Maximizing privacy in Variable Bit rate Coding

Variable Bitrate Coding (VBR) has shown to be an advantageous method of encoding data streams, with particular application to speech, audio and video streams. While the primary disadvantage of VBR has long been considered as the increasing encoding complexity, recent research into traffic analysis of VBR coded audio streams has exposed an important privacy vulnerability wherein an eavesdropper can utilize the observed length of VBR encoded data packets and determine the contents of the communication such as spoken words and audio. In this work, the privacy-utility tradeoff for VBR coding is studied from a theoretical foundational perspective. Specifically, the data source is modeled a mixture distribution, wherein the length of the encoded data packet is varied to maintain a constant quality (distortion) with respect to the source. Using Shannon´s equivocation as a measure of data privacy, the tradeoff between privacy and utility (as measured by delay and overall bit rate) of VBR is investigated analytically. In particular, the tradeoffs are expressed as classical information theoretic rate distortion functions, which shed light into methods to increase the privacy of VBR encoded data without compromising on the desired output fidelity.