2,208 research outputs found
Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures
A mathematical characterization of serially-pruned permutations (SPPs)
employed in variable-length permuters and their associated fast pruning
algorithms and architectures are proposed. Permuters are used in many signal
processing systems for shuffling data and in communication systems as an
adjunct to coding for error correction. Typically only a small set of discrete
permuter lengths are supported. Serial pruning is a simple technique to alter
the length of a permutation to support a wider range of lengths, but results in
a serial processing bottleneck. In this paper, parallelizing SPPs is formulated
in terms of recursively computing sums involving integer floor and related
functions using integer operations, in a fashion analogous to evaluating
Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is
presented, and closed-form expressions for BRP statistics are derived. It is
shown that BRP sequences have weak correlation properties. A new statistic
called permutation inliers that characterizes the pruning gap of pruned
interleavers is proposed. Using this statistic, a recursive algorithm that
computes the minimum inliers count of a pruned BR interleaver (PBRI) in
logarithmic time complexity is presented. This algorithm enables parallelizing
a serial PBRI algorithm by any desired parallelism factor by computing the
pruning gap in lookahead rather than a serial fashion, resulting in significant
reduction in interleaving latency and memory overhead. Extensions to 2-D block
and stream interleavers, as well as applications to pruned fast Fourier
transforms and LTE turbo interleavers, are also presented. Moreover,
hardware-efficient architectures for the proposed algorithms are developed.
Simulation results demonstrate 3 to 4 orders of magnitude improvement in
interleaving time compared to existing approaches.Comment: 31 page
FFT-Based Deep Learning Deployment in Embedded Systems
Deep learning has delivered its powerfulness in many application domains,
especially in image and speech recognition. As the backbone of deep learning,
deep neural networks (DNNs) consist of multiple layers of various types with
hundreds to thousands of neurons. Embedded platforms are now becoming essential
for deep learning deployment due to their portability, versatility, and energy
efficiency. The large model size of DNNs, while providing excellent accuracy,
also burdens the embedded platforms with intensive computation and storage.
Researchers have investigated on reducing DNN model size with negligible
accuracy loss. This work proposes a Fast Fourier Transform (FFT)-based DNN
training and inference model suitable for embedded platforms with reduced
asymptotic complexity of both computation and storage, making our approach
distinguished from existing approaches. We develop the training and inference
algorithms based on FFT as the computing kernel and deploy the FFT-based
inference model on embedded platforms achieving extraordinary processing speed.Comment: Design, Automation, and Test in Europe (DATE) For source code, please
contact Mahdi Nazemi at <[email protected]
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
We present algorithms for the discrete cosine transform (DCT) and discrete
sine transform (DST), of types II and III, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N.
Furthermore, we show that a further N multiplications may be saved by a certain
rescaling of the inputs or outputs, generalizing a well-known technique for N=8
by Arai et al. These results are derived by considering the DCT to be a special
case of a DFT of length 4N, with certain symmetries, and then pruning redundant
operations from a recent improved fast Fourier transform algorithm (based on a
recursive rescaling of the conjugate-pair split radix algorithm). The improved
algorithms for DCT-III, DST-II, and DST-III follow immediately from the
improved count for the DCT-II.Comment: 9 page
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