DOI : https://doi.org/10.5281/zenodo.19402037
- Open Access

- Authors : Dr. P Sudhakar Reddy, Tummala Govardhan Sai, Chandrappa Gari Kare Gowd, Mutal Mohan Kumar, Dande Yugandar, Chappidi Sasi Vardhan, Gajula Jayanth
- Paper ID : IJERTV15IS031592
- Volume & Issue : Volume 15, Issue 03 , March – 2026
- Published (First Online): 03-04-2026
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Low Power Design of Approximate Bilateral Filters for Image Denoising with Clock Gating Techniques
Dr. P Sudhakar Reddy
Department of ECE, Sri Venkateswara College of Engineering, Tirupati, A.P., India
Mutal Mohan Kumar
Department of ECE, Sri Venkateswara College of Engineering, Tirupati, A.P., India
Tummala Govardhan Sai
Department of ECE, Sri Venkateswara college of Engineering, Tirupati, A.P., India
Dande Yugandar
Department of ECE, Sri Venkateswara College of Engineering, Tirupati, A.P., India
Chandrappa Gari Kare Gowd
Department of ECE, Sri Venkateswara college of Engineering, Tirupati, A.P., India
Chappidi Sasi Vardhan
Department of ECE, Sri Venkateswara College of Engineering, Tirupati, A.P., India
Gajula Jayanth
Department of ECE, Sri Venkateswara College of Engineering Tirupati, A.P., India
Abstract – Image denoising is a very important process in image processing, the purpose of which is to eliminate noise without affecting important details of the image. An example of an edge- preserving denoising filter that is popular and suitable in the denoising process in that it can preserve sharp edges and minimise noise is the bilateral filter (BF). Nevertheless, the bilateral filter has a relatively high cost of computation that restricts its real-time use especially where the environment has limited resources. This paper will provide a power-efficient FPGA implementation of a bilateral filter (denoising of images) in its approximate form. The given design employs hardware-based approximations to decrease the complexity of computationally intensive processes involved in the bilateral filter, namely the range filter part. Using the paralleling nature of FPGA and optimizing access patterns in memory we will record great gains in power and processing speed without compromising image quality. Experimental evidence shows that the suggested FPGA implementation is more efficient in power consumption and execution time compared to the traditional methods based on the CPU and it is therefore applicable to real-time image processing applications in embedded systems and mobile devices. Scalability and flexibility are also made possible by the design as it can be adapted to various levels of resolution and noise. This strategy opens the avenue towards viable energy efficient image denoising in hardware based applications.
Keywords bilateral filter, Hardware Optimization, Low-Power, Vivado Simulation, Xilinx Vivado Design Suite Image processing.
I.INTRODUCTION
There has been a rising need to use efficient and high- performance digital systems hence the FPGA (Field- Programmable Gate Array) technology has been widely utilized in numerous applications such as image processing, communication systems, and embedded systems. A bilateral
filter (BF) is one of the fundamental operations in the image processing used in large amounts to achieve edge-preserving denoising.
The bilateral filter is a useful tool because it allows one to smooth an image and keeps sharp edges intact, thus finding use in noise reduction, object recognition, and image enhancement applications. Its computational complexity and huge resource needs, particularly in real-time processing, however, pose problems in implementing the filter in hardware platforms such as FPGA [1] [2]. On the FPGA, power consumption is a critical issue because of the heavy computations that are required to run the bilateral filter on large data sets of images. In cases where a lot of real-time high-speed processing is required, such as FPGA platforms, there is usually a high dynamic power dissipation, since the logic gates are switched on and off all the time. This is even aggravated in embedded systems where power efficiency is critical in extending battery life, minimized heat production and optimum energy usage efficiency [3]. Therefore, the development of power efficient FPGA implementations of the bilateral filter is essential in addressing the high standards of the modern image processing applications [4]. Clock gating ( Selectively disabling the clock signal to the inactive parts ) is one of the promising methods to handle the power consumption, basically, it aims at eliminating the unnecessary switching activities in the system by turning off the clock signal to components that are not required [5].
This power-saving method comes in especially handy in FPGA- based image-processing systems, where the image-processing system uses large numbers of flip-flops and registers to store the intermediate results in storage during image filtering operation [6]. Within the framework of the bilateral filter, these flip-flops
are continuously switching particularly during real-time processing thus consuming a lot of power. Clock gating can be introduced to selectively switch off these flip-flops during other operations which are not participating in the active operations and thereby use less power without impacting on the functionality or accuracy of the bilateral filter [7]. In this paper, the integration of clock gating in FPGA based bilateral filter design is researched to achieve power optimization. The proposed solution is expected to minimize switching traffic and total power leakage by selectively enabling flip-flops upon the need to perform active processing. The experiment is a comparison between the conventional bilateral filter design based on FPGA and one which implements clock gating to evaluate the effect of power consumption, processing speed, and resource utilization [8] [9]. The experimental outcomes are conducted with the help of Artix-7 FPGA platform that has low power consumption and high performance that prove that clock gating may be used successfully to save power without deteriorating the performance of the bilateral filter. The findings also point out a correlation to clock gating on the total area of the FPGA design. Though FPGA devices are not as endowed as the other devices, the clock gating will ensure that any methods used to save power are utilized without wasting the resources [10].
- RELATED WORK
Image processing systems based on FPGA, and especially power efficiency, have become a critical field of research in recent years with the rise in demands of energy-efficient embedded systems. Numerous researches have been on different approaches to lower power consumption of FPGA- based designs, particularly computationally intensive image processing, such as bilateral filtering [11]. The bilateral filter is widely applied in the automatic processing of digital images because it allows removing noise, and the edges of the image are not distorted. A number of FPGA-based implementations of bilateral filters have been offered, with the initial efforts being on optimization of the hardware implementation to enhance the processing speed and reduce the usage of resources. The designs use parallelism and pipelining usually to get high throughput but they fail to put into consideration the very crucial factor of power consumption. A comparative study of bilateral filter variants to filter medical imaging where the computational cost of bilateral filters is very high in medical image enhancement but power consumption is not explicitly optimized by FPGA [12].
With the increased adoption of FPGA-based design researchers started concentrating on the power efficiency versus speed. Application of fast bilateral filters with arbitrary range and domain kernels, which offer a solution to the issue of increasing speed of processing without compromising onperformance [13]. This design however failed to deal with the power dissipation problems of high-speed operations. FPGA designs with many flip-flops and many registers to store intermediate values during filtering operations consume a lot of power particularly in real-time image processing [14]. Although it was faster in processing power efficiency was still an issue because a lot of resources were consumed in such high-performance designs. Clock gating is one of the most useful methods to lower power consumption in the FPGA design and it is a technique
that enables the clock signal to be disenabled to inactive circuit components [15]. Clock gating greatly minimizes dynamic power dissipation by eliminating needless switching of flip- flops and registers. This paper presents the sensitivity of using a combination of approximate techniques and clock gating to optimize the bilateral filters of FPGA in terms of power consumption [16]. Dynamic clock gating application on the implementation of bilateral filters in FPGA based real time image processing systems. They proposed an intelligent clock- gating mechanism that adjusted to the nature of the input signal of the bilateral filter, where the clock was turned off when the signal was not needed. This method had the benefit of consuming a lot less power without affecting the performance of filtering. Their experiment showed that they could save up to 30 percent of their power consumption, which has made it one of the possible solutions to real-time image processing problems where speed and power efficiency are highly important [17] [18]. A small hardware design of the bilateral filter that integrates approximate computing with a look up table. This method resulted in saving of large amounts of power since the number of active components was reduced when less computationally intensive tasks were being performed without reducing the performance of the filter [19].
Their effort demonstrated that clock gating was able to result in high power savings, particularly in high performance design where dynamic power dissipation was of interest. The work by Robertson was a foundation of the future research in the areas of designing power-efficient FPGA-based solutions, especially in signal processing such as image filtering [20].
- EXISTING METHOD
Bilateral filter is a non-linear image processing method, which is popular in edge-saving smoothing and grass removal. Contrary to the normal linear filters, it is based on the consideration of the spatial distance between the pixels and the differences in intensities as well. The filter averages the intensity value of the neighboring pixels, however, it weighs them considering their spatial closeness and resemblance to the central pixel in terms of intensity.
Fig. 1. Existing Block Diagram
This is the only method that can maintain sharp edges even though it is also effective in reducing noise levels, hence especially in those applications where sharp edges are essential, including medical imaging, computer vision, and graphics. Mathematically, the bilateral filter implements two Gaussian functions, one of which uses the distance between pixels, and the other one uses the difference between the intensity of pixels. The spatial component makes sure that pixel close to the center pixel have a greater impact, whereas the range component makes sure that the pixels with similar intensity have greater effects on the average. The two-fold consideration of this
enables the filter to maintain significant features such as edges, and to eliminate noise in homogeneous parts of the image. The outcome is that, the details are maintained and noise has been reduced successfully without distorting the edges.
Fig.2. Base Filter Internal RTL Schematic Diagram
Fig.3. Base Filter Simulation Waveform
This is expensive in computation, as the filter has to perform spatial and intensity kernels of each pixel and its neighbors, and this turns out to be a large number of calculations. Hence, although bilateral filter is a great tool in activities where an edge must be maintained in an improved image, it cannot always be used in real-time processing unless an optimized version is implemented. Bilateral filter has been highly valued in its ability to smooth an image and at the same time retain the edges, and it is a powerful tool used in image enhancement and denoising tasks. The thing is, that its preserving edge quality is provided with the help of paying attention to the spatial distance and the intensity contrast among pixels. Such a property is especially useful in applications in which sharp edges are important and in which the aesthetic appearance is essential like in medical imaging, computer vision, and artistic effects. This makes its computational cost higher, particularly when large images are being operated on or in real time uses. In an attempt to reduce the computational cost, a number of optimized versions of the bilateral filter have been suggested. Such methods consist of methods such as fast bilateral filtering which approximates calculations of the filter by use of less efficient data structures or simplifying range and spatial kernels. The other optimization technique is hardware accelerations or GPUs or FPGAs which can use parallel processing to accelerate the bilateral filtering process.
control mechanism is the Enable signal. It also allows the filter to be turned off when not needed, which also helps in saving power since it can turn, or can switch off, some components of the circuit when necessary.
Fig.4. Proposed Flip Flop Based Clock Gating
Clock gating with flip-flop design is usually designed to use more logic, like an AND gate, to make the clock signal and a control signal, which may be indicative of whether to clock the flip-flop or the register. The clock is gated when the control signal is to ensure that the flip-flop is not changing its state (i.e. when the logic block is not busy), which is important so that there is no unnecessary switching activity. The method assists in lowering dynamic power usage that is primarily triggered by switching of flip-flops and other sequential components in the circuit. Flip-flop-based clock gating may substantially reduce power consumption by making sure that these components do not run at a time when they are not required.
Fig.5. Proposed Flip Flop Based Clock Gating RTL Schematic Diagram
The Fig: 5 schematic shows a safe clock-gating scheme that is done by a flip-flop near the bilateral filter design. The control signal is then synchronized by first passing the system clock through a D flip-flop. Such synchronisation prevents undesirable glitches on the clock line. The flip-flop output is used to drive an AND gate into the clock. When the control signal is high, the clock is permitted to flow on. When it is low, clock activity is halted and it assists in saving power.
- PROPOSED METHOD
- Clock Input and Control
A Clock input is the first towards the system that is necessary in driving the whole processing unit. The Clock Gating block (marked in yellow) is very important in the regulation of the clock signal arrival at specific sections of the system. Flip-flop clock gating is used to switch off the clock signal to the inactive flip-flops avoiding unnecessary switching activity and thus saving dynamic power consumption. The other
Fig. 6. Proposed Flip Flop Based Clock Gating Simulation Waveform
The behaviour of the proposed bilateral filter design flip-flop- based clock-gating circuit is described by this Fig: 6 simulation waveform. The enable signal is low and the input clock (clk) is continuously switching indicating that the gating control is defined as required. Due to this, the gated clock (gated_clk) will
behave as expected and occurrence of undesired transitions will not be realised. The registered output (q out) remains constant, and this proves that the enable signal issafely synchronized by the flip-flop. Generally, the waveform confirms that the clock is not propagated when not needed and this proves proper and glitch free clock gating thereby reduces redundant switching and power in the bilateral filter.
- Pixel and Data Inputs
Pixel block is the input to the FIR filter system, which is generally an image or signal processing model. The pixel block data drives the Data Inputs which are the raw data that is going to be filtered by the filters. This may include the insertion of values pertaining to an image or signal which can be worked on by the filter and the noise removed, features bettered or other filtering functions.
- Area Detection Logic
The Area Detection Logic block contributes to the significance of the choice of which part of the filter processing unit is to be active or not. The area detection is aimed at defining regions of interest or sections of the signal that should undergo processing. When this logic has identified the required areas, it invokes the Case Statement which is the invocation of the selection of the required filtering operation depending on the area that has been detected. The area detection and the combination with case selection will guarantee that the system only focuses on the relevant sections of the input data, which further minimizes ineffective computation and power usage.
- Area Detection Logic
The main subunit of the system is the Filter Processing Unit in which the actual filtering operations are found. This unit contains several examples of Filter 1 blocks, each of them depicting a separate filter stage. The fundamental signal processing operations, e.g. convolution, smoothing, or noise removal, are done by these filters. With the help of multiple filter stages, the system can perform various kinds of filtering operations consecutively until the required output is achieved. Digital multipliers and adders generate part products and have to be summed up and finally added.
Fig.7. Proposed Implemented Algorithm
- Done Logic and Output
A Done Logic block is also part of the system and it has the role of indicating that the filtering operation is done. After the processing of the input data by the filter, the done signal is generated, and this shows that the system has completed the
processing. That filtered data is subsequently published to the Output Register where the processed data is ultimately output and the system also has a Done Logic block which has the responsibility of indicating when the filtering operation is complete. After the filter has acted upon the input data, the done in this implementation, we would now like to act upon a noisy image using a system that runs on our FPGA with an adjusted flip-flop-based system clock gating bilateral filtering.
Fig.8. Proposed Block Diagram
This is broken down into two key phases, image preprocessing and filtering with Verilog to do the bilateral filter implementation and finally post-processing to restore the final image that is denoised. The image made noisy is first turned into digital form in MATLAB where pixel data is taken out and worked with on an FPGA board using a Verilog based bilateral filter. Depending on how the system is designed, the data of the noisy picture is sent over to the FPGA either using serial communication of a parallel communication interface. The hardware description of the bilateral filter in this case is being done in Verilog. All the filter tap coefficients are preset according to the required filtering properties. This clock gating system will make sure that the FPGA will enable the sections of the filter processing unit that are required to perform the calculation in question only, thus consuming significantly fewer power. The bilateral filter is used as follows: the values of the incoming pixels are processed according to their spatial distance and contrast with their neighboring pixels. Its modified flip-flop clock gating also means that only a set of registers and multipliers are needed at any point at any point in time within a filter operation, resulting in improved efficiency.
- Clock Input and Control
- EXPERIMENT RESULTS
A synthesis and simulation of the proposed efficient power FPGA design of bilateral filter of the image denoising process were performed in the Xilinx Vivado Design Suite 2020.2. The idea behind the hardware implementation was to use the Xilinx Artix-7 FPGA (xc7a100t-1csg324) which is a common high- performance platform characterized by power-efficient digital systems. The design aimed on maximizing computationally heavy operations of bilateral filter especially the range filter aspect to gain energy efficient performance that can be used in real time application. The paralleling processing of the FPGA was used to accelerate the functions, and optimization of access patterns to the memory assisted to minimize power consumption which made it appropriate to embedded systems and mobile devices. The results indicated that a great power savings was achieved at the same time preserving the quality of the image processing, and hence the filter can be used
effectively even with large images and in resource-limited settings. Besides, the design is scalable and flexible, and is suitable to a wide range of image resolutions and noise levels, and opens the way to viable, energy efficient image denoising in hardware-accelerated applications.
TABLE. I Comparison Of Existing And Proposed
Work In Parameters
Method Area Delay(ns) Power(W) Existing method 619 8.141 12.24 Proposed method 620 8.141 8.228 It is a table comparing the bilateral filters that are currently used and the proposed ones based on the area, delay, and power. The suggested method has 620 area units that is nearly similar to the current method with 619 units. The delay of both techniques is identical (8.141ns), and shows no timing deterioration. There is a major enhancement in power consumption. The suggested design cuts down power by 12.24 W to 8.228 W.
Fig. 9. Input Sample Image 1 (B) Output Image 1 (C) Input Sample Image 2 (D) Output Image
In the initial two images (A B), there is granular noise that can be observed all over the surface of the input image. The result of the bilateral filter (B) has a lot of noise reduction and retained the edges and object shapes. The filter blurs continuous areas but does not blur edges and this is clearly visible in the preserved sharpness of the features of circles and structure. The performance measures voice PSNR = 19.5990 dB SNR = 13.9549 dB, and show that the signal quality was improved over the noisy input. A similar effect is witnessed in the second pair (CD). The high frequency texture in the input image (C) is lowered in the output (D) that is filtered. Linear patterns and detail elements can also be seen and it is seen that the bilateral filter is effective in balancing noise minimization and edge conservation. The values of PSNR = 19.2602 dB and SNR = 14.5975 dB reported prove that the filtering process did not overly smooth the images and it provided an improvement in the picture quality.
Fig.10. Simulation waveform
Fig: 10 image presents the output of the bilateral filter design simulation waveform in case of functioning verification. Some of the signals that are found in the waveform are clk, write, start, pixel input data (pixel [31:0] or data in), and output signals (done, out, count [31:0]). Based on the timing diagram, the clock signal is running in an uninterrupted manner and this implies a synchronous work mode of the filter. The write and start control signals are asserted to start the process of filtering. The values on the pixe input are fed one at a time as observed in the evolving values of the data as time goes by. Following a processing, the processed signal is stabilized to a filtered signal (in the waveform 256). The done signal is used to signal the end of the filtering process, and is used to show that the bilateral filtering logic was properly implemented.
Fig. 11. Area
Fig: 11 indicates resource usage of your Bilateral Filter design when synthesized in the FPGA hardware. It does not actually display the filtered image, but instead the amount of FPGA area that one of your designs occupies, and the type of hardware blocks that you are using. Your design has 620 Slice LUTs and that implies that there is middle level of combinational logic needed. This reasoning is primarily based on comparing pixels, arithmetic, and making decisions that are required in the bilateral filter. The use of LUT is an indication that your implementation is quite efficient and not too complex. The number of Slice Registers utilized is very low, only 9. This means that you have a largely combinational design that does not have much pipelining or storage. This will save space, but may limit speed since long combinational routes decrease the highest clock frequency. The design employs 26 F7 multiplexers indicating that conditional choices are present in the design, e.g. between pixel values or dealing with boundary conditions in the filter window. Bonded IOBs are 115, and this implies that numerous input and output pins are utilized. This tends to occur when pixel information and control signals are attached directly to the pins of FPGA rather than being stored and read via internal memory such as BRAM.
Fig.12. Delay
Fig: 12 overall delay is approximately 8.14ns on the majority of paths. This implies that the highest safe clock rate is approximately 120 MHz (1/ 8.14 ns). Any attempt to run the design even faster than this can result in timing violations. High value of fanout 33 depicts that many logic blocks are driven by the signal pixel [2] concurrently. Great fanout upsurges latency and is typical in picture-processing designs where a single value of the pixel is utilized in numerous calculations.
Fig: 13 Total on-chip power
The output of this Fig: 13 indicates the power and thermal analysis of your bilateral filter FPGA design. The overall power on-chip is 8.228 W and of this is the dynamic power (switching activity in logic, routing, and I/O) and the static power (leakage). It is an indication that your design is relatively power-intensive, probably as a result of the high switching activity in the bilateral filter calculations and the large number of I/O signals. There is no specification on design power budget and therefore the tool cannot know whether this power consumption is within acceptable limit of your target board. Due to this fact, the margin of power budget is displayed as N/A. The definition of power budget is useful to assess the fact of tenure of whether the design would be safe and efficient. The cross-over temperature is 40.4 o C and that is well within the safe operating temperatures of an FPGA. This is to say that, despite the significant power consumption, the device is not overheating which is why the thermal conditions are stable.
- CONCLUSION
The suggested power-efficient FPGA implementation of the bilateral filter contributes in a significant manner to the viability of the real-time image denoising software and its use in the context of resource-limited settings. The design ensures that a significant power reduction is realized and a significant power- consumption controlled by the bilateral filter is specifically the range filter component and, by taking advantage of the parallel processing capabilities of FPGA, the operation of the bilateral filter is optimized to reduce power consumption without affecting the quality of the image. The experimental data confirms the fact that FPGA implementation even with a simple case of power consumption as well as running speed beats the traditional methods that are based on the CPU and therefore should be used in the embedded systems and mobile devices. Moreover, the design is scaled and flexible in its implementation, which improves its applicability in practice by multiple real-time image processing applications of different noise levels and image resolutions. The strategy has enabled the use of hardware-accelerated image denoising solutions, which are energy-efficient, to be contemplated, thus offering a way
forward to more developments in FPGA-based image processing systems.
- REFERENCE
- P. K. R. Maddikunta, Q.-V. Pham, B. Prabadevi, N. Deepa, andK. Dev, Industry 5.0: A survey on enabling technologies and potential applications, J. Ind. Inf. Integr., vol. 26, pp. 131, Mar. 2022.
- J. Nakamura, Image Sensors and Signal Processing for Digital Still Cameras. New York, NY, USA: Taylor & Francis, 2006, ch. 3, pp. 5590.
- D.-H. Shin, R.-H. Park, S. Yang, and J.-H. Jung, Block-based noise estimation using adaptive Gaussian filtering,IEEE Trans. Consum. Electron., vol. 51, no. 1, pp. 218226, Feb. 2005.
- C. Liu, W. T. Freeman, R. Szeliski, and S. B. Kang, Noise estimation from a single image, in Proc. IEEE CVPR, Jun. 2006, pp. 901908.
- B. Y. Kong and I.-C. Park, “Improved Sorting Architecture for K-Best MIMO Detection,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 64, no. 9, pp. 10421046, Sep. 2017.
- N. Govindaraju, J. Gray, R. Kumar, and D. Manocha, “GPUTeraSort: High-Performance Graphics Co-Processor Sorting for Large Database Management,” in Proc. ACM SIGMOD Int. Conf. Manag. Data, Jun. 2006, pp. 325336.
- J. Casper and K. Olukotun, “Hardware Acceleration of Database Operations,” in Proc. ACM/SIGDA FPGA, Monterey, CA, USA, 2014,
pp. 151160.
- H. Inoue, T. Moriyama, H. Komatsu, and T. Nakatani, “AA-Sort: A New Parallel Sorting Algorithm for Multi-Core SIMD Processors,” in Proc. 16th Int. Conf. Parallel Archit. Compilation Techn. (PACT), Sep. 2007,
pp. 189198.
- D. Merrill and A. Grimshaw, “High Performance and Scalable Radix Sorting: A Case Study of Implementing Dynamic Parallelism for GPU Computing,” Parallel Process. Lett., vol. 21, no. 2, pp. 245272, Jun. 2011.
- A. Davidson, D. Tarjan, M. Garland, and J. D. Owens, “Efficient Parallel Merge Sort for Fixed and Variable Length Keys,” in Proc. Innov. Parallel Comput. (InPar), 2012, pp. 19.
- J. Casper and K. Olukotun, “Hardware Acceleration of Database Operations,” in Proc. ACM/SIGDA FPGA, Monterey, CA, USA, 2014,
pp. 151160.
- J. Chhugani, A. D. Nguyen, V. W. Lee, W. Macy, M. Hagog, Y.-K. Chen,
A. Baransi, S. Kumar, and P. Dubey, “Efficient Implementation of Sorting on Multi-Core SIMD CPU Architecture,” Proc. VLDB Endowment, vol. 1, no. 2, pp. 13131324, 2008.
- R. Marcelino, H. C. Neto, and J. M. Cardoso, “Unbalanced FIFO Sorting for FPGA-Based Systems,” in 2009 16th IEEE ICECS, IEEE, 2009, pp. 431434.
- D. Koch and J. Torresen, “FPGA-Sort: A High-Performance Sorting Architecture Exploiting Run-Time Reconfiguration on FPGAs for Large Problem Sorting,” in Proc. 19th ACM/SIGDA International Symposium on FPGAs, ACM, 2011, pp. 4554.
- R. Mueller, J. Teubner, and G. Alonso, “Sorting Networks on FPGAs,” VLDB J. – Int. J. Very Large Data Bases, vol. 21, no. 1, pp. 123, 2012.
- D. Merrill and A. Grimshw, “High Performance and Scalable Radix Sorting: A Case Study of Implementing Dynamic Parallelism for GPU Computing,” Parallel Process. Lett., vol. 21, no. 2, pp. 245272, 2011.
- A. Davidson, D. Tarjan, M. Garland, and J. D. Owens, “Efficient Parallel Merge Sort for Fixed and Variable Length Keys,” in 2012 Innov. Parallel Comput. (InPar), IEEE, 2012, pp. 19.
- N. Tsuda, T. Satoh, and T. Kawada, “A Pipeline Sorting Chip,” in 1987 IEEE Int. Solid-State Circuits Conf. Dig. Technical Pap., vol. 30, IEEE, 1987, pp. 270271.
- B. Y. Kong, H. Yoo, and I.-C. Park, “Efficient Sorting Architecture for Successive-Cancellation-List Decoding of Polar Codes,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 63, no. 7, pp. 673677, 2016.H. Jiang,
- J. H. Santiago, H. Mo, L. Liu and J. Han, “Approximate arithmetic circuits: A survey characterization and recent applications”, Proc. IEEE, vol. 108, no. 12, pp. 2108-2135, Dec. 2020.
- S. Saha Ray and S. Ghosh, K-degree parallel comparison-free hardware sorter for complete sorting, IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 42, no. 5, pp. 14381449, May 2023.
