Uwe Meyer-Bäse

Implementation of a Communications Channelizer using FPGAs and RNS Arithmetic

Field-programmable logic (FPL), often grouped under the popular name field-programmable gate arrays (FPGA), are on the verge of revolutionizing sectors of digital signal processing (DSP) industry as programmable DSP microprocessor did nearly two decades ago. Historically, FPGAs were considered to be only a rapid prototyping and low-volume production technology. FPGAs are now attempting to move into the mainstream DSP as their density and performance envelope steadily improve. While evidence now supports the claim that FPGAs can accelerate selected low-end DSP applications (e.g., FIR filter), the technology remains limited in its ability to realize high-end DSP solutions. This is due primarily to systemic weaknesses in FPGA-facilitated arithmetic processing. It will be shown that in such cases, the residue number system (RNS) can become an enabling technology for realizing embedded high-end FPGA-centric DSP solutions. This thesis is developed in the context of a demonstrated RNS/FPGA synergy and the application of the new technology to communication signal processing.

Design and Implementation of High-Performance RNS Wavelet Processors Using Custom IC Technologies

The design of high performance, high precision, real-time digital signal processing (DSP) systems, such as those associated with wavelet signal processing, is a challenging problem. This paper reports on the innovative use of the residue number system (RNS) for implementing high-end wavelet filter banks. The disclosed system uses an enhanced index-transformation defined over Galois fields to efficiently support different wavelet filter instantiations without adding any extra cost or additional look-up tables (LUT). A selection of a small wordwidth modulus set are the keys for attaining low-complexity and high-throughput. An exhaustive comparison against existing twos complement (2C) designs for different custom IC technologies was carried out. Results reveal a performance improvement of up to 100% for high-precision RNS-based systems. These structures demonstrated to be well suited for field programmable logic (FPL) assimilation as well as for CBIC (cell-based integrated circuit) technologies.

New power-of-2 RNS scaling scheme for cell-based IC design

Previous scaling schemes are based on the conversion of the unpositional residue number system (RNS) digits into a positional number system via Chinese remainder theorem (CRT) or mixed-radix-conversion (MRC) and the back conversion into RNS with an associated size and speed penalty in cell-based integrated circuit (CBIC) designs. This paper presents a new scaling approach, which allows faster and more efficient schemes, because the scaling uses only RNS operations within the small word length channels.

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).

Design and Implementation of RNS-Based Adaptive Filters

This paper presents the residue number system (RNS) implementation of reduced complexity and high performance adaptive FIR filters on Altera APEX20K field-programmable logic (FPL) devices. Index arithmetic over Galois fields along with a selection of a small wordwidth modulus set are keys for attaining low-complexity and high-throughput. The replacement of a classical modulo adder tree by a binary adder with extended precision followed by a single modulo reduction stage improved area requirements by 10% for a 32-tap FIR filter. A block LMS (BLMS) implementation was preferred for the update of the adaptive FIR filter coefficients. RNS-FPL merged filters demonstrated its superiority when compared to 2C (two’s complement) filters, being about 65% faster and requiring fewer logic elements for most study cases.

Index-based RNS DWT architectures for custom IC designs

The design of high-performance, high-precision, real-time digital signal processing (DSP) systems, such as those associated with wavelet signal processing, is a challenging problem. This paper reports on the innovative use of the residue number system (RNS) for implementing high-end wavelet filter banks. The disclosed system uses an enhanced index-transformation defined over Galois fields to efficiently support different wavelet filter instantiations without adding any extra cost or additional lookup tables (LUT). An exhaustive comparison against existing twos complement (2C) designs for different custom IC technologies was carried out. These structures have been demonstrated to be well suited for field programmable logic (FPL) assimilation as well as for CBIC (cell-based integrated circuit) technologies.

EFFICIENT RNS-BASED DESIGN OF PROGRAMMABLE FIR FILTERS TARGETING FPL TECHNOLOGY

FIR filters are routinely used in the implementation of modern digital signal processing systems. Their efficient implementation using commercially available VLSI technology is a subject of continuous study and development. This paper presents the residue number system (RNS) implementation of reduced-complexity and high-performance FIR filters, using modern Altera APEX20K field-programmable logic (FPL) devices. Index arithmetic over Galois fields and the Quadratic Residue Number System (QRNS), along with a selection of a small wordwidth modulus set, are the keys for attaining low complexity and high throughput in real and complex FIR filters. RNS–FPL merged FIR filters demonstrated its superiority when compared to 2C (twos complement) filters, being about 65% faster and requiring fewer logic elements for most study cases. Special attention was paid to an efficient implementation of the multi-operand modulo adders. The replacement of a classical modulo adder tree by a binary adder with extended precision followed by a single modulo reduction stage reduced area requirements by 10% for a 32-tap FIR filter. On the other hand, an index arithmetic QRNS-based complex FIR filter yielded up to 60% performance improvement over a three-multiplier-per-tap 2C filter, while requiring fewer LEs for filters having more than eight taps. Particularly, a 32-tap filter needed 24% LEs less than the classical design.

Hardware implementation of machine vision systems: image and video processing

This contribution focuses on different topics covered by the special issue titled ‘Hardware Implementation of Machine vision Systems’ including FPGAs, GPUS, embedded systems, multicore implementations for image analysis such as edge detection, segmentation, pattern recognition and object recognition/interpretation, image enhancement/restoration, image/video compression, image similarity and retrieval, satellite image processing, medical image processing, motion estimation, neuromorphic and bioinspired vision systems, video processing, image formation and physics based vision, 3D processing/coding, scene understanding, and multimedia.

Fast discrete Fourier transform computations using the reduced adder graph technique

It has recently been shown that thse-dimensional reduced adder graph (RAG-) technique is beneficial for many DSP applications such as for FIR and IIR filters, where multipliers can be grouped in multiplier blocks. This paper highlights the importance of DFT and FFT as DSP objects and also explores how the RAG- technique can be applied to these algorithms. This RAG- DFT will be shown to be of low complexity and possess an attractively regular VLSI data flow when implemented with the Rader DFT algorithm or the Bluestein chirp- algorithm. ASIC synthesis data are provided and demonstrate the low complexity and high speed of the design when compared to other alternatives.

Faster than the FFT: The chirp-z RAG-n Discrete Fast Fourier Transform

DFT and FFTs are important but resource intensive building blocks and have found many application in communication systems ranging from fast convolution to coding of OFDM signals. It has recently be shown that the n-Dimensional Reduced Adder Graph (RAG-n) technique is beneficially in many applications such as FIR or IIR filters, where multiplier can be grouped in multiplier blocks. This paper explores how the RAG-n technique can be applied to DFT algorithms. A RAG-n fast discrete Fourier transform will be shown to be of low latency and complexity and posses a VLSI attractive regular data flow when implemented with the Bluestein chirp-z algorithm. VHDL code synthesis results for Xilinx Virtex II FPGAs are provided and demonstrate the superior properties when compared with Xilinx FFT IP cores. Index Terms – Fast Fourier Transform, OFDM, FPGA, n-Dimensional Reduced Adder Graph