ShannonHartleyligningen

The ShannonHartleyligningen, often referred to as the Shannon-Hartley theorem, is a fundamental concept in information theory that describes the maximum rate at which information can be reliably transmitted over a communication channel with a given bandwidth in the presence of noise. It was independently derived by Claude Shannon and Robin Hartley.

The equation quantifies the channel capacity, denoted by C, as the product of the channel's bandwidth (B) and the logarithm (base 2) of the sum of the signal power (S) and the noise power (N). Mathematically, it is expressed as C = B log2(1 + S/N). The bandwidth B is measured in Hertz (Hz), and the signal-to-noise ratio (S/N) is a dimensionless quantity.

The theorem states that if the transmission rate is below the channel capacity, reliable communication is possible by using appropriate error-correcting codes. Conversely, if the transmission rate exceeds the channel capacity, error-free communication is impossible, and errors are inevitable regardless of the coding scheme employed.

The Shannon-Hartley theorem has profound implications for the design and optimization of communication systems, including wireless networks, telecommunications, and data storage. It sets a theoretical upper bound on data transmission rates and guides engineers in achieving efficient and robust communication in real-world scenarios where noise is an inherent factor.