Improved MDLNS Number System Addition and Subtraction by Use of the Novel Co-Transformation

Multi-Dimensional Logarithmic Number System (MDLNS) is a generalized version of the Logarithmic Number System (LNS) which has multiple dimensions or bases. These generalizations can increase accuracy and hardware efficiency. However, addition and subtraction operations are the major obstruction of all logarithmic number systems circuits and so far a fair amount of research has been done to find practical techniques in LNS to implement these operations efficiently without the need for large tables. In order to achieve this goal, several methods such as interpolation, multipartite tables, and co-transformation have been introduced to decrease the cost and complexity. One of the most recent works is Novel Co-transformation. This thesis investigates the application of the Novel Co-Transformation on MDLNS. The goal is to reduce the table sizes over previously published method which utilizes a different address decoder on its tables which requires greater overhead. The results show that the table sizes are reduced significantly when a minimal error is allowed. Other common LNS techniques for table reductions may be applied to obtain better results

Multiplierless CSD techniques for high performance FPGA implementation of digital filters.

I leverage FastCSD to develop a new, high performance iterative multiplierless structure based on a novel real-time CSD recoding, so that more zero partial products are introduced. Up to 66.7% zero partial products occur compared to 50% in the traditional modified Booth's recoding. Also, this structure reduces the non-zero partial products to a minimum. As a result, the number of arithmetic operations in the carry-save structure is reduced. Thus, an overall speed-up, as well as low-power consumption can be achieved. Furthermore, because the proposed structure involves real time CSD recoding and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters.My work is based on a dramatic new technique for converting between 2's complement and CSD number systems, and results in high-performance structures that are particularly effective for implementing adaptive systems in reconfigurable logic.My research focus is on two key ideas for improving DSP performance: (1) Develop new high performance, efficient shift-add techniques ("multiplierless") to implement the multiply-add operations without the need for a traditional multiplier structure. (2) There is a growing trend toward design prototyping and even production in FPGAs as opposed to dedicated DSP processors or ASICs; leverage this trend synergistically with the new multiplierless structures to improve performance.Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multipliers. Fast, low area multiply-adds have become critical in modern commercial and military DSP applications. In many contemporary real-time DSP and multimedia applications, system performance is severely impacted by the limitations of currently available speed, energy efficiency, and area requirement of an onboard silicon multiplier.I also introduce a new multi-input Canonical Signed Digit (CSD) multiplier unit, which requires fewer shift/add/subtract operations and reduced CSD number conversion overhead compared to existing techniques. This results in reduced power consumption and area requirements in the hardware implementation of DSP algorithms. Furthermore, because all the products are produced simultaneously, the multiplication speed and thus the throughput are improved. The multi-input multiplier unit is applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters. The implementation cost of these digital filters can be further reduced by limiting the wordlength of the input signal with little or no sacrifice to the filter performance, which is confirmed by my simulation results. The proposed multiplier unit can also be applied to other DSP algorithms, such as digital filter banks or matrix and vector multiplications.Finally, the tradeoff between filter order and coefficient length in the design and implementation of high-performance filters in Field Programmable Gate Arrays (FPGAs) is discussed. Non-minimum order FIR filters are designed for implementation using Canonical Signed Digit (CSD) multiplierless implementation techniques. By increasing the filter order, the length of the coefficients can be decreased without reducing the filter performance. Thus, an overall hardware savings can be achieved.Adaptive system implementations require real-time conversion of coefficients to Canonical Signed Digit (CSD) or similar representations to benefit from multiplierless techniques for implementing filters. Multiplierless approaches are used to reduce the hardware and increase the throughput. This dissertation introduces the first non-iterative hardware algorithm to convert 2's complement numbers to their CSD representations (FastCSD) using a fixed number of shift and logic operations. As a result, the power consumption and area requirements required for hardware implementation of DSP algorithms in which the coefficients are not known a priori can be greatly reduced. Because all CSD digits are produced simultaneously, the conversion speed and thus the throughput are improved when compared to overlap-and-scan techniques such as Booth's recoding

Design of approximate overclocked datapath

Embedded applications can often demand stringent latency requirements. While high degrees of parallelism within custom FPGA-based accelerators may help to some extent, it may also be necessary to limit the precision used in the datapath to boost the operating frequency of the implementation. However, by reducing the precision, the engineer introduces quantisation error into the design. In this thesis, we describe an alternative circuit design methodology when considering trade-offs between accuracy, performance and silicon area. We compare two different approaches that could trade accuracy for performance. One is the traditional approach where the precision used in the datapath is limited to meet a target latency. The other is a proposed new approach which simply allows the datapath to operate without timing closure. We demonstrate analytically and experimentally that for many applications it would be preferable to simply overclock the design and accept that timing violations may arise. Since the errors introduced by timing violations occur rarely, they will cause less noise than quantisation errors. Furthermore, we show that conventional forms of computer arithmetic do not fail gracefully when pushed beyond the deterministic clocking region. In this thesis we take a fresh look at Online Arithmetic, originally proposed for digit serial operation, and synthesize unrolled digit parallel online arithmetic operators to allow for graceful degradation. We quantify the impact of timing violations on key arithmetic primitives, and show that substantial performance benefits can be obtained in comparison to binary arithmetic. Since timing errors are caused by long carry chains, these result in errors in least significant digits with online arithmetic, causing less impact than conventional implementations.Open Acces

An efficient implementation of lattice-ladder multilayer perceptrons in field programmable gate arrays

The implementation efficiency of electronic systems is a combination of conflicting requirements, as increasing volumes of computations, accelerating the exchange of data, at the same time increasing energy consumption forcing the researchers not only to optimize the algorithm, but also to quickly implement in a specialized hardware. Therefore in this work, the problem of efficient and straightforward implementation of operating in a real-time electronic intelligent systems on field-programmable gate array (FPGA) is tackled. The object of research is specialized FPGA intellectual property (IP) cores that operate in a real-time. In the thesis the following main aspects of the research object are investigated: implementation criteria and techniques. The aim of the thesis is to optimize the FPGA implementation process of selected class dynamic artificial neural networks. In order to solve stated problem and reach the goal following main tasks of the thesis are formulated: rationalize the selection of a class of Lattice-Ladder Multi-Layer Perceptron (LLMLP) and its electronic intelligent system test-bed – a speaker dependent Lithuanian speech recognizer, to be created and investigated; develop dedicated technique for implementation of LLMLP class on FPGA that is based on specialized efficiency criteria for a circuitry synthesis; develop and experimentally affirm the efficiency of optimized FPGA IP cores used in Lithuanian speech recognizer. The dissertation contains: introduction, four chapters and general conclusions. The first chapter reveals the fundamental knowledge on computer-aideddesign, artificial neural networks and speech recognition implementation on FPGA. In the second chapter the efficiency criteria and technique of LLMLP IP cores implementation are proposed in order to make multi-objective optimization of throughput, LLMLP complexity and resource utilization. The data flow graphs are applied for optimization of LLMLP computations. The optimized neuron processing element is proposed. The IP cores for features extraction and comparison are developed for Lithuanian speech recognizer and analyzed in third chapter. The fourth chapter is devoted for experimental verification of developed numerous LLMLP IP cores. The experiments of isolated word recognition accuracy and speed for different speakers, signal to noise ratios, features extraction and accelerated comparison methods were performed. The main results of the thesis were published in 12 scientific publications: eight of them were printed in peer-reviewed scientific journals, four of them in a Thomson Reuters Web of Science database, four articles – in conference proceedings. The results were presented in 17 scientific conferences

Low power two-channel PR QMF bank using CSD coefficients and FPGA implementation

Finite impulse response (FIR) filter is a fundamental component in digital signal processing. Two-channel perfect reconstruction (PR) QMF banks are widely used in many applications, such as image coding, speech processing and communications. A practical lattice realization of two-channel QMF bank is developed in this thesis for dealing with the wide dynamic range of intermediate results in lattice structure. To achieve low complexity and low power consumption of two-channel perfect reconstruction QMF bank, canonical signed digit (CSD) number system is used for representing lattice coefficients in FPGA implementation. Utilization of CSD number system in lattice structures leads to more efficient hardware implementation. Many fixed-point simulations were done in Matlab in order to obtain the proper fixed-point word-length for different signals. Finally, FPGA implementation results show that perfect reconstruction signal is obtained by using the proposed method. Furthermore, the power consumption using CSD number system for representing lattice coefficients is less than that obtained by using two\u27s complement number system in two-channel QMF bank. A low complexity and low power two-channel PR QMF bank using CSD coefficients was realized