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Canonical Huffman code

About: Canonical Huffman code is a research topic. Over the lifetime, 761 publications have been published within this topic receiving 11399 citations.


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Journal ArticleDOI
TL;DR: Four new results about Huffman codes are presented and a simple algorithm for adapting a Huffman code to slowly varying esthnates of the source probabilities is presented.
Abstract: In honor of the twenty-fifth anniversary of Huffman coding, four new results about Huffman codes are presented. The first result shows that a binary prefix condition code is a Huffman code iff the intermediate and terminal nodes in the code tree can be listed by nonincreasing probability so that each node in the list is adjacent to its sibling. The second result upper bounds the redundancy (expected length minus entropy) of a binary Huffman code by P_{1}+ \log_{2}[2(\log_{2}e)/e]=P_{1}+0.086 , where P_{1} is the probability of the most likely source letter. The third result shows that one can always leave a codeword of length two unused and still have a redundancy of at most one. The fourth result is a simple algorithm for adapting a Huffman code to slowly varying esthnates of the source probabilities. In essence, one maintains a running count of uses of each node in the code tree and lists the nodes in order of these counts. Whenever the occurrence of a message increases a node count above the count of the next node in the list, the nodes, with their attached subtrees, are interchanged.

593 citations

Journal ArticleDOI
TL;DR: This note shows how to maintain a prefix code that remains optimum as the weights change, preserving minimality of the weighted path length in a Huffman tree.

459 citations

Journal ArticleDOI
TL;DR: A new one-pass algorithm for constructing dynamic Huffman codes is introduced and analyzed, and it is shown that the number of bits used by the new algorithm to encode a message containing t letters is < t bits more than that use by the conventional two-pass Huffman scheme, independent of the alphabet size.
Abstract: A new one-pass algorithm for constructing dynamic Huffman codes is introduced and analyzed. We also analyze the one-pass algorithm due to Faller, Gallager, and Knuth. In each algorithm, both the sender and the receiver maintain equivalent dynamically varying Huffman trees, and the coding is done in real time. We show that the number of bits used by the new algorithm to encode a message containing t letters is

368 citations

Journal ArticleDOI
TL;DR: Results indicate that the proposed scheme can provide test data compression nearly equal to that of an optimum Huffman code with much less area overhead for the decoder.
Abstract: This paper presents a compression/decompression scheme based on selective Huffman coding for reducing the amount of test data that must be stored on a tester and transferred to each core in a system-on-a-chip (SOC) during manufacturing test. The test data bandwidth between the tester and the SOC is a bottleneck that can result in long test times when testing complex SOCs that contain many cores. In the proposed scheme, the test vectors for the SOC are stored in compressed form in the tester memory and transferred to the chip where they are decompressed and applied to the cores. A small amount of on-chip circuitry is used to decompress the test vectors. Given the set of test vectors for a core, a modified Huffman code is carefully selected so that it satisfies certain properties. These properties guarantee that the codewords can be decoded by a simple pipelined decoder (placed at the serial input of the core's scan chain) that requires very small area. Results indicate that the proposed scheme can provide test data compression nearly equal to that of an optimum Huffman code with much less area overhead for the decoder.

281 citations

Book
01 Sep 1999
TL;DR: This book discusses JPEG Compression Modes, Huffman Coding in JPEG, and Color Representation in PNG, the Representation of Images, and more.
Abstract: Preface. Acknowledgments. 1. Introduction. The Representation of Images. Vector and Bitmap Graphics. Color Models. True Color versus Palette. Compression. Byte and Bit Ordering. Color Quantization. A Common Image Format. Conclusion. 2. Windows BMP. Data Ordering. File Structure. Compression. Conclusion. 3. XBM. File Format. Reading and Writing XBM Files. Conclusion. 4. Introduction to JPEG. JPEG Compression Modes. What Part of JPEG Will Be Covered in This Book? What are JPEG Files? SPIFF File Format. Byte Ordering. Sampling Frequency. JPEG Operation. Interleaved and Noninterleaved Scans. Conclusion. 5. JPEG File Format. Markers. Compressed Data. Marker Types. JFIF Format. Conclusion. 6. JPEG Human Coding. Usage Frequencies. Huffman Coding Example. Huffman Coding Using Code Lengths. Huffman Coding in JPEG. Limiting Code Lengths. Decoding Huffman Codes. Conclusion. 7. The Discrete Cosine Transform. DCT in One Dimension. DCT in Two Dimensions. Basic Matrix Operations. Using the 2-D Forward DCT. Quantization. Zigzag Ordering. Conclusion. 8. Decoding Sequential-Mode JPEG Images. MCU Dimensions. Decoding Data Units. Decoding Example. Processing DCT Coefficients. Up-Sampling. Restart Marker Processing. Overview of JPEG Decoding. Conclusion. 9. Creating Sequential JPEG Files. Compression Parameters. Output File Structure. Doing the Encoding. Down-Sampling. Interleaving. Data Unit Encoding. Huffman Table Generation. Conclusion. 10. Optimizing the DCT. Factoring the DCT Matrix. Scaled Integer Arithmetic. Merging Quantization and the DCT. Conclusion. 11. Progressive JPEG. Component Division in Progressive JPEG. Processing Progressive JPEG Files. Processing Progressive Scans. MCUs in Progressive Scans. Huffman Tables in Progressive Scans. Data Unit Decoding. Preparing to Create Progressive JPEG Files. Encoding Progressive Scans. Huffman Coding. Data Unit Encoding. Conclusion. 12. GIF. Byte Ordering. File Structure. Interlacing. Compressed Data Format. Animated GIF. Legal Problems. Uncompressed GIF. Conclusion. 13. PNG. History. Byte Ordering. File Format. File Organization. Color Representation in PNG. Device-Independent Color. Gamma. Interlacing. Critical Chunks. Noncritical Chunks. Conclusion. 14. Decompressing PNG Image Data. Decompressing the Image Data. Huffman Coding in Deflate. Compressed Data Format. Compressed Data Blocks. Writing the Decompressed Data to the Image. Conclusion. 15. Creating PNG Files. Overview. Deflate Compression Process. Huffman Table Generation. Filtering. Conclusion. Glossary. Bibliography. Index. 0201604434T04062001

190 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202216
20211
20202
201715
201616