furthermore, we demonstrate the virtues of our automatic selection for regularization parameter when ? 1 norm regularization is applied.

LDPC code design for binary-input binary-output Z interference channels

In this paper, we explore code optimization for two-user discrete memoryless interference channels (DMICs) wherein the inputs and outputs of the channel are from a finite alphabet. For encoding, we employ irregular low-density parity-check (LDPC) codes combined with non-linear trellis codes (NLTCs) to satisfy the desired distribution of zeros and ones in the transmitted codewords. At the receiver sides, we adopt BCJR algorithm based decoders to compute the symbol-by-symbol log-likelihood ratios (LLRs) of LDPC coded bits to be fed to message passing decoders. As a specific example, we consider the binary-input binary-output Z interference channel (BIBO ZIC) for which the transmitted and received signals are binary and one of the receivers is interference free. For a specific example of a BIBO ZIC, we examine the Han-Kobayashi inner bound on the achievable rate pairs and show that with a simple scheme of sending the messages as private one can achieve the sum-capacity of the channel. We also perform code optimization and demonstrate that the jointly optimized codes outperform the optimal single user codes with time sharing.

Denoising AMP for MRI Reconstruction: BM3D-AMP-MRI

There is a recurrent idea being promoted in the recent literature on iterative solvers for imaging problems, the idea being the use of an actual denoising step in each iteration. We give a brief review of some algorithms from the literature which utilize this idea, and we broadly label these algorithms as Iterative Denoising Regularization (IDR) algorithms. We extend the Denoising Approximate Message Passing (D-AMP) algorithm from this list to the magnetic resonance imaging (MRI) reconstruction problem. We utilize Block Matching 3D (BM3D) as the denoiser of choice for the introduced MRI reconstruction algorithm. The application of the denoiser for complex-valued data necessitates a special handling of the denoiser. The use of the adaptive and image-dependent BM3D image model prior together with D-AMP results in highly competitive MRI reconstruction performance.

Short block length trellis-based codes for interference channels

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis-based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error-rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi-static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

Short block length code design for interference channels

We focus on short block length code design for Gaussian interference channels (GICs) using trellis-based codes. We employ two different decoding techniques at the receiver side, namely, joint maximum likelihood (JML) decoding and single user (SU) minimum distance decoding. For different interference levels (strong and weak) and decoding strategies, we derive error-rate bounds to evaluate the code performance. We utilize the derived bounds in code design and provide several numerical examples for both strong and weak interference cases. We show that under the JML decoding, the newly designed codes offer significant improvements over the alternatives of optimal point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check (LDPC) codes with the same block lengths.

MRI reconstruction with analysis sparse regularization under impulsive noise

We will be considering analysis sparsity based regularization for Magnetic Resonance Imaging reconstruction. The analysis sparsity regularization is based on the recently introduced Transform Learning framework, which has reduced complexity regarding other sparse regularization methods. We will formulate a variational reconstruction problem which utilizes the analysis sparsity regularization together with an ℓ1 norm based data fidelity term. The use of the non-smooth data fidelity term results in robustness against outliers and impulsive noise in the observed data. The resulting algorithm with the ℓ1 observation fidelity showcases enhanced performance under impulsive observation noise when compared to a similar algorithm utilizing the conventional quadratic error term.