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You are permitted to copy and distribute material from this book provided (1) any material you distribute includes this license, (2) the material is not modified, and (3) you do not charge a fee or require any other considerations for copies or for any works that incorporate material from this book. Sources are linked when appropriate, but you don't need to click on them to understand the material.These restrictions do not apply to normal "fair use", defined as cited quotations totaling less than one page. Data compression is the art of reducing the number of bits needed to store or transmit data. 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.A universal compressor would have to encode each input differently.Otherwise, if two inputs compressed to the same output, then the decompresser would not be able to decompress that output correctly. For example, less than 0.4% of strings can be compressed by one byte.
Prior programming ability and some math skills will be needed.
The decompresser would decode the data by dividing it into 4 bit strings. The decoder would read bits one at a time and decode a digit as soon as it found a match in the table (after either 3 or 4 bits). For example, 111 could be decoded as 7 or 31 or 13 or 111.
The code is uniquely decodable because no code is a prefix of any other code. There are better codes than the Huffman code given above.
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. Assume our model is that each digit occurs with probability 0.1, independent of any other digits.