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Huffman tree generated from the exact frequencies of the text "this is an example of a huffman tree". Encoding the sentence with this code requires 135 (or 147) bits, as opposed to 288 (or 180) bits if 36 characters of 8 (or 5) bits were used (This assumes that the code tree structure is known to the decoder and thus does not need to be counted as part of the transmitted information).
5- substitute the selected messages by a composite message summing their probability, and re-order it. 6- while there remains more than one message, do steps thru 8. 7- select D least probable messages, and assign them each a digit code. 8- substitute the selected messages by a composite message summing their probability, and re-order it.
The optimal length-limited Huffman code will encode symbol i with a bit string of length h i. The canonical Huffman code can easily be constructed by a simple bottom-up greedy method, given that the h i are known, and this can be the basis for fast data compression. [2]
A code is non-singular if each source symbol is mapped to a different non-empty bit string; that is, the mapping from source symbols to bit strings is injective.. For example, the mapping = {,,} is not non-singular because both "a" and "b" map to the same bit string "0"; any extension of this mapping will generate a lossy (non-lossless) coding.
UTF-8-encoded, preceded by varint-encoded integer length of string in bytes Repeated value with the same tag or, for varint-encoded integers only, values packed contiguously and prefixed by tag and total byte length — Smile \x21
The type and length are fixed in size (typically 1–4 bytes), and the value field is of variable size. These fields are used as follows: Type A binary code, often simply alphanumeric, which indicates the kind of field that this part of the message represents; Length The size of the value field (typically in bytes); Value
An encoded match to an earlier string consists of an 8-bit length (3–258 bytes) and a 15-bit distance (1–32,768 bytes) to the beginning of the duplicate. Relative back-references can be made across any number of blocks, as long as the distance appears within the last 32 KiB of uncompressed data decoded (termed the sliding window ).
But an integer number of bits must be used in the binary encoding, so an encoder for this message would use at least 8 bits, resulting in a message 8.4% larger than the entropy contents. This inefficiency of at most 1 bit results in relatively less overhead as the message size grows.