Predictive Encoding in data compression

Idea: Remove mutual redundancy among successive pixels in a region of support (ROS) or neighborhood and encode only the new information. This method is based upon linear prediction. Let us start with 1-D linear predictors. An Nth order linear prediction of x(n) based on N previous samples is generated using a 1-D autoregressive (AR) model.


ai s are model coefficients determined based on some sample signals. Now instead of encoding x(n) the prediction error.


Is encoded as it requires substantially small number of bits. Then, at the receiver we reconstruct x(n) using the previous encoded values x(n-k) and the encoded error signal, i.e.,


This method is also referred to as differential PCM (DPCM).

A video is a sequence of video frames where each frame is full color still image. Because video player must display the frames sequentially at rates near 30 fps. Standard definition data must be accessed 30fps x (720 x 480) ppf x 3bpp = 31,104,000 bps

fps: frames per second, ppf: pixels per frame, bpp: bytes per pixel, bps: bytes per second.

Thus a 2 hour movie consists of : = 31,104,000 bps x (602 ) sph x 2hrs

where sph is second per hour = 2.24 x 1011 bytes = 224 GB of data.

TWENTY SEVEN 8.5 GB dual layer DVD’s are needed to store it.

To put 2 hours movie on a single DVD, each frame must be compressed by a factor of around
The compression must be even higher for HD, where image resolution reach 1920 x 1080 x
24 bits per image.
Webpage images & High-resolution digital camera photos also are compressed to save
storage space & reduce transmission time.
Residential Internet connection delivers data at speeds ranging from 56kbps (conventional
phone line) to more than 12 mbps (broadband).
Time required to transmit a small 128 x 128 x 24 bit full color image over this range of speed
is from 7.0 to 0.03 sec.
Compression can reduce the transmission time by a factor of around 2 to 10 or more.
Similarly, number of uncompressed full color images that an 8 Megapixel digital camere can
store on a 1GB Memory card can be increased.
Data compression: It refers to the process of reducting the amount of data required to
represent a given quantity of information.
Data Vs Information:
Data and information are not the same thing; data are the means by which information is
Because various amount of data can be used to represent the same amount of information,
representations that contain irrelevant or repeated information are said to contain redundant.