Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.Comment: 16 pages, 22 figures, 2 table

Digital VLSI Architectures for Advanced Channel Decoders

Error-correcting codes are strongly adopted in almost every modern digital communication and storage system, such as wireless communications, optical communications, Flash memories, computer hard drives, sensor networks, and deep-space probes. New and emerging applications demand codes with better error-correcting capability. On the other hand, the design and implementation of those high-gain error-correcting codes pose many challenges. They usually involve complex mathematical computations, and mapping them directly to hardware often leads to very high complexity. This work aims to focus on Polar codes, which are a recent class of channel codes with the proven ability to reduce decoding error probability arbitrarily small as the block-length is increased, provided that the code rate is less than the capacity of the channel. This property and the recursive code-construction of this algorithms attracted wide interest from the communications community. Hardware architectures with reduced complexity can efficiently implement a polar codes decoder using either successive cancellation approximation or belief propagation algorithms. The latter offers higher throughput at high signal-to-noise ratio thanks to the inherently parallel decision-making capability of such decoder type. A new analysis on belief propagation scheduling algorithms for polar codes and on interconnection structure of the decoding trellis not covered in literature is also presented. It allowed to achieve an hardware implementation that increase the maximum information throughput under belief propagation decoding while also minimizing the implementation complexity

Modelling and extraction of fundamental frequency in speech signals

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.One of the most important parameters of speech is the fundamental frequency of vibration of voiced sounds. The audio sensation of the fundamental frequency is known as the pitch. Depending on the tonal/non-tonal category of language, the fundamental frequency conveys intonation, pragmatics and meaning. In addition the fundamental frequency and intonation carry speaker gender, age, identity, speaking style and emotional state. Accurate estimation of the fundamental frequency is critically important for functioning of speech processing applications such as speech coding, speech recognition, speech synthesis and voice morphing. This thesis makes contributions to the development of accurate pitch estimation research in three distinct ways: (1) an investigation of the impact of the window length on pitch estimation error, (2) an investigation of the use of the higher order moments and (3) an investigation of an analysis-synthesis method for selection of the best pitch value among N proposed candidates. Experimental evaluations show that the length of the speech window has a major impact on the accuracy of pitch estimation. Depending on the similarity criteria and the order of the statistical moment a window length of 37 to 80 ms gives the least error. In order to avoid excessive delay as a consequence of using a longer window, a method is proposed ii where the current short window is concatenated with the previous frames to form a longer signal window for pitch extraction. The use of second order and higher order moments, and the magnitude difference function, as the similarity criteria were explored and compared. A novel method of calculation of moments is introduced where the signal is split, i.e. rectified, into positive and negative valued samples. The moments for the positive and negative parts of the signal are computed separately and combined. The new method of calculation of moments from positive and negative parts and the higher order criteria provide competitive results. A challenging issue in pitch estimation is the determination of the best candidate from N extrema of the similarity criteria. The analysis-synthesis method proposed in this thesis selects the pitch candidate that provides the best reproduction (synthesis) of the harmonic spectrum of the original speech. The synthesis method must be such that the distortion increases with the increasing error in the estimate of the fundamental frequency. To this end a new method of spectral synthesis is proposed using an estimate of the spectral envelop and harmonically spaced asymmetric Gaussian pulses as excitation. The N-best method provides consistent reduction in pitch estimation error. The methods described in this thesis result in a significant improvement in the pitch accuracy and outperform the benchmark YIN method

New Coding/Decoding Techniques for Wireless Communication Systems

Wireless communication encompasses cellular telephony systems (mobile communication), wireless sensor networks, satellite communication systems and many other applications. Studies relevant to wireless communication deal with maintaining reliable and efficient exchange of information between the transmitter and receiver over a wireless channel. The most practical approach to facilitate reliable communication is using channel coding. In this dissertation we propose novel coding and decoding approaches for practical wireless systems. These approaches include variable-rate convolutional encoder, modified turbo decoder for local content in Single-Frequency Networks, and blind encoder parameter estimation for turbo codes. On the other hand, energy efficiency is major performance issue in wireless sensor networks. In this dissertation, we propose a novel hexagonal-tessellation based clustering and cluster-head selection scheme to maximize the lifetime of a wireless sensor network. For each proposed approach, the system performance evaluation is also provided. In this dissertation the reliability performance is expressed in terms of bit-error-rate (BER), and the energy efficiency is expressed in terms of network lifetime

Digital receiver study and implementation

Computer software was developed which makes it possible to use any general purpose computer with A/D conversion capability as a PSK receiver for low data rate telemetry processing. Carrier tracking, bit synchronization, and matched filter detection are all performed digitally. To aid in the implementation of optimum computer processors, a study of general digital processing techniques was performed which emphasized various techniques for digitizing general analog systems. In particular, the phase-locked loop was extensively analyzed as a typical non-linear communication element. Bayesian estimation techniques for PSK demodulation were studied. A hardware implementation of the digital Costas loop was developed

Coordinated design of coding and modulation systems

The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations