Computation of cyclic redundancy checks may use whichever form is more convenient. Parallel update for a byte or a word at a time can also be done explicitly, without a table. This is normally used in high-speed hardware implementations. For each bit an equation is solved after 8 bits have been shifted in. The following tables list the equations for some commonly used polynomials, using following symbols: As the CRC-32 polynomial has a large number of terms, when computing the remainder a byte at a time each bit depends on several bits of the previous iteration. In byte-parallel hardware implementations this calls for either multiple-input
Stochastic computing computing paradigm. Further information can be found in the referenced book by Mars and Poppelbaum. "Bundle Processing" involves sending a fixed number of bits instead of a stream. One of the advantages of this approach is that the precision is improved. To see why, suppose we transmit formula_26 bits. In regular stochastic computing, we can represent a precision of roughly formula_27 different values, because of the variance of the estimate. In bundle processing, we can represent a precision of formula_28. However, bundle processing retains the same robustness to error of regular stochastic processing. "Ergodic Processing" involves sending a stream of