Updating cumulative distribution functions (CDFs) during arithmetic encoding can be a challenge because the final element of the CDF should remain fixed during the update calculations. If the probabilities were floating-point numbers, this would not be too much of a challenge; nevertheless, the probabilities and hence the CDFs are represented as integers to take advantage of infinite-precision arithmetic. Some of these difficulties may be alleviated by introducing a “mixing” CDF along with the active CDF being updated; the mixing CDF provides nonlocal context for updating the CDF due to the introduction of a particular symbol in the encoding. Improved techniques of performing arithmetic encoding include updating the CDF using two, one-dimensional mixing CDF arrays: a symbol-dependent array and a symbol-dependent array. The symbol-dependent array is a sub array of a larger, fixed array such that the sub array selected depends on the symbol being used.