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A new ensemble of structured codes is introduced. These codes are calledQuasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linearcodes. They have a looser structure compared to linear codes and are not closedunder addition. We argue that these codes provide gains in terms of achievableRate-Distortions (RD) in different multi-terminal source coding problems. Wederive the necessary covering bounds for analyzing the performance of QLC's. Wethen consider the Multiple-Descriptions (MD) problem, and prove through anexample that the application of QLC's gives an improved achievable RD regionfor this problem. Finally, we derive an inner bound to the achievable RD regionfor the general MD problem which strictly contains all of the previous knownachievable regions.

Quasi Linear Codes: Application to Point-to-Point and Multi-Terminal Source Coding