Abstract:
A mapping of k symbols to n symbols is said to be alpha-beta if it sends any two strings of relative distance more than alpha to two strings of relative distance more than beta. We will discuss the relevance of such maps to the joint-source channel coding (JSCC) problem. Most existing results attempt to address the question of achievable alpha-beta pairs in the space of all codes. In this talk we explore the same question for some families of good error-correcting codes. We ask, for instance,what are the limits for codes that have large minimum distance?What are the alpha-beta limits for codes that can achieve capacity over BEC?We present some results in this direction and give some explicit constructions for good alpha-beta maps and good JSCC codes.