In information theory, symbol coding-lengths {coding length} are inversely proportional to symbol probability, compared to other possible symbols. Number of bits needed equals negative of base-2 logarithm of probability. More-frequently-occurring symbols can use shorter-length strings, while less-frequently-occurring symbols can use longer strings {variable length code}. String length can increase to provide more redundancy {geometric code}.
Instead of binary code, codes can represent series, to make total length shorter {compression, information}. Instead of using 0 series, code can denote series length. For example, 000000000000000 can have code 1111, because number of 0's is 15.
symbol number
Compression requires that code has few symbols, allowing more repetition.
predictability
Series make predictability high. If predictability is high, number of possible states is less, and code can use fewer information bits.
arithmetic coding
Symbol probability can be relative symbol memory-amount needed.
amount
Maximum compression is about 100 times.
no compression
If system can have new elements, bits must be independent, allowing no compression.
Information can change from analog into digital form {Gray code}. Analog changes can change digital code by one.
String length can be inversely proportional to symbol or state probability {Huffman code}.
Coding {instantaneous code} can use no prefixes, so no reverse processing is necessary.
Modulo 37 can progressively digitize message, because 37 is prime {modulo-37 arithmetic}.
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Date Modified: 2022.0225