On the Capacity of Channels with Deletions and States

TL;DR

This paper investigates the capacity of channels combining deletions and states, proving the equality of operational and stationary capacities, and demonstrating that a specific polar coding scheme achieves this capacity.

Contribution

It establishes the equality of operational and stationary capacities for deletion and state channels and confirms the effectiveness of a polar coding scheme for these channels.

Findings

Operational capacity equals stationary capacity.

Capacity can be approached by Markov processes.

Polar coding scheme achieves the channel capacity.

Abstract

We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operational capacity is equal to the stationary capacity, which can be approached by a sequence of Markov processes with increasing Markovian orders. As a by-product, we show that the polar coding scheme constructed by Tal, Pfister, Fazeli and Vardy achieves the capacity of the deletion channel.