A Rate-Distortion Approach to Index Coding

• Published in: IEEE transactions on information theory Vol. 62; no. 11; pp. 6359 - 6378
• Main Authors: Unal, Sinem, Wagner, Aaron B.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Codes; Coding; Cryptography; Decoders; Decoding; Distortion; Encoding; Index coding; Indexes; Information theory; Lower bounds; multiple decoders; Optimization; Random variables; Rate-distortion; Receivers; Receivers & amplifiers; side information; Upper bounds
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2608943

We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds and one lower bound on the optimal index coding rate. The upper bounds involve specific choices of the auxiliary random variables in the best existing scheme for the rate-distortion problem. The lower bound is based on a new lower bound for the general rate-distortion problem. The bounds are shown to coincide for a number of (groupcast) index coding instances, including all instances for which the number of decoders does not exceed three.