Since their introduction in 1998, the applications of space-time trellis codes have been, and still are, increasing rapidly. In this thesis, unequal error protecting ST trellis codes are designed then used to transmit images over a rapid fading channel. The idea is to use ST trellis codes that provide strong error protection to one of its multiple input bits and send the important part of the image through that bit. This requires modifying the existing performance measurement techniques such that they show the weight of error protection on each input bit. This is done using a modi ed transfer function and new upper bounds for each individual input bit. To nd the desired codes, two approaches are used: design and exhaustive search. Both approaches are used to nd several QPSK and 8PSK codes that provide strong error protection properties to the most signi cant bit. To complete the application, the JPEG image processing technique is modi ed to separate the important from the less important bits. Finally, test images are simulated using the new codes in addition to several codes from the literature for comparison.