Runlength encoding of quantized DCT coefficients

Abstract

Runlength encoding is used in image and video compression methods to efficiently store quantized Discrete Cosine Transform (DCT) coefficients. The coefficients for each block are scanned in a zig-zag fashion, and runs of zeros are entropy coded. In this paper we present a comparison of the bit-rate resulting from runlength encoding with the bit-rate calculated as the coefficient-wise sum of entropies. Our experiments with several images show that the two are very close in practice. This is a useful result, for example, for designing quantization matrices to meet any bit-rate requirement. We also present an analytical framework to study these bit-rates. We consider two variants of runlength encoding. In the first one, the symbols that are entropy-coded are (runlength, value) pairs. In the second variant, which is the one used in JPEG, values are grouped together into categories based on magnitude.