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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).
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]
For the example mentioned above, the encoding becomes: (1,1,2), ('B','A','C','D') This means that the first symbol B is of length 1, then the A of length 2, and remaining 2 symbols (C and D) of length 3. Since the symbols are sorted by bit-length, we can efficiently reconstruct the codebook.
Modified Huffman coding is used in fax machines to encode black-on-white images . It combines the variable-length codes of Huffman coding with the coding of repetitive data in run-length encoding . The basic Huffman coding provides a way to compress files with much repeating data, like a file containing text, where the alphabet letters are the ...
Truncated binary encoding is a straightforward generalization of fixed-length codes to deal with cases where the number of symbols n is not a power of two. Source symbols are assigned codewords of length k and k+1, where k is chosen so that 2 k < n ≤ 2 k+1. Huffman coding is a more sophisticated technique for constructing variable-length ...
Second and third bits: Encoding method used for this block type: 00: A stored (a.k.a. raw or literal) section, between 0 and 65,535 bytes in length; 01: A static Huffman compressed block, using a pre-agreed Huffman tree defined in the RFC; 10: A dynamic Huffman compressed block, complete with the Huffman table supplied; 11: Reserved—don't use.
The next step is to encode this ternary number using a fixed-point binary number of sufficient precision to recover it, such as 0.0010110001 2 – this is only 10 bits; 2 bits are saved in comparison with naïve block encoding. This is feasible for long sequences because there are efficient, in-place algorithms for converting the base of ...
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages. Checksum schemes include parity bits, check digits, and longitudinal redundancy checks.