Semiconstrained Systems

When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, 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 paper, we analyze a middle road, which we call a semiconstrained system. In such a system, which is an extension of the channel with the cost constraints model, we do not eliminate the error-causing sequences entirely, but rather restrict the frequency in which they appear. We address several key issues in this paper. 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 key issue is devising efficient encoding and decoding procedures that asymptotically achieve capacity with vanishing error. Finally, we consider delicate issues involving the continuity of the capacity and a relaxation of the definition of semiconstrained systems.