Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA)

We propose an algorithm for identifying vertices from three dimensional (3D) meshes that are most important for a geometric shape creation. Extracting such a set of vertices from a 3D mesh is important in applications such as digital watermarking, but also as a component of optimization and triangulation. In the first step, the Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA) estimates precisely the local curvature, and most important topological features of mesh geometry. Using the vertex geometric importance ranking, the algorithm traces and extracts a vector of vertices, ordered by decreasing index of importance.Comment: Accepted for publishing and Copyright transfered to Advances in Electrical and Computer Engineering, November 23th 201

LDPC Codes Which Can Correct Three Errors Under Iterative Decoding

In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results.Comment: 5 pages, 3 figures, submitted to IEEE Information Theory Workshop (ITW), 200

Analysis and Design of Finite Alphabet Iterative Decoders Robust to Faulty Hardware

This paper addresses the problem of designing LDPC decoders robust to transient errors introduced by a faulty hardware. We assume that the faulty hardware introduces errors during the message passing updates and we propose a general framework for the definition of the message update faulty functions. Within this framework, we define symmetry conditions for the faulty functions, and derive two simple error models used in the analysis. With this analysis, we propose a new interpretation of the functional Density Evolution threshold previously introduced, and show its limitations in case of highly unreliable hardware. However, we show that under restricted decoder noise conditions, the functional threshold can be used to predict the convergence behavior of FAIDs under faulty hardware. In particular, we reveal the existence of robust and non-robust FAIDs and propose a framework for the design of robust decoders. We finally illustrate robust and non-robust decoders behaviors of finite length codes using Monte Carlo simulations.Comment: 30 pages, submitted to IEEE Transactions on Communication

Two-Bit Bit Flipping Decoding of LDPC Codes

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the min-sum algorithm at much lower complexity. Concatenation of two-bit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.Comment: 6 pages. Submitted to IEEE International Symposium on Information Theory 201