Error analysis of correlation dependent stochastic circuit

Abstract

Stochastic computing has emerged as an important research area because of its low hardware requirements and error tolerance. In stochastic computing, many things are important, like random number generation, derandomizer unit, correlation among input values, etc. Here, each number is represented as a sequence of random bit streams where the probability of 1 is taken as its value. Stochastic circuits perform well under severe error conditions. Here, the design of stochastic computing circuits is such that many errors have a very negligible impact because if one bit flip occurs in the entire bit stream, then there is a negligible impact on the result. However, this is relevant that noisy channels, such as binary symmetric channels and binary asymmetric channels, will impact the processes of stochastic computing. We can also expect some robustness against those types of errors in stochastic circuits. However, Alaghi showed that we can expert correlation to make some complicated functions using very simple circuits. In this thesis, it is shown that conventional basic circuits like AND, OR, and XOR can be used with the help of correlation to get certain functions like absolute difference, multiplication, addition, etc. This type of circuit depends on correlation. Hence, apart from channel noise, there is an additional source of noise that is due to the correlation value. Suppose we generate an approximate circuit for a complex function that is dependent on the correlation value to be +1, 0, or in a minor case, say 0.6. But, there is no guarantee that the generation process is capable of generating exact values with high precision enough to meet the exact correlation. Hence, the input sequence is slightly different from the correlation needed to achieve the complex functionality. Here, the functions of the circuits depend on the correlation itself. An XOR gate is used to perform absolute subtraction between two bit streams. There, correlation plays an important role because we want the inputs to be perfectly correlated, which will be +1. It might so happen that the correlation gets slightly reduced. That result of a slight error will impact the calculation of absolute subtraction. So, the same error will propagate everywhere this output is used. Whenever such a scenario happens, the output will be slightly erroneous and any other functionality that uses the same output will see the same error propagate through multiple stages of the stochastic circuit. Hence, the output of a circuit design exploiting correlation is dependent on the particular correlation value of the input sequences. Thus, it is important to study how the output performs when the actual correlation between the inputs varies. This thesis stochastically analysed the error pattern and suggested what level of deviation from the required correlation value (to perform a particular operation) can be tolerated.