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Evaluation analytique de la précision des systèmes en virgule fixe pour des applications de communication numérique

Aymen Chakhari 1
1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
Abstract : In designing applications of signal processing, the traditional approach leads the designer of appli- cations to use initially floating point arithmetic in order to avoid problems related to the accuracy of calculations. However, the implementation of these applications requires the use of fixed-point arithmetic because it is more advantageous in terms of constraints of cost and consumption. Therefore, the designed application in floating point arithmetic must be converted to fixed-point arithmetic. This conversion is tedious, so tools for automatic conversion of floating-point arithmetic to the fixed point were established to meet the requirements of time-to-market of these applications. In this conversion process, one of the basic steps concerns the evaluation of the accuracy of the fixed-point specification. Indeed, the change of the data format of the application is performed by removing bits. This conversion results in the generation of quantization noise propagating within the system and degrading the accuracy of calculations of the application output. Therefore, this reduction in the calculation accuracy must be mastered and evaluated in order to ensure the integrity of the algorithm and meet the initial requirements of the application. Traditionally, evaluation of accuracy is performed through two different approaches. The first approach is to perform simulations fixed-point implementation in order to assess its performance. These approaches based on simulation require large computing capacities and lead to prohibitive time evaluation. To avoid this problem, the work done in this thesis focuses on approaches based on the accuracy evaluation through analytical models. These models describe the behavior of the system through analytical expressions that evaluate a defined metric of precision. Several analytical models have been proposed to evaluate the fixed- point accuracy of Linear Time Invariant systems (LTI) and of non-LTI non-recursive and recursive linear systems. The objective of this thesis is to propose analytical models to evaluate the accuracy of digital communications systems and algorithms of digital signal processing made up of non-smooth and non-linear operators in terms of noise. In a first step, analytical models for evaluation of the accuracy of decision operators and their iterations and cascades are provided. In a second step, an optimization of the data length is given for fixed-point hardware implementation of the Decision Feedback Equalizer DFE based on analytical models proposed and for iterative decoding algorithms such as turbo decoding and LDPC decoding-(Low-Density Parity-Check) in a particular quantization law. The first aspect of this work concerns the proposition analytical models for evaluating the accuracy of the non-smooth decision operators and the cascading of decision operators. So, the characterization of the quantization errors propagation in the cascade of decision operators is the basis of the proposed analytical models. These models are applied in a second step to evaluate the accuracy of the spherical decoding algo- rithm SSFE (Selective Spanning with Fast Enumeration) used for transmission MIMO systems (Multiple- Input Multiple - Output). In a second step, the accuracy evaluation of the iterative structures of decision operators has been the interesting subject. Characterization of quantization errors caused by the use of fixed-point arithmetic is introduced to result in analytical models to evaluate the accuracy of application of digital signal processing including iterative structures of decision. A second approach, based on the estimation of an upper bound of the decision error probability in the convergence mode, is proposed for evaluating the accuracy of these applications in order to reduce the evaluation time. These models are applied to the problem of evaluating the fixed-point specification of the Decision Feedback Equalizer DFE. An extension of these models is introduced for the evaluation of DFE in its adaptive version. The second aspect of our work focuses on the optimization of fixed-point data widths. This optimi- zation process is based on minimizing the decision error probability through the implementation on an FPGA (Field-Programmable Gate Array) of the complex DFE algorithm under the constraint of a given accuracy. Therefore, for each fixed-point specification, accuracy is evaluated through the proposed analy- tical models. The estimation of resources and power consumption on the FPGA is then obtained using the Xilinx tools to make a proper choice of the data widths aiming to a compromise accuracy/cost. The last step of our work concerns the fixed-point modeling of iterative decoding algorithms. A model of the turbo decoding algorithm and the LDPC decoding is then given. This approach integrates the particular structure of these algorithms which implies that the calculated quantities in the decoder and the operations are quantified following an iterative approach. Furthermore, the used fixed-point representation is different from the conventional representation using the number of bits accorded to the integer part and the fractional part. The proposed approach is based on the dynamic and the total number of bits. Besides, the dynamic choice causes more flexibility for fixed-point models since it is not limited to only a power of two. In a second step, the memory size reduction using saturation and truncation techniques is given in order to be able to target low - complexity architectures. Finally, the fixed-point performance analysis is done through the evaluation of Frame Error Ratio FER versus SNR (Signal to Noise Ratio) package.
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Submitted on : Friday, December 19, 2014 - 9:29:16 AM
Last modification on : Thursday, January 20, 2022 - 4:13:11 PM
Long-term archiving on: : Monday, March 23, 2015 - 5:32:37 PM


  • HAL Id : tel-01097176, version 1


Aymen Chakhari. Evaluation analytique de la précision des systèmes en virgule fixe pour des applications de communication numérique. Traitement du signal et de l'image [eess.SP]. Université de Rennes 1, 2014. Français. ⟨tel-01097176⟩



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