Excess rate for model selection in interactive compression using belief propagation decoding
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Excess rate for model selection in interactive compression using belief propagation decoding Navid Mahmoudian Bidgoli1
· Thomas Maugey1 · Aline Roumy1
Received: 11 May 2020 / Accepted: 20 August 2020 © Institut Mines-T´el´ecom and Springer Nature Switzerland AG 2020
Abstract Interactive compression refers to the problem of compressing data while sending only the part requested by the user. In this context, the challenge is to perform the extraction in the compressed domain directly. Theoretical results exist, but they assume that the true distribution is known. In practical scenarios instead, the distribution must be estimated. In this paper, we first formulate the model selection problem for interactive compression and show that it requires to estimate the excess rate incurred by mismatched decoding. Then, we propose a new expression to evaluate the excess rate of mismatched decoding in a practical case of interest: when the decoder is the belief propagation algorithm. We also propose a novel experimental setup to validate this closed-form formula. We show a good match for practical interactive compression schemes based on fixed-length Low-Density Parity-Check (LDPC) codes. This new formula is of great importance to perform model and rate selection. Keywords Source coding · Interaction · Model selection · Mismatched decoding
1 Introduction The way videos are consumed have considerably evolved in the last decade. With the arrival of new data formats and new streaming platforms, users have been enabled to interact with the content they watch, mostly by choosing part of the data they want to access. Compressing data so that users are able to extract only a part of it, called interactive compression/coding (IC), requires new tools. More precisely, it has been proven that predictive coding, widely used in standard video coders, can not be efficient in both storage and transmission [1]. Indeed, the challenge in IC is to deal with the uncertainty of the users’ request upon compression. This can be formulated as a source coding problem, where a side information is available at the decoder, whereas the encoder has access to the set of Navid Mahmoudian Bidgoli
[email protected] Thomas Maugey [email protected] Aline Roumy [email protected] 1
INRIA, Univ. Rennes, CNRS, IRISA, Rennes, France
possible side information [1, 2]. It differs from predictive coding, where the side information is available at both encoder and decoder. Therefore, the encoder in IC relies on the statistics of the side information, and not on its realization, and belongs to the general class of modelbased coding problems. Despite the efficiency of some proposed architectures to solve the IC problem [3–5], two key questions, related to IC (and thus model-based coding) remain: (i) which statistical model should we select and send to the decoder for the data to be compressed? (ii) at which encoding rate should we compress the data? These two questions require to determine the excess rate for mismatched decoding, i.e., when a
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