Tham khảo tài liệu 'a concise introduction to data compression- p2', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 60 1. Approaches to Compression 4. The matrix of Equation is a rotation matrix in two dimensions. Use books on geometric transformations to understand rotations in higher dimensions. 5. Prepare an example of vector quantization similar to that of Figure . The best angle from which to approach any problem is the try-angle. Unknown Please purchase PDF Split-Merge on to remove this watermark. 2 Huffman Coding Prelude Huffman coding is a popular method for compressing data with variable-length codes. Given a set of data symbols an alphabet and their frequencies of occurrence or equivalently their probabilities the method constructs a set of variable-length codewords with the shortest average length and assigns them to the symbols. Huffman coding serves as the basis for several applications implemented on popular platforms. Some programs use just the Huffman method while others use it as one step in a multistep compression process. The Huffman method Huffman 52 is somewhat similar to the Shannon-Fano method proposed independently by Claude Shannon and Robert Fano in the late 1940s Shannon 48 and Fano 49 . It generally produces better codes and like the Shannon-Fano method it produces the best variable-length codes when the probabilities of the symbols are negative powers of 2. The main difference between the two methods is that Shannon-Fano constructs its codes from top to bottom and the bits of each codeword are constructed from left to right while Huffman constructs a code tree from the bottom up and the bits of each codeword are constructed from right to left . Since its inception in 1952 by D. Huffman the method has been the subject of intensive research in data compression. The long discussion in Gilbert and Moore 59 proves that the Huffman code is a minimum-length code in the sense that no other encoding has a shorter average length. A much shorter proof of the same fact was discovered by Huffman himself Motil 07 . An algebraic approach to
