Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios
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This paper treats point-to-point, multiple access and random access lossless source coding in the finite-blocklength regime. A random coding technique is developed, and its power in analyzing the third-order-optimal coding performance is demonstrated in all three scenarios. Results include a third-order-optimal characterization of the Slepian-Wolf rate region and a proof showing that for dependent sources, the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding, which generalizes the multiple access scenario to allow for a number of participating encoders that is unknown a priori to both the encoders and the decoder, is introduced. Contributions include a new definition of the probabilistic model for a random access-discrete multiple source (RA-DMS), a general random access source coding scheme that employs a rateless code with sporadic feedback, and an analysis for the proposed scheme demonstrating via a random coding argument that there exists a deterministic code of the proposed structure that simultaneously achieves the third-order-optimal performance of Slepian-Wolf codes for all possible numbers of encoders. While the analysis for random access codes focuses on a class of permutation-invariant RA-DMSs, it also extends to more general sources.
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