Huffman coding research paper

Following the single DC component entry, one or more entries are used to describe the remaining 63 entries in the MCU. These entries (1..63) represent the low and high-frequency AC coefficients after DCT transformation and quantization. The earlier entries represent low-frequency content, while the later entries represent high-frequency image content. Since the JPEG compression algorithm uses quantization to reduce many of these high-frequency values to zero, one typically has a number of non-zero entries in the earlier coefficients and a long run of zero coefficients to the end of the matrix.

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The p-adic numbers provides clear interpretation of the algorithm. In fact, all the intermediate data and the result can be seen as p-adic integers with p=2. The modified algorithm operates on p-adic semi intervals in the same way, as the original works with real semi intervals. For example the magic rules E1, E2 mean that the current p-adic semi interval lies completely in a p-adic ball. In this case the p-adic ball can be pushed out and p-adic semi interval rescaled. From this point of view Huffman algorithm is just a specific variant of arithmetic coding when semi intervals are always p-adic balls.

Huffman coding research paper

huffman coding research paper

The p-adic numbers provides clear interpretation of the algorithm. In fact, all the intermediate data and the result can be seen as p-adic integers with p=2. The modified algorithm operates on p-adic semi intervals in the same way, as the original works with real semi intervals. For example the magic rules E1, E2 mean that the current p-adic semi interval lies completely in a p-adic ball. In this case the p-adic ball can be pushed out and p-adic semi interval rescaled. From this point of view Huffman algorithm is just a specific variant of arithmetic coding when semi intervals are always p-adic balls.

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