Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback

Abstract

The input-constrained erasure channel with feedback is considered, where the input sequence contains no consecutive 1's, i.e. the (1, ∞)-RLL constraint. The capacity is calculated using an equivalent dynamic program, which shows that the optimal average reward is equal to the capacity. The capacity can be expressed aswhere ǫ is the erasure probability and H b (·) is the binary entropy. This capacity also serves as an upper bound on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

Asymptotics of Input-Constrained Erasure Channel Capacity

“…In [37], Sabag et al computed an explicit formula of feedback capacity for BEC with (1, ∞)-RLL input constraint S 0 . Theorem 5.2.…”

The feedback capacity of the binary symmetric channel with a no-consecutive-ones input constraint

“…, w t−1 ), we take the disturbance at time t to be the channel, w t = y t . In [9], it was shown that this formulation satisfies the DP properties. The system equation (2) takes the recursive form of:…”

“…Theorem 2 (Theorem 3, [9]). The capacity of an inputconstrained memoryless channel with feedback can be written as:…”

“…h k+1 = T h k , with h 0 (z) = 0 for all z ∈ [0, 1]. We omit the detailed process of this evaluation since the methods are identical to the ones in [9]- [11]. The numerical evaluation gave us sufficient insight for a good "guess" of a solution for the Bellman equation that is presented in the next section.…”