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Besides using entropy coding as a way to compress digital data, an entropy encoder can also be used to measure the amount of similarity between streams of data and already existing classes of data. This is done by generating an entropy coder/compressor for each class of data; unknown data is then classified by feeding the uncompressed data to ...
For this example it is assumed that the decoder knows that we intend to encode exactly five symbols in the base 10 number system (allowing for 10 5 different combinations of symbols with the range [0, 100000)) using the probability distribution {A: .60; B: .20; <EOM>: .20}. The encoder breaks down the range [0, 100000) into three subranges:
Arithmetic coding applies especially well to adaptive data compression tasks where the statistics vary and are context-dependent, as it can be easily coupled with an adaptive model of the probability distribution of the input data. An early example of the use of arithmetic coding was in an optional (but not widely used) feature of the JPEG ...
Initialize the data model as per agreement. While there is more data to receive Decode the next symbol using the data model and output it. Modify the data model based on the decoded symbol. Any adaptive coding method has a corresponding static model method, in which the data model is precalculated and then transmitted with the data.
Data can be seen as a random variable:, where appears with probability [=].. Data are encoded by strings (words) over an alphabet.. A code is a function : (or + if the empty string is not part of the alphabet).
The encoder divides the current interval into sub-intervals, each representing a fraction of the current interval proportional to the probability of that symbol in the current context. Whichever interval corresponds to the actual symbol that is next to be encoded becomes the interval used in the next step. Example: for the four-symbol model above:
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
Autoencoders are often trained with a single-layer encoder and a single-layer decoder, but using many-layered (deep) encoders and decoders offers many advantages. [2] Depth can exponentially reduce the computational cost of representing some functions. Depth can exponentially decrease the amount of training data needed to learn some functions.