11. Error Analysis and Optimization in Approximate Arithmetic Circuits

This chapter presents a comprehensive study of various error analysis methodologies for evaluating the accuracy of approximate circuits, and the importance of such methodologies in their design. Although approximate circuits leverage the inherent perceptual limitations of human senses, they should be deployed in a manner that does not compromise user experience. In other words, the errors introduced due to using approximate circuits should be within acceptable margins. These margins depend on the target applications, and a systematic approach is required to ensure that the designed approximate circuit indeed meets the specifications in terms of the margins. The first step in achieving this goal is to obtain the error introduced in the output of the circuit due to approximation, and the first part of this chapter discusses various metrics to quantify that error. Since the error not only depends on the circuit structure, but also on the input vectors, these metrics are derived statistically. The error is then modeled as a function of various design parameters of the circuit, as well as the statistics of the input vector. The second part of the chapter discusses these modeling techniques in detail for various types of approximate circuits. Finally, the error model is utilized during the design phase to limit the maximum inaccuracy in approximate circuits. In other words, similar to the timing, power, and area constraints in regular circuit design, error is treated as an additional constraint for approximate circuit design. In this connection, the last part of this chapter discusses a set of optimization algorithms for circuit design using this additional error constraint.