Shannon Capacity

Last Updated : 20 Mar, 2024

In this article, we will be discussing the Shannon capacity theorem. Shannon Capacity or Shannon’s Channel Capacity theorem is a widely used theorem used in digital signal processing. This theorem helps in deciding the capacity of any noise-transmitting channel. It is very helpful in digital signals. In this article, we will learn about the Shannon capacity theorem, its formula, diagram, applications and full explanation.

Table of Content

Shannon’s Channel Capacity
Statement of the Theorem
Applications
Advantages
Disadvantages

What is Shannon’s Channel Capacity?

In the 1940s, Claude Shannon Developed the Channel Capacity using the Concept of Nyquist and Hartley. He called this the channel capacity Theorem.

The Shannon’s Capacity theorem states that

Shannon’s Channel Capacity theorem States that the maximum rate at which information can be transmitted over a communication channel of a specified bandwidth in the presence of noise.

In simple terms, Shannon’s channel capacity tells us the theoretical highest limit in which any channel can transmit signals with the presence of noise. It tells us about any channel’s capacity and its limitations. Shannon’s channel capacity theorem is a fundamental concept in Digital Signals, It can tell us about the upper bound of any channel.

Let us understand this theorem with the help of a diagram.

Shannon’s Limit

In this diagram, the signal reaching from point 0-10, 0-20 has a theoretical limit beyond which it may encounter several errors, data loss or packet loss. Shannon theorem has helped us derived this theoretical limit, Also this signal can be produced with noise, because noiseless communication is expensive. Such communication will not disrupt the signal in any way, this is also another advantages of shannon theorem.

History of Shannon’s Channel Capacity Theorem

The shannon capacity theorem is a part of a bigger model of communication known as the Shannon-Weaver (or Shannon-Hartley) model of communication, It was created by Claude Shannon and Warren Weaver in the late 1940s which helped communication engineers perform their job more efficiently. This model was based on the Shannon’s concept of channel capacity, which we have learned in this article tells us about the capacity of any channel to withstand noise in a signal.

Shannon greatly increased the understanding of data communication after deriving this theorem for us. For years, sending data was stuck at a maximum rate of 9.6 kilobits per second and we tried increasing that rate a number of errors would occur in the data.

Some common terms related to Shannon Capacity

Channel: A channel is a medium used to transmit signals, data or any information.
Noise: A noise is any unwanted signal which can negatively impact the quality of any transmission.
Shannon’s limit: Shannon’s limit is a theoretical limit which tells us the maximum capacity for a signal to be transmitted through a channel.

Statement of the Theorem

Shannon’s Channel Capacity theorem States that the maximum rate at which information can be transmitted over a communication channel of a specified bandwidth in the presence of noise.

[Tex]C = Blog₂( 1 + S/N )[/Tex]

C is the channel capacity in bits per second.
B is the bandwidth of the channel.
S is the average received signal.
N is the average power or noise.
S/N is the signal to noise ratio.

Applications of Shannon’s Channel Capacity

The theorem has numerous applications in a variety of fields

Telecommunications: The Shannon theorem helps maintain the capacity of any telecommunication channel which can help in error-less communication and aid engineers, or system architects to build a better model.
In wireless communication: The Shannon theorem helps us calculate the maximum data that can be transferred in a wireless channel without error or data loss.
Digital Signals: Shannon theorem is also used in signals to calculate the amount of information that can be recovered from a signal with a particular noise.
Audio and Video compression: Shannon theorem is also widely used in audio and video compression to derive an upper bound for the compression of data or data communication signals.
Storage and Maintenance of data: Shannon theorem helps us understand a mathematical derivation for storing and maintaining data efficiently and preventing data loss by implementing concepts such as Quantization.

Advantages of Shannon Capacity

Given below is the some of the Advantages of Shannon Capacity

Structured framework: Shannon’s theorem breaks down communication processes into components such as sender, message channel, noise, receiver and feedback
Enables enhanced communication: It helps boost the communication by outlining the major aspects that may cause an error in communication and makes the functioning easier.
Clarity and Simplicity: It provides a straightforward way of communication and can be understood by any new scholar or practitioner.
Flexible: Shannon capacity provides a wide range of applications ranging from high speed data transfer to simple voice communication
Cost effective: Shannon capacity allows us to use noisy channels which are more cost effective as compared to noiseless channel.

Disadvantages of Shannon Capacity

Given below is the some of the Disadvantages of Shannon Capacity

Longer delays: Shannon capacity may cause delays considering it requires theoretical proof to proceed with the communication inside a channel.
Error rate Increases with Information rate: Shannon theorem may be error prone if the amount of information increases.
Errorless Channel: Due to noise an errorless channel may not be possible considering this theorem only provides conceptual proof.
Increased Complexity: Shannon capacity theorem may increase complexity since deriving a channel capacity requires complex and expensive methods which can largely impact the complexity of data communication.
Limited Scope: Shannon theorem only considers noise while modern communication faces a lot of other challenges such as interference, fading, packet loss and security concerns.

Conclusion

In conclusion, Shannon greatly increased our understanding of how data communication works. By deriving this theorem we understand the theoretical limit of any channel, the maximum amount of data which can be sent over the channel without error-prone communication. It is a very important concept in Digital & Signal Communication and to this day widely used by various engineers.