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Coding Theory: Semiconstrained Systems
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Ohad Elishco (Ben-Gurion University)
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Sunday, 18.12.2016, 14:30
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Taub 601
When transmitting information over a noisy channel, two approaches are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this talk we analyze a middle road, which we call a semiconstrained system. In such a system we do not eliminate the error-causing sequences entirely, but rather restrict the frequency in which they appear.

We will address several key issues. The first is proving closed-form bounds on the capacity which allow us to bound the asymptotics of the capacity. In particular, we bound the rate at which the capacity of the semiconstrained (0, k)-RLL tends to 1 as k grows. The second is consider delicate issues involving the continuity of the capacity and a relaxation of the definition of semiconstrained systems. The third is devising an encoding and decoding procedures that asymptotically achieve capacity with vanishing error probability. Finally, we study sequences of constrained systems that are contained in, or contain, a given semiconstrained system.
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