Introduction:
The maximum rate at which nearly error-free data can be theoretically transmitted over a communication channel is known as the channel capacity. It represents the upper limit of data transmission and is influenced by various factors such as modulation, signal-to-noise ratio, and frequency bandwidth.

Explanation:
Modulation:
Modulation refers to the process of encoding information onto a carrier signal. It allows the transmission of data by varying the characteristics of the carrier signal, such as amplitude, frequency, or phase. While modulation techniques play a crucial role in data transmission, they do not directly determine the maximum achievable data rate.

Signal-to-Noise Ratio:
The signal-to-noise ratio (SNR) is a measure of the strength of the desired signal compared to the level of background noise. A higher SNR indicates a better quality signal. In communication systems, a higher SNR allows for more reliable transmission and reduces the likelihood of errors. However, SNR alone cannot determine the maximum data rate.

Frequency Bandwidth:
Frequency bandwidth refers to the range of frequencies available for communication in a channel. A wider bandwidth allows for a greater amount of data to be transmitted simultaneously, resulting in a higher data rate. However, the frequency bandwidth alone does not determine the maximum achievable data rate.

Channel Capacity:
The channel capacity is the maximum data rate at which information can be reliably transmitted over a communication channel. It takes into account various factors such as modulation, signal-to-noise ratio, and frequency bandwidth. The Shannon Capacity Formula, developed by Claude Shannon, provides a theoretical upper bound on the channel capacity. It states that the channel capacity is equal to the bandwidth multiplied by the logarithm of one plus the signal-to-noise ratio (C = B log2(1+SNR)).

The channel capacity is a measure of the channel's ability to transmit information without errors. It represents the maximum achievable data rate under ideal conditions. Achieving a data rate close to the channel capacity requires advanced modulation techniques, efficient error-correction coding, and signal processing algorithms.

In conclusion, the maximum rate at which nearly error-free data can be theoretically transmitted over a communication channel is defined as the channel capacity. It is determined by factors such as modulation, signal-to-noise ratio, and frequency bandwidth. The channel capacity represents the upper limit of data transmission and can be calculated using the Shannon Capacity Formula.