These restrictions do not binary options winning formula pdf to jpg to normal “fair use”, defined as cited quotations totaling less than one page. About this Book This book is for the reader who wants to understand how data compression works, or who wants to write data compression software. Prior programming ability and some math skills will be needed.
This book is intended to be self contained. Sources are linked when appropriate, but you don’t need to click on them to understand the material. Information Theory Data compression is the art of reducing the number of bits needed to store or transmit data. Compression can be either lossless or lossy.
Losslessly compressed data can be decompressed to exactly its original value. Each letter of the alphabet is coded as a sequence of dots and dashes. The most common letters in English like E and T receive the shortest codes. The coder assigns shorter codes to the more likely symbols. There are efficient and optimal solutions to the coding problem.
However, optimal modeling has been proven not computable. Lossy compression discards “unimportant” data, for example, details of an image or audio clip that are not perceptible to the eye or ear. An example is the 1953 NTSC standard for broadcast color TV, used until 2009. Lossy compression consists of a transform to separate important from unimportant data, followed by lossless compression of the important part and discarding the rest.
The transform is an AI problem because it requires understanding what the human brain can and cannot perceive. There is no such thing as a “universal” compression algorithm that is guaranteed to compress any input, or even any input above a certain size. In particular, it is not possible to compress random data or compress recursively. Efficient and optimal codes are known. Data has a universal but uncomputable probability distribution. M in bits, almost independent of the language in which M is written.
There is no algorithm that tests for randomness or tells you whether a string can be compressed any further. Suppose there were a compression algorithm that could compress all strings of at least a certain size, say, n bits. There are exactly 2n different binary strings of length n. A universal compressor would have to encode each input differently. In fact, the vast majority of strings cannot be compressed by very much. The fraction of strings that can be compressed from n bits to m bits is at most 2m – n. Every compressor that can compress any input must also expand some of its input.
However, the expansion never needs to be more than one symbol. Any compression algorithm can be modified by adding one bit to indicate that the rest of the data is stored uncompressed. The counting argument applies to systems that would recursively compress their own output. In general, compressed data appears random to the algorithm that compressed it so that it cannot be compressed again. Coding is Bounded Suppose we wish to compress the digits of π, e.
Assume our model is that each digit occurs with probability 0. 1, independent of any other digits. Digit BCD Huffman Binary —- —- —- —- 0 0000 000 0 1 0001 001 1 2 0010 010 10 3 0011 011 11 4 0100 100 100 5 0101 101 101 6 0110 1100 110 7 0111 1101 111 8 1000 1110 1000 9 1001 1111 1001 — —- —- —- bpc 4. The code is uniquely decodable because no code is a prefix of any other code. The binary code is not uniquely decodable. For example, 111 could be decoded as 7 or 31 or 13 or 111. There are better codes than the Huffman code given above.
For example, we could assign Huffman codes to pairs of digits. There are 100 pairs each with probability 0. The average code length is 6. 72 bits per pair of digits, or 3.