Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Stochastic computing is distinct from the study of randomized algorithms.
Stochastic computing was first introduced in a pioneering paper by John von Neumann in 1953. However, the theory could not be fully developed until advances in computing of the 1960s,  mostly through a series of simultaneous and parallel efforts in the US and the UK. By the late 1960s, attention turned to the design of special-purpose hardware to perform stochastic computation. A host of these machines were constructed between 1969 and 1974; RASCEL is pictured in this article.
Despite the intense interest in the 1960s and 1970s, stochastic computing ultimately failed to compete with more traditional digital logic, for reasons outlined below. The first (and last) International Symposium on Stochastic Computing took place in 1978; active research in the area dwindled over the next few years.
Although stochastic computing declined as a general method of computing, it has shown promise in several applications. Research has traditionally focused on certain tasks in machine learning and control.  Somewhat recently, interest has turned towards stochastic decoding, which applies stochastic computing to the decoding of error correcting codes. More recently, stochastic circuits have been successfully used in image processing tasks such as edge detection  and image thresholding.
Although stochastic computing has a number of defects when considered as a method of general computation, there are certain applications that highlight its strengths. One notable case occurs in the decoding of certain error correcting codes.
In developments unrelated to stochastic computing, highly effective methods of decoding LDPC codes using the belief propagation algorithm were developed. Belief propagation in this context involves iteratively reestimating certain parameters using two basic operations (essentially, a probabilistic XOR operation and an averaging operation).
In 2003, researchers realized that these two operations could be modeled very simply with stochastic computing. Moreover, since the belief propagation algorithm is iterative, stochastic computing provides partial solutions that may lead to faster convergence. Hardware implementations of stochastic decoders have been built on FPGAs.  The proponents of these methods argue that the performance of stochastic decoding is competitive with digital alternatives.
Deterministic Methods to Stochastic Computing
Deterministic methods of SC has been developed to perform completely accurate computation with SC circuits. The essential principle of these methods is that every bit of one bit-streams interacts with every bit of the other bit-streams exactly once. To produce completely accurate result with these methods, the operation must run for the product of the length of input bit-streams. Deterministic methods are developed based on unary bit-streams, pseudo-random bit-streams, and low-discrepancy bit-streams.
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