Parallel and Pipelined Architectures for Cyclic Convolution by Block Circulant Formulation Using Low-Complexity Short-Length Algorithms

Fully pipelined parallel architectures are derived for high-throughput and reduced-hardware realization of prime-factor cyclic convolution using hardware-efficient modules for short-length rectangular transform (RT). Moreover, a new approach is proposed for the computation of block pseudocyclic conv...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems for video technology Vol. 18; no. 10; pp. 1422 - 1431
Main Author: Meher, P.K.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Architecture
Block-cyclic convolution
Blocking
Complexity
Computation
Computational efficiency
Computer architecture
Concurrent computing
Convolution
cyclic convolution
Design. Technologies. Operation analysis. Testing
Discrete cosine transforms
Discrete Fourier transforms
Electronics
Exact sciences and technology
Fast Fourier transforms
Finite impulse response filter
Hardware
Integrated circuits
Iterative algorithms
pseudocyclic convolution
Reduction
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Studies
Systems, networks and services of telecommunications
systolic array
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
Very large scale integration
very large-scale integration (VLSI)
VLSI circuit
Segmentation
Block-cyclic convolution
Information rate
Parallel architectures
Systolic network
Algorithm
Information transmission
Implementation
Pipeline processing
pseudocyclic convolution
Convolution
Computation error
cyclic convolution
Integrated circuit
systolic array
Delay time
very large-scale integration (VLSI)
ISSN:1051-8215, 1558-2205
Online Access:Get full text
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Summary:Fully pipelined parallel architectures are derived for high-throughput and reduced-hardware realization of prime-factor cyclic convolution using hardware-efficient modules for short-length rectangular transform (RT). Moreover, a new approach is proposed for the computation of block pseudocyclic convolution using a block cyclic convolution of equal length along with some correction terms, so that the block pseudocyclic representation of cyclic convolution for non-prime-factor-length ( N = rP , when r and P are not mutually prime) could be computed efficiently using the algorithms and architectures of short-length cyclic convolutions. Low-complexity algorithms are derived for efficient computation of those error terms, and overall complexities of the proposed technique are estimated for r =2, 3, 4, 6, 8 and 9. The proposed algorithms are used further to design high-throughput and reduced-hardware structures for cyclic convolution where the cofactors are not relatively prime. The proposed structures for high-throughput implementation are found to offer a reduction of nearly 50%-75% of area-delay product over the existing structures for several convolution-lengths. Low-complexity structures for input/output addition units of short length convolutions are derived and used them along with high-throughput modules for hardware-efficient realization of multifactor convolution, which offers nearly 25%-75% reduction of area-delay complexity over the existing structures for various non-prime-factor length convolutions.
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ISSN:1051-8215
1558-2205
DOI:10.1109/TCSVT.2008.2004918