We focus on two-user Gaussian interference channels (ICs) with fast fading and study implementation of explicit all public and Han-Kobayashi (HK) coding schemes with low-density parity-check (LDPC) codes. Stability conditions for the coding schemes are derived, and a modified form of the EXIT chart analysis is proposed to estimate the decoding threshold of LDPC code ensembles. The proposed code design is employed in several examples and the obtained rate pairs are compared with the achievable rate region (ARR) boundaries demonstrating that rate pairs very close to the ARR boundaries are attained. Performance of finite block length codes are also studied through simulations of specific codes picked from the optimized LDPC code ensembles in order to verify the analysis.

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.

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.

We study the design of explicit and implementable codes for the two-user discrete memoryless interference channels (DMICs). We consider Han-Kobayashi (HK) type encoding where both public and private messages are used and propose coding techniques utilizing a serial concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. Since exact analytical treatment of the BCJR decoder for the inner trellis-based code appears infeasible, we analytically investigate the iterative decoding process in the asymptotic regime where the probability of decoding error tends to zero. Based on this approximate analysis, we derive a stability condition for this type of a concatenated coding scheme for the first time in the literature. Furthermore, we use an extrinsic information transfer analysis to design the outer LDPC code while fixing the inner NLTC, and utilize the derived stability condition to accelerate the design process and to avoid code ensembles that potentially produce high error floors. Via numerical examples, we demonstrate that our designed codes achieve rate pairs close the optimal boundary of the HK subregion, which cannot be obtained without the use of nonlinear codes. Also, we verify that the estimated thresholds of the designed codes via finite block length simulations and show that our designs significantly outperform the point-to-point optimal codes, hence demonstrating the need for designs specifically tailored for DMICs.

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.

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.

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.

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.

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.

In this paper, the authors propose a new method to construct a low complexity and general purpose 2D lattice structure for modeling of random fields. The algorithm for obtaining this structure by employing the auxiliary vertical and horizontal prediction error fields is outlined. It is shown that the proposed 2D lattice structure with a rectangular prediction support region can be used to simultaneously obtain all possible causal and noncausal 2D models.

In this letter, the RLS adaptive algorithm is considered in the system identification setting. The RLS algorithm is regularized using a general convex function of the system impulse response estimate. The normal equations corresponding to the convex regularized cost function are derived, and a recursive algorithm for the update of the tap estimates is established. We also introduce a closed-form expression for selecting the regularization parameter. With this selection of the regularization parameter, we show that the convex regularized RLS algorithm performs as well as, and possibly better than, the regular RLS when there is a constraint on the value of the convex function evaluated at the true weight vector. Simulations demonstrate the superiority of the convex regularized RLS with automatic parameter selection over regular RLS for the sparse system identification setting.