An Analytical Approach for Error PMF Characterization in Approximate Circuits

ErrorModelingLPAA.pdf

“…The first assumption is an approximation when the circuit has reconvergent fanouts. However, it is a reasonable approximation in many cases as correlations are diluted as the logic depth increases, as argued in [15]. We do not have a rigorous justification for the second assumption, but estimates for Pĉ i are close to what is obtained using c −1 = 0 and working out the statistics for each bit location as in [4].…”

“…The expression for MSE also involves joint probabilities P (a i b i ) = P ai P bi and P (a i a j ), i = j. In addition to the assumption that the inputs are independent, we also assume that individual bits of each input are independent, which is a reasonal approximation as discussed in [15]. An exception to this method for deriving error models is ETA-I [6], where the lower part sum is not constructed using similar approximate full adders.…”

“…While the assumption of uniformly distributed lower order bits may be justified for the primary inputs, neither the output nor the error is uniformly distributed at the output of most LPAAs. A more accurate method of obtaining the probability mass function (PMF) of error is proposed in [15]. However, including this method within an optimization routine would require extensive computations.…”

AxHLS

“…As previously mentioned, faster explorations of approximate accelerator designs can be performed through analytical models to estimate accuracy and required resources. For the first, state-ofthe-art contributions have proposed methods to estimate the error propagation using error distributions of the approximate functional units used [18,20], mainly using a Probability Mass Function (PMF) to depict such error distributions [8,27]. In this context, a PMF represents the probability of a particular ED, and those values depend on the configuration of the approximate circuit.…”

“…Previous work has proposed models to estimate how the errors generated by approximate functional units accumulate and propagate to the outputs in approximate designs [8,20,27]. Due to the deterministic nature of the errors produced by reported approximate functional units (as considered in this work), their error distribution can be pre-characterized according to their bit-width and configuration.…”