Cascade, Triangular, and Two-Way Source Coding With Degraded Side Information at the Second User

• Published in: IEEE transactions on information theory 2012-01, Vol.58 (1), p.189-206
• Main Authors: Yeow-Khiang Chia, Permuter, H. H., Weissman, T.
• Format: Article
• Language: English
• Subjects: Applied sciences; Cascade source coding; Cascades; Codes; Coding; Coding, codes; Decoding; Degradation; Exact sciences and technology; Gaussian; Information theory; Information, signal and communications theory; Links; Markov processes; Normal distribution; Optimization; Peer to peer computing; quadratic Gaussian; Random variables; Rate-distortion; Reconstruction; Signal and communications theory; Source coding; source coding with a helper; Telecommunications and information theory; triangular source coding; two-way source coding; Zinc
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2167738

In this paper, we consider the cascade and triangular rate-distortion problems where the same side information is available at the source node and user 1, and the side information available at user 2 is a degraded version of the side information at the source node and user 1. We characterize the rate-distortion region for these problems. For the cascade setup, we show that, at user 1, decoding and rebinning the codeword sent by the source node for user 2 is optimum. We then extend our results to the two-way cascade and triangular setting, where the source node is interested in lossy reconstruction of the side information at user 2 via a rate limited link from user 2 to the source node. We characterize the rate-distortion regions for these settings. Complete explicit characterizations for all settings are given in the quadratic Gaussian case. We conclude with two further extensions: a triangular source coding problem with a helper, and an extension of our two-way cascade setting in the quadratic Gaussian case.