Block Codes with Embedded Quantization Step Size Information

If we quantize a block of n samples and then transmit information about quantization step size in the same bitstream, we may naturally expect such a code to be at least O(1/n) redundant. However, as we will show in this paper, this may not necessarily be true. Moreover, we prove that asymptotically, such codes can be as efficient as block codes without embedded step-size information. The proof relies on results from the Diophantine approximations theory. We discuss the significance of this finding for practical applications, such as the design of audio and video coding algorithms.