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July 29 2024

This section from the paper discusses the concept of a discrete noiseless channel.

Overview

A discrete noiseless channel is a system for transmitting information without errors. This means that the transmitted symbols are received exactly as sent. Two historical examples are the teletype and telegraphy.

Symbols and Transmission

In such a channel, symbols $S_1, S_2, \ldots, S_n$ can be transmitted, each taking a specific amount of time $t_i$. For instance, in telegraphy:

1. A dot (one unit of time and one unit open).
2. A dash (three units of close and one unit open).
3. A letter space (three units open).
4. A word space (six units open).

The capacity of the channel, which is the maximum rate at which information can be transmitted, is the main focus.

Channel Capacity Definition

The capacity $C$ of a discrete channel is defined as:

$$ C = \lim_{T \to \infty} \frac{\log N(T)}{T} $$

Where $N(T)$ is the number of allowed signals of duration $T$.

Explanation

• $N(T)$: Number of allowed sequences of length $T$.