Ergodic Rate and Achievable Rate（自用笔记）

Ergodic Rate and Achievable Rate（自用笔记）

Distinguish Ergodic Rate and Achievable Rate

The terms “ergodic rate” and “achievable rate” describe different aspects of the data transmission rate in communication channels.

1. Ergodic Rate:

• Definition: Ergodic rate refers to the long-term average rate of information transfer that can be expected in a communication channel. It is calculated by taking the expected value of the rate over all possible channel states.

• Context: It is often associated with stationary and ergodic random processes, where the statistical properties of the process can be deduced from a single, sufficiently long, random sample of the process.

• Calculation: It’s typically calculated under the assumption that the channel state information is known at both the transmitter and receiver, allowing the communication system to adapt to varying channel conditions to maximize the rate of information transfer.

• Application: It’s a theoretical measure often used in the analysis and design of communication systems to provide an upper bound on the average rate of information transfer.

2. Achievable Rate:

• Definition: Achievable rate refers to the maximum rate at which information can be reliably transmitted over a communication channel for a given channel state. It is not an average measure but rather indicates the rate that can be achieved for specific conditions.

• Context: It is associated with specific channel conditions and can vary depending on factors like the signal-to-noise ratio (SNR), modulation scheme, coding rate, and other transmission and channel characteristics.

• Calculation: Achievable rate can be calculated based on the channel’s current state information, without requiring long-term averaging. It often involves the use of Shannon’s capacity formula, which provides the maximum rate of error-free data transmission over a noisy channel.

• Application: Achievable rate is often used in adaptive communication systems where the transmission rate, power, modulation scheme, or coding rate can be dynamically adjusted to maximize the rate of information transfer under current channel conditions.

Summary:

• Ergodic Rate: Long-term average rate, calculated over all possible channel states, provides an upper bound on the average information transfer rate.
• Achievable Rate: Instantaneous rate achievable under specific channel conditions, not an average measure, used for adaptive communication systems.

These concepts are crucial in designing and optimizing communication systems, especially wireless networks.