Soft Content Fingerprinting With Bit Polarization Based on Sign-Magnitude Decomposition

Content identification based on digital content fingerprinting attracts significant attention in different emerging applications. In this paper, we consider content identification based on the sign-magnitude decomposition of fingerprint codewords and analyze the achievable rates for sign and magnitude components. We demonstrate that the bit robustness in the sign channel, often used in binary fingerprinting, is determined by the value of the corresponding magnitude component. Correspondingly, one can distinguish between two systems depending how the information about the magnitude component is used at the decoding process, i.e., hard fingerprinting when this information is disregarded, and soft fingerprinting when this information is used. To reveal the advantages of soft information at the decoding, we consider a case of soft fingerprinting where the decoder has access to the complete information about the uncoded magnitude component. However, since it requires a lot of extra memory storage or secure communication, the magnitude information is often quantized to a single bit or extracted directly from the noisy observation. To generalize the existing methods and estimate the impact of quantization and noise in the side information about the magnitude components on the achievable rate, we introduce a channel splitting approach and reveal certain interesting phenomena related to channel polarization. We demonstrate that under proper quantization of the magnitude component, one can clearly observe the existence of strong components whose sign is very robust, even to strong distortions. We demonstrate that under certain conditions, a great portion of the rate in the sign channel is concentrated in strong channel components. Finally, we demonstrate how to use the channel splitting property in the design of efficient low-complexity identification methods.