Capacity and Coding for the Ising Channel With Feedback

2013 IEEE International Symposium on Information Theory

Weissman

2013

We consider finite state channels where the state of the channel is its previous output. We refer to such channels as POST (Previous Output is the STate) channels. Our focus is on a simple binary POST channel, with binary inputs and outputs where the state determines if the channel behaves as a Z or an S channel (of equal capacities). We show that the non feedback capacity equals the feedback capacity, despite the memory in the channel. The proof of this surprising result is based on showing that the induced output distribution, when maximizing the directed information in the presence of feedback, can also be achieved by an input distribution that is ignorant of the feedback. Indeed, we show that this is a necessary and sufficient condition for the feedback capacity to equal the non feedback capacity for any finite state channel.

Section: Introductionmentioning

confidence: 99%

Capacity of a POST channel with and without feedback

Asnani

2013 IEEE International Symposium on Information Theory

Weissman

2013

“…We conducted several experiments to verify the effectiveness of our formulation. First, we focused on experimenting channels whose analytic solution was proven in the past, such as the Trapdoor channel [4], Ising channel with a binary alphabet [5], [8], Binary Erasure channel with input constraint [6], and the Dicode channel [12]. The results showed that the obtained achievable rates were within 99.99% of the feedback capacity for all channels.…”

Section: Methodsmentioning

confidence: 99%

Computing the Feedback Capacity of Finite State Channels using Reinforcement Learning

Aharoni

Sabag

2019 IEEE International Symposium on Information Theory (ISIT)

2019

In this paper, we propose a novel method to compute the feedback capacity of channels with memory using reinforcement learning (RL). In RL, one seeks to maximize cumulative rewards collected in a sequential decision-making environment. This is done by collecting samples of the underlying environment and using them to learn the optimal decision rule. The main advantage of this approach is its computational efficiency, even in high dimensional problems. Hence, RL can be used to estimate numerically the feedback capacity of unifilar finite state channels (FSCs) with large alphabet size. The outcome of the RL algorithm sheds light on the properties of the optimal decision rule, which in our case, is the optimal input distribution of the channel. These insights can be converted into analytic, single-letter capacity expressions by solving corresponding lower and upper bounds. We demonstrate the efficiency of this method by analytically solving the feedback capacity of the well-known Ising channel with a ternary alphabet. We also provide a simple coding scheme that achieves the feedback capacity.

“…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.…”

Section: A the Bsc Capacity As Dpmentioning

confidence: 99%

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

Sabag

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Kashyap

2015

The binary symmetric channel (BSC) with feedback is considered, where the input sequence contains no consecutive ones, i.e., satisfies the (1, ∞)-RLL constraint. In [1], the capacity of this setting was formulated as dynamic programming (DP); however, analytic expressions for capacity and optimal input distribution were left as an open problem. In this paper, we derive explicit expressions for both feedback capacity and optimal input distribution. The solution was obtained by using an equivalent DP and solving its corresponding Bellman equation. The feedback capacity also serves as an upper bound on the capacity of the input-constrained BSC channel without feedback, a problem that is still open.