Data Compression and encryption for security
- 1. Data Compression and Encryption- (DCE) TE-EXTC-Elective Subject
- 4. What is Data Compression? • Data can be Text, image, audio or video information • Data compression is about storing and sending a smaller number of bits. . • Data compression is the art or science of representing information in a compact form. • We create these compact representations by identifying and using structures that exist in the data.
- 5. How data compression is possible DATA = INFORMATION + REDUNDANT DATA
- 7. Need of data compression? • Less storage space • Less transmission time • Reduced Bandwidth. • During compression data is converted in coded form, that secures the information.
- 9. Application • In Satellite Communication • In Radar • In Mobile Communication • In Digital Television • In Banking Software • Medical applications and so on..
- 11. Data Compression Techniques 1. Lossless Compression Techniques: No loss of information Original data can be recovered exactly from compressed data Loss of information is not tolerable Lower compression ratio Fidelity and Quality is high Highly Robust and Reliable Distortion is less Rate is high Text and Image compression Lossless Algorithm: Huffman coding, Arithmetic coding Applications: Medical, Satellite, Banking etc.
- 12. Data Compression Techniques 2. Lossy Compression Techniques: Some loss of information Original data cannot be recovered exactly from compressed data Higher compression ratio Loss of information is tolerable Fidelity and Quality is low Less Robust and Reliable Distortion is more. Rate is low Audio and Video compression Lossy Algorithm : MPEG,JPEG etc. Applications: Telephone, Mobile,Tv etc.
- 13. Measure of performance A compression algorithm can be evaluated in different ways: 1. Relative complexity of algorithm 2. Memory required to implement the algorithm 3. How fast the algorithm, performs on given machine 4. Amount of compression 5. How close reconstruction resembles the original data
- 14. Measure of performance cont.. 1. Compression Ratio: CR = If CR<1 = then there is expansion instead of compression. This is known as negative compression. The compression ratio is always greater than 1.
- 15. Measures of Performance 2. Compression Factor: • Compression factor is inverse of compression ratio. • CF= • Compression factor is always less than 1. • If CF>1 then there is expansion instead of compression. • Thus smaller the factor better the compression.
- 16. Measure of performance cont.. 3. Rate: • Average number of bits required to represent a single sample is called rate. • Eg. Image compression (bits/pixel). 4. Distortion: • The difference between original data and reconstructed data is called distortion. • Eg. Lossy compression
- 17. Measure of performance cont.. 5. Performance measure speed: • Speed of compression can be measured by cycle/byte. • It is important when compression is done by special hardware. 6. Fidelity and Quality: • It indicates the difference between reconstructed and original data. • When fidelity and quality is high, means difference between reconstructed and original data is small. • Eg. Lossless compression(image/text)
- 18. Lossless Compression • Lossless compression techniques, as their name implies, involve no loss of information. • If data have been losslessly compressed, the original data can be recovered exactly from the compressed data. • Lossless compression is generally used for applications that cannot tolerate any difference between the original and reconstructed data. • Text compression is an important area for lossless compression. It is very important that the reconstruction is identical to the text original, as very small differences can result in statements with very different meanings.
- 19. Classification of Lossless Compression Techniques Lossless techniques are classified into static, adaptive (or dynamic), and hybrid. • In a static method the mapping from the set of messages to the set of code words is fixed before transmission begins, so that a given message is represented by the same codeword every time it appears in the message being encoded. • Static coding requires two passes: one pass to compute probabilities (or frequencies) and determine the mapping, and a second pass to encode. • Examples: Static Huffman Coding • In an adaptive method the mapping from the set of messages to the set of code words changes over time. • All of the adaptive methods are one-pass methods; only one scan of the message is required. • Examples: LZ77, LZ78, LZW, and Adaptive Huffman Coding • An algorithm may also be a hybrid, neither completely static nor completely dynamic.
- 21. Lossy Compression • Lossy compression techniques involve some loss of information, and data that have been compressed using lossy techniques generally cannot be recovered or reconstructed exactly. • In return for accepting this distortion in the reconstruction, we can generally obtain much higher compression ratios than is possible with lossless compression. • In many applications, this lack of exact reconstruction is not a problem. For example, when storing or transmitting speech, the exact value of each sample of speech is not necessary. • Depending on the quality required of the reconstructed speech, varying amounts of loss of information about the value of each sample can be tolerated.
- 22. Compression Utilities and Formats • Compression tool examples: winzip, pkzip, compress, gzip „ • General compression formats: .zip, .gz „ • Common image compression formats: JPEG, JPEG 2000, BMP, GIF, PCX, PNG, TGA, TIFF, WMP • Common audio (sound) compression formats: MPEG-1 Layer III (known as MP3), RealAudio (RA, RAM, RP), AU, Vorbis, WMA, AIFF, WAVE, G.729a • Common video (sound and image) compression formats: MPEG-1, MPEG-2, MPEG-4, DivX, Quicktime (MOV), RealVideo (RM), Windows Media Video ( WMV), Video for Windows ( AVI), Flash video (FLV)
- 23. Modeling and Coding An compression technique which work well for the compression of text may not work well for compressing images. Development of data compression algorithm for a variety of data is divided into two phases: 1. Modeling 2. Coding Modeling: • In this method we try to extract information about redundancy that exist in the data & describes the redundancy in the form of model. • The description of model and description how data differs from model are encoded generally using binary. • The difference between data and model is often referred to as residual. • We can obtain compression by transmitting or storing the parameters of the model and the residual sequence.
- 24. Modeling and Coding Coding: • In this we perform different arithmetic operations on modeled data according to simplicity & quality required. • There are different coding techniques used for compression of data are Huffman coding, Shannon fano coding, Arithmetic coding.
- 25. Different MODELS • Physical Models • Probability Models • Markov Models • Composite Source Model Different Coding • Uniquely Decodable Codes • Prefix Codes • Huffman Codes • Shannon Fanon Codes
- 26. Different Types of Models 1. Physical Model: • If we know something about physics of data generation process, we can use that information to reconstruct the model, this model called as physical model. • Eg: In speech applications, the knowledge about the physics of speech production is used to construct mathematical model for sampled speech process. • Sample speech is encoded using this model. • The physics of data generation is too complicated to understand so the are rarely used.
- 27. Different Types of Models cont.. 2. Probability Model: • This model is used when there is no any idea about statics of source. • In this model the probability of redundant letters are calculated which are generated from source. • It assumes that each letter generated by source is independent of every other letter and so this model is called as “ignorance model”. • It is useful for text and image compression.
- 28. Different Types of Models cont.. 3. Markov Model: • In this model, the present state depends on previous state of samples. • This model is useful for lossless data compression. • A specific type of Markov process is used called ‘Discrete Time Markov Process’. • Let Xn be the sequence of observations, follow Kth order model, P(Xn|Xn-1,Xn-2,…….Xn-k) = P(Xn|Xn-1,Xn-2,…….Xn-k-1) • It means knowledge of past k symbols is equivalent to the knowledge of entire past history of the process. Xn-1,Xn-2,…….Xn-k is called states of process • The first order Markov model is written as, P(Xn|Xn-1) = P(Xn|Xn-1,Xn-2,…….) • Markov model : Complex Accurate results
- 29. Different Types of Models cont.. 4. Composite source Model: • In many application it is not easy to use a single model to describe this source. • In such cases composite source model is useful. • It uses number of different sources Si, each with its own model Mi. • The switch is used to select a particular source according to requirement. Source 1 1 Source 2 Source n Switch
- 30. • The first phase is usually referred to as modeling. • In this phase we try to extract information about any redundancy that exists in the data and describe the redundancy in the form of a model. • The second phase is called coding. A description of the model and a “description” of how the data differ from the model are encoded, generally using a binary alphabet. • The difference between the data and the model is often referred to as the residual
- 31. Coding When we talk about coding we mean the assignment of binary sequences to elements of an alphabet. The set of binary sequences is called a code, and the individual members of the set are called code words. An alphabet is a collection of symbols called letters.
- 34. Shannon Fano Coding • Its a method of constructing prefix code based on a set of symbols and their probabilities estimated or measured. • The technique was proposed in Shannon's "A Mathematical Theory of Communication", his 1948 article introducing the field of information theory. • In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is a technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). • It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding; however unlike Huffman coding, it does guarantee that all code word lengths are within one bit of their theoretical ideal .
- 35. Basic Technique In Shannon–Fano coding, the symbols are arranged in order from most probable to least probable, and then divided into two sets whose total probabilities are as close as possible to being equal. All symbols then have the first digits of their codes assigned; symbols in the first set receive "0" and symbols in the second set receive "1". As long as any sets with more than one member remain, the same process is repeated on those sets, to determine successive digits of their codes. When a set has been reduced to one symbol this means the symbol's code is complete and will not form the prefix of any other symbol's code.
- 38. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.4 0 X2 0.19 0 x3 0.16 1 x4 0.15 1 x5 0.1 1 1)x1 and x2 = UP = Yelow = 0.4+0.19= 0.59, x3,x4 and x4= LP = Red = 0.16+0.15+0.1= 0.41. UP and LP are almost equal probable or same
- 39. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.4 0 0 X2 0.19 0 1 x3 0.16 1 x4 0.15 1 x5 0.1 1
- 40. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.4 0 0 X2 0.19 0 1 x3 0.16 1 0 x4 0.15 1 1 x5 0.1 1 1
- 41. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.4 0 0 00 2 X2 0.19 0 1 01 2 x3 0.16 1 0 10 2 x4 0.15 1 1 0 110 3 x5 0.1 1 1 1 111 3
- 44. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 X2 0.25 x3 0.15 x4 0.12 X5 0.10 x6 0.08
- 45. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 0 X2 0.25 0 x3 0.15 1 x4 0.12 1 X5 0.10 1 x6 0.08 1 1) 0.3+0.25= 0.55, x1 and x2 = UP=Yelow 0.15+0.12+0.1+0.08= 0.45, x3,x4 and x4= LP= Red
- 46. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 0 0 X2 0.25 0 1 x3 0.15 1 x4 0.12 1 X5 0.10 1 x6 0.08 1
- 47. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 0 0 X2 0.25 0 1 x3 0.15 1 0 x4 0.12 1 0 X5 0.10 1 1 x6 0.08 1 1
- 48. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 0 0 X2 0.25 0 1 x3 0.15 1 0 0 x4 0.12 1 0 1 X5 0.10 1 1 x6 0.08 1 1
- 49. Messag e Prob Step 1 Step 2 Step 3 Code Code length x1 0.30 0 0 00 2 X2 0.25 0 1 01 2 x3 0.15 1 0 0 100 3 x4 0.12 1 0 1 101 3 X5 0.10 1 1 0 110 3 x6 0.08 1 1 1 111 3 1) 0.3+0.25= 0.55, x1 and x2 = UP=Yelow ; 0.15+0.12+0.1+0.08= 0.45, x3,x4 and x4= LP= Red
- 50. The Huffman Coding Algorithm This technique was developed by David Huffman as part of a class assignment; the class was the first ever in the area of information theory and was taught by Robert Fano at MIT. The codes generated using this technique or procedure are called Huffman codes. These codes are prefix codes and are optimum for a given model (set of probabilities). The Huffman procedure is based on two observations regarding optimum prefix codes. 1. In an optimum code, symbols that occur more frequently (have a higher probability of occurrence) will have shorter codewords than symbols that occur less frequenly. 2. In an optimum code, the two symbols that occur least frequently will have the same length.
- 51. Design of a Huffman code Let us design a Huffman code for a source that puts out letters from an alphabet = a1, a2, a3, a4, a5 with P(a1) = P(a3) = 0. 2, P(a2) = 0.4, and P(a4) = P(a5) = 0.1. The entropy for this source is 2.122 bits/symbol. To design the Huffman code, we first sort the letters in a descending probability order as shown in Table 3.1. Here c(ai) denotes the codeword for ai.
- 55. Minimum Variance Huffman Codes