Related papers: Iterative Soft Input Soft Output Decoding of Reed-…

We consider spatially coupled low-density parity-check (SC-LDPC) codes within a non-orthogonal interleave division multiple access (IDMA) scheme to avoid cumbersome degree profile matching of the LDPC code components to the iterative…

An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…

Proximal gradient algorithms (PGA), while foundational for inverse problems like image reconstruction, often yield unstable convergence and suboptimal solutions by violating the critical non-negativity constraint. We identify the gradient…

A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC)…

We derive the Wu list-decoding algorithm for Generalised Reed-Solomon (GRS) codes by using Gr\"obner bases over modules and the Euclidean algorithm (EA) as the initial algorithm instead of the Berlekamp-Massey algorithm (BMA). We present a…

We propose a novel soft-aided low-complexity decoder for product codes based on dynamic reliability scores and error-and-erasure decoding. We observe coding gains of up to 1.2 dB compared to conventional hard-decision decoders.

Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. We check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations to find the probability…

In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for…

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

In this paper, we study a concatenate coding scheme based on sparse regression code (SPARC) and tree code for unsourced random access in massive multiple-input and multiple-output systems. Our focus is concentrated on efficient decoding for…

Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…

The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…

Decoding a Reed-Solomon code can be modeled by a bilinear system which can be solved by Gr\"obner basis techniques. We will show that in this particular case, these techniques are much more efficient than for generic bilinear systems with…

Sparse code multiple access (SCMA) is one of the most promising methods among all the non-orthogonal multiple access techniques in the future 5G communication. Compared with some other non-orthogonal multiple access techniques such as low…

Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, termed "distributed arithmetic coding", which exploits the fact that arithmetic codes are good…

This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…