<title>Quantizer characteristics important for quantization index modulation</title>

Abstract

Quantization Index Modulation (QIM) has been shown to be a promising method of digital watermarking. It has recently been argued that a version of QIM can provide the best information embedding performance possible in an information theoretic sense. This performance can be demonstrated via random coding using a sequence of vector quantizers of increasing block length, with both channel capacity and optimal rate-distortion performance being reached in the limit of infinite quantizer block length. For QIM, the rate-distortion performance of the component quantizers is unimportant. Because the quantized values are not digitally encoded in QIM, the number of reconstruction values in each quantizer is not a design constraint, as it is in the design of a conventional quantizer. The lack of a rate constraint in QIM suggests that quantizer design for QIM involves different condiderations than does quantizer design for rate-distortion performance. Lookabaugh has identified three types of advantages of vector quantizers vs. scalar quantizers. These advantages are called the space-filling, shape, and memory advantages. This paper investigates whether all of these advantages are useful in the context of QIM. QIM performance of various types of quantizers is presented and a heuristic sphere-packing argument is used to show that, in the case of high-resolution quantization and a Gaussian attack channel, only the space-filling advantage is necessary for nearly optimal QIM performance. This is important because relatively simple quantizers are available that do not provide shape and memory gain but do give a space-filling gain.