## Table of Contents

### What is Shannon Capacity for Noisy Channel

The Shannon capacity, which was named after Claude Shannon, is the highest rate at which information that is free of errors may be conveyed over a communication channel that is noisy. In the presence of noise, it is a theoretical limit that establishes an upper limit for the data rate that can be achieved. The idea is fundamental to Shannon’s information theory, which he developed throughout his career.

**Shannon Capacity for Noisy Channel**

The formula for Shannon capacity for Noisy Channel *C* is given by:

C=B⋅log2(1+SNR)*C*=*B*⋅log2(1+SNR)

where:

*C*is the channel capacity in bits per second,*B*is the bandwidth of the channel in hertz,- SNRSNR is the signal-to-noise ratio, which is the ratio of the signal power to the noise power.

This formula assumes additive white Gaussian noise (AWGN), a commonly used model for channel noise. The higher the signal-to-noise ratio, the greater the achievable data rate. The logarithmic term reflects the fact that the capacity increases logarithmically with the signal-to-noise ratio.

It’s important to note that the Shannon capacity is a theoretical limit and doesn’t necessarily mean that practical communication systems can achieve this rate. Various factors, including the coding scheme, modulation techniques, and practical constraints, can affect the actual data rate achieved in real-world communication systems.We hope this article on **Shannon Capacity for Noisy Channel** helps our reader to better understand about the topic.Also you can check our other related articles on Explain the four metrics in Web analytics? What questions do they help us answer??