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Unformatted text preview: Signal Compression 1 Copyright © 20052008 – Hayder Radha Entropy Coding Entropy coding is also known as “zeroerror coding”, “data compression” or “lossless compression”. Entropy coding is widely used in virtually all popular international multimedia compression standards such as JPEG and MPEG. Signal Compression 2 Copyright © 20052008 – Hayder Radha A complete entropy codec, which is an encoder/decoder pair, consists of the process of “encoding” or “compressing” a random source (typically quantized transform coefficients) and the process of “decoding” or “decompressing” the compressed signal to “perfectly” regenerate the original random source. In other words, Signal Compression 3 Copyright © 20052008 – Hayder Radha there is no loss of information due to the process of entropy coding. Thus, entropy coding does not introduce any distortion, and hence, the combination of the entropy encoder and entropy decoder faithfully reconstructs the input to the entropy encoder. Signal Compression 4 Copyright © 20052008 – Hayder Radha Entropy Encoding Random Source Compressed Source Entropy Decoding Random Source Compressed Source Signal Compression 5 Copyright © 20052008 – Hayder Radha Therefore, any possible lossofinformation or distortion that may be introduced in a signal compression system is not due to entropy encoding/decoding. As we discussed previously, a typical image compression system, for example, includes a transform process, a quantization process, and an entropy coding stage. In such system, the distortion is introduced due to quantization. Moreover, Signal Compression 6 Copyright © 20052008 – Hayder Radha for such a system, and from the perspective of the entropy encoder, the input “random source” to that encoder is the quantized transform coefficients. Transform Quantization Entropy Coding Random Source Examples KLT DCT Wavelets Transform Coefficients Quantized Coefficients Compressed Source Examples Huffman Arithmetic Signal Compression 7 Copyright © 20052008 – Hayder Radha Code Design and Notations In general, entropy coding (or “source coding”) is achieved by designing a code , C , which provides a one toone mapping from any possible outcome a random variable X (“source”) to a codeword . There two alphabets in this case; one alphabet is the traditional alphabet of the random source X , and the Signal Compression 8 Copyright © 20052008 – Hayder Radha second alphabet ! is the one that is used for constructing the codewords. Based on the second alphabet ! , we can construct and define the set * D , which is the set of all finitelength string of symbols withdrawn from the alphabet ! . S i g n a l C o m p r e s s i o n 9 C o p y r i g h t © 2 5 2 8 – H a y d e r R a d h a T h e m o s t c o m m o n a n d p o p u l a r c o d e s a r e b i n a r y c o d e s , w h e r e t h e a l p h a b e t o f t h e c o d e w o r d s i s s i m p l y t h e b i n a r y b i t s “...
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