SWE 423: Multimedia Systems Chapter 7: Data Compression (4)

Outline Source Coding –Predictive Coding Lossless Lossy –DPCM –DM

Predictive Coding Predictive coding simply means transmitting differences –Predict the next sample as being equal to the current sample More complex prediction schemes can be used –Instead of sending the current sample, send the error involved in the previous assumption

Predictive Coding: Why? The idea of forming differences is to make the histogram of sample values more peaked. –In this case, what happens to the entropy? –As a result, which is better to compress?

Predictive Coding: Why?

Lossless Predictive Coding Formally, define the integer signal as the set of values f n. Then, we predict values f^ n and compute the error e n as follows: –when t = 1, we get... –Usually, t is between 2 and 4 (in this case it is called a linear predictor –We might need to have a truncating or rounding operation following the prediction computation

Lossless Predictive Coding

Lossless Predictive Coding: Example Consider the following predictor: Show how to code the following sequence

Lossless Predictive Coding Examples in the Image Compression Domain –Differential Coding –Lossless JPEG

Lossy Predictive Coding: DPCM DPCM = Differential Pulse Code Modulation –Form the prediction f ^ n –Form an error e n –Quantize the error

Lossy Predictive Coding: DPCM The distortion is the average squared error –To illustrate the quality of a compression scheme, diagrams of distortion vs. the number of bit levels used are usually shown –Quantization used Uniform Lloyd-Max –Does better than “Uniform”

Lossy Predictive Coding: DPCM

Example Show how to code the following sequence

Lossy Predictive Coding DM (Delta Modulation) is a simplified version of DPCM that is used as a quick analog-to-digital converter. –Note that the prediction simply involves a delay