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High Efficiency Video Coding. (HEVC) is the product of a large collaborative effort from industry and academic community and reflects the new international standardization for digital video coding technology. Compression capability is the main goal behind the digital video compression technology. HEVC achieves this goal at the expense of dramatically increasing coding complexity. One such area of increased complexity is due to the use of a recursive quad-tree to partition every frame to various block sizes, a process called prediction mode.

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.