Loop Optimizations of MGS-QRD Algorithm for FPGA High-Level Synthesis

Tan, Chong Yeam; Ooi, Chia Yee; Ismail, Nordinah

doi:10.1109/socc46988.2019.1570548480

Cited by 2 publications

(2 citation statements)

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“…31 Therefore, the MGS-QRD algorithm is chosen for implementation in this work. 32 QR decomposition is used to decompose a given m Â n square matrix A, into an m Â n orthogonal matrix Q and an n Â n upper triangular matrix R where m is the row size, n is the column size and m≥n, such that A ¼ Q Â R. As shown in Algorithm 5, the outer for-loop computes the diagonal element r i, i of matrix R and the column vector q i of matrix Q, whereas the non-diagonal element r i, j of matrix R and the column vector a j of matrix A is computed in the inner forloop. Note that column vectors of matrix A are modified to be used in computing the above-mentioned column vector q i .…”

Section: Modified Gram-schmidt Qr Decompositionmentioning

confidence: 99%

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Efficient hardware‐accelerated pseudoinverse computation through algorithm restructuring for parallelization in high‐level synthesis

Tan

Ooi

Choo

et al. 2021

Circuit Theory & Apps

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This paper describes a fast and efficient hardware-accelerated pseudoinverse computation through algorithm restructuring and leveraging FPGA synthesis directives for parallelism prior to high-level synthesis (HLS). The algorithm, which is composed of modified Gram-Schmidt QR decomposition (MGS-QRD), triangular matrix inversion (TMI), and matrix multiplication (MM), is synthesized and implemented on a field-programmable gate array (FPGA). MGS-QRD is restructured and augmented with parallelism directives prior to synthesizing the algorithm, which yielded an MGS-QRD hardware accelerator with high throughput. Modifications to the current TMI algorithm were also proposed, in which the removal of redundant computational tasks was done in order to speed up overall operation. Data dependencies in the MM algorithm were carefully considered such that appropriate parallelism directives were inserted, and matching the data flow of MM with MGS-QRD and TMI modules was also performed to accelerate the pseudoinverse computation. The results showed that the proposed pseudoinverse module is better than the naïve implementation which is composed of existing MGS-QRD, TMI and a standard MM in terms of maximum frequency (1.24Â speedup), hardware resources (48% of reduction of DSP usage), latency (23% reduction), and throughput (62% increase).

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Section: Modified Gram-schmidt Qr Decompositionmentioning

confidence: 99%

“…However, the processing latency of the QRD implementation using GR is still greater than that using MGS with similar hardware resources as in 31 . Therefore, the MGS‐QRD algorithm is chosen for implementation in this work 32 …”

Section: Previous Workmentioning

confidence: 99%