Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and $C$-symmetric, and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Also, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the minimum distance $d_{\rm min}$ and/or the stopping distance $h_{\rm min}$ is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both the $d_{\rm min}$ and the $h_{\rm min}$, and 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication

VLSI Implementation of LDPC Codes

Coded modulation is a bandwidth-efficient scheme that integrates channel coding and modulation into one single entity to improve performance with the same spectral efficiency compared to uncoded modulation. Low-density parity-check (LDPC) codes are the most powerful error correction codes (ECCs) and approach the Shannon limit, while having a relatively low decoding complexity. Therefore, the idea of combining LDPC codes and bandwidth-efficient modulation has been widely considered. In this thesis we will consider LDPC codes as an Error Correcting Code and study it’s performance with BPSK system in AWGN environment and study different kind of characteristics of the system. LDPC system consists of two parts Encoder and Decoder. LDPC encoder encodes the data and sends it to the channel. The LDPC encoding performance depends on Parity matrix behavior which has characteristics like Rate, Girth, Size and Regularity. We will study the performance characteristics according to these characteristics and find performance variation in term of SNR performance. The decoder receives the data from the channel and decodes it. LDPC decoder has characteristics like time of iteration in addition all parity check matrix characteristics. We will also study the performance according to these characteristics. The main objective of this thesis is to implement LDPC system in FPGA. LDPC Encoder is implementation is done using Shift-Register based design to reduce complexity. LDPC decoder is used to decode the information received from the channel and decode the message to find the information. In the decoder we have used Modified Sum Product (MSP) Algorithm to decode, In the MSP we have used some quantized values to decode the data using Look Up Table (LUT) approximation. Finally we compare the SNR performance of theoretical LDPC system’s with FPGA implemented LDPC system’s performance

Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning

The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text overlap with arXiv:2109.08184 by other author

Optimization and Applications of Modern Wireless Networks and Symmetry

Due to the future demands of wireless communications, this book focuses on channel coding, multi-access, network protocol, and the related techniques for IoT/5G. Channel coding is widely used to enhance reliability and spectral efficiency. In particular, low-density parity check (LDPC) codes and polar codes are optimized for next wireless standard. Moreover, advanced network protocol is developed to improve wireless throughput. This invokes a great deal of attention on modern communications

Recent Results on the Implementation of a Burst Error and Burst Erasure Channel Emulator Using an FPGA Architecture

The behaviour of a transmission channel may be simulated using the performance abilities of current generation multiprocessing hardware, namely, a multicore Central Processing Unit (CPU), a general purpose Graphics Processing Unit (GPU), or a Field Programmable Gate Array (FPGA). These were investigated by Cullinan et al. in a recent paper (published in 2012) where these three devices capabilities were compared to determine which device would be best suited towards which specific task. In particular, it was shown that, for the application which is objective of our work (i.e., for a transmission channel simulation), the FPGA is 26.67 times faster than the GPU and 10.76 times faster than the CPU. Motivated by these results, in this paper we propose and present a direct hardware emulation. In particular, a Cyclone II FPGA architecture is implemented to simulate a burst error channel behaviour, in which errors are clustered together, and a burst erasure channel behaviour, in which the erasures are clustered together. The results presented in the paper are valid for any FPGA architecture that may be considered for this scope

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

NASA Tech Briefs, September 2009

opics covered include: Filtering Water by Use of Ultrasonically Vibrated Nanotubes; Computer Code for Nanostructure Simulation; Functionalizing CNTs for Making Epoxy/CNT Composites; Improvements in Production of Single-Walled Carbon Nanotubes; Progress Toward Sequestering Carbon Nanotubes in PmPV; Two-Stage Variable Sample-Rate Conversion System; Estimating Transmitted-Signal Phase Variations for Uplink Array Antennas; Board Saver for Use with Developmental FPGAs; Circuit for Driving Piezoelectric Transducers; Digital Synchronizer without Metastability; Compact, Low-Overhead, MIL-STD-1553B Controller; Parallel-Processing CMOS Circuitry for M-QAM and 8PSK TCM; Differential InP HEMT MMIC Amplifiers Embedded in Waveguides; Improved Aerogel Vacuum Thermal Insulation; Fluoroester Co-Solvents for Low-Temperature Li+ Cells; Using Volcanic Ash to Remove Dissolved Uranium and Lead; High-Efficiency Artificial Photosynthesis Using a Novel Alkaline Membrane Cell; Silicon Wafer-Scale Substrate for Microshutters and Detector Arrays; Micro-Horn Arrays for Ultrasonic Impedance Matching; Improved Controller for a Three-Axis Piezoelectric Stage; Nano-Pervaporation Membrane with Heat Exchanger Generates Medical-Grade Water; Micro-Organ Devices; Nonlinear Thermal Compensators for WGM Resonators; Dynamic Self-Locking of an OEO Containing a VCSEL; Internal Water Vapor Photoacoustic Calibration; Mid-Infrared Reflectance Imaging of Thermal-Barrier Coatings; Improving the Visible and Infrared Contrast Ratio of Microshutter Arrays; Improved Scanners for Microscopic Hyperspectral Imaging; Rate-Compatible LDPC Codes with Linear Minimum Distance; PrimeSupplier Cross-Program Impact Analysis and Supplier Stability Indicator Simulation Model; Integrated Planning for Telepresence With Time Delays; Minimizing Input-to-Output Latency in Virtual Environment; Battery Cell Voltage Sensing and Balancing Using Addressable Transformers; Gaussian and Lognormal Models of Hurricane Gust Factors; Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft; Integrated Modeling of Spacecraft Touch-and-Go Sampling; Spacecraft Station-Keeping Trajectory and Mission Design Tools; Efficient Model-Based Diagnosis Engine; and DSN Simulator

Analysis and improvement of GNSS navigation message demodulation performance in urban environments

Global Navigation Satellite Systems (GNSS) are increasingly present in our everyday life. Further operational needs are emerging, mainly in urban environments. In these obstructed environments, the signal emitted by the satellite is severely degraded due to the many obstacles. Consequently, the data demodulation and the user position calculation are difficult. GNSS signals being initially designed in an open environment context, their demodulation performance is thus generally studied in the associated AWGN propagation channel model. But nowadays, GNSS signals are also used in degraded environments. It is thus essential to provide and study their demodulation performance in urban propagation channel models. It is in this context that this PhD thesis is related, the final goal being to improve GNSS signals demodulation performance in urban areas, proposing a new signal. In order to be able to provide and study GNSS signals demodulation performance in urban environments, a simulation tool has been developed in this PhD thesis context: SiGMeP for ‘Simulator for GNSS Message Performance'. It allows simulating the entire emission/reception GNSS signal chain in urban environment. Existing and modernized signals demodulation performance has thus been computed with SiGMeP in urban environments. In order to represent this demodulation performance faithfully to reality, a new methodology adapted to urban channels is proposed in this dissertation. Then, to improve GNSS signals demodulation performance in urban environments, the research axis of this thesis has focused on the ‘Channel Coding' aspect. In order to decode the transmitted useful information, the receiver computes a detection function at the decoder input. But the detection function used in classic receivers corresponds to an AWGN propagation channel. This dissertation thus proposes an advanced detection function which is adapting to the propagation channel where the user is moving. This advanced detection function computation considerably improves demodulation performance, just in modifying the receiver part of the system. Finally, in order to design a new signal with better demodulation performance in urban environments than one of existing and future signals, a new LDPC channel code has been optimized for a CSK modulation. Indeed, the CSK modulation is a promising modulation in the spread spectrum signals world, which permits to free from limitation sin terms of data rate implied by current GNSS signals modulations

Extracting Signals and Graphical Models from Compressed Measurements

The thesis is to give an integrated approach to efficiently learn the interdependency relation among high dimensional signal components and reconstruct signals from observations collected in a linear sensing system, Broadly speaking, the research topics consists of three parts: (i) interdependency relation learning; (ii) sensing system design; and (iii) signal reconstruction. In the interdependency relation learning part, we considered both the parametric and non-parametric methods to learn the graphical structure under the noisy indirect measurements. In the sensing system design part, we introduced a density evolution framework to design sensing systems for compressive sensing for the first time. In the signal reconstruction part, we focused on the signal reconstruction with a given sensing system, which consists of three parts: signal reconstruction with inexact knowledge of the sensing system; signal reconstruction with the signal being contaminated by undesired noise; signal reconstruction with the signal belonging to a union of convex sets.Ph.D