The paper will present a compression algorithm that will allow for both random and non-random sequential binary strings of data to be compressed for storage and transmission of media information. The compression system has direct applications to the storage and transmission of digital media such as movies, television, audio signals and other visual and auditory signals needed for engineering practicalities in such industries.
The algorithmic compression program addressed in this paper was discovered by the author in 1998 as the only known algorithm that could ‘compress’ a random binary sequential string . The key features of this algorithmic program are that they can be used on both random and non-random sequential strings of binary, and larger radix base numbers, and that both universal, whole, and specific, partial, aspects of compression of a linear sequential string can be utilized .
The foundational aspects of this algorithm are that it treats all aspects of a linear sequential string as a concatenation of symbols that are based on the relevancy of the type of symbol, the placement of that symbol, upon a linear sequential string, and the adjoining symbols that my come before and after that specific symbol . In other words, the environment that each and every specific symbol is upon a linear sequential string. In literature, the notion of a non-random sequential binary string is as follows:
Non-random binary sequential string: 1010101010
A random sequential binary string is as follows:
Random binary sequential string: 11101000011001111100
Notice that the non-random sequential binary string has a pattern of ‘regularity’ to it that has a 1 in the initial position followed by 0’s and 1’s for a collective of alternating five 1’s and five 0’s for a total of 10 characters and is able to be compressed and de-compressed to its original form .
The random sequential binary string has a ‘less’ harmonious, or balanced, pattern of symbols and is considered by traditional literature on the subject as being unable to compress .
Foundations – Examples
The following example, Example A, will be used to show the compression of a non-random binary sequential string:
Non-random sequential binary string:  of a total length of 20 symbols.
A practical notation for compression of the 20 symbols is to have the initials of the two different symbols;  and , and a symbol for a multiple of those two symbols [x] and for the number of times both symbols;  and , are accounted for in their respective place in the collective whole of the string, ten times, ten [1’s] and ten [0’s]. This results in the following formula: 10x10.
This compression can be notated as the following:  or a two, 2, character length.
Note that the figures  and  are not numbers, quantities, but rather qualities of divergence, separate values based on symbolic rather than numerical value. In other words, a  is the ‘symbol’ one rather than the number 1 and the figure  is the symbol zero rather than the numerical value of 0.
The random binary sequential string is compressed in Example B;
Random binary sequential string:  of a total length of 20 symbols.
Example B can be grouped into subdivisions of the whole by taking each common cluster of common, or like-natured, symbols into sub-groups of the complete string.
Sub-groups of a random binary sequential string as found in Example B:
The resulting eight sub-groups provide for specific compression of each sub-group as follows:
This compression can be notated as the following:  or an eight, 8, character length.
Applications to Visual and Auditory Signals
The author originally designed the compression algorithm for telecommunications and computing applications . The same qualities that give maximal compression to data signals also has direct applications to visual and auditory signals used in the various media arts industry that transmit and store digital data. In other words, compressed data for the movie industry.
Existing compression coding systems, such as Huffman coding, are not optimal when symbol-by-symbol coding is not used for lossless data compression . While Huffman and arithmetic coding compression is superior to universal coding compression, universal code compression is simple and quick compared to Huffman coding .
In some respects all these older compression systems have a common extraneous feature of a ‘prefix’ code the is part of the core data and ‘added on’ like an arcane ‘punch card’ computer program. While necessary for the operation of these compression code systems the development of a ‘prefix’ free operating system has been developed by the author in the form of a simple computer system and my compression algorithm program .