Real (4,2) BCH code for image communications

Image communication over telephone wireline and wireless networks is becoming a standard way of communication due to very efficient compression algorithms for reducing the required channel capacity. However, all standard compression techniques are strongly sensitive to channel noise and their application is suitable only for practically noiseless channels. For noisy channels it is reasonable to investigate an integrated source and channel coding method as a tradeoff between the image quality and the ability to control errors caused by noise. A real number (4,2) BCH code defined in the frequency domain via the DFT is presented. The major contribution of this paper is a new approach to decoding real number codes based on not only one but three syndromes which is not possible with binary codes. It is shown that a real number (4,2) code has the ability to correct up to 3 errors regardless of the presence of noise or even all i.e. four errors. The efficiency of the proposed decoding method is tested on a 2-D example of a gray scale image