Introduction:
The Binary Symmetric Channel (BSC) is a communication channel model that is widely used to analyze the performance of digital communication systems. It is a simple and commonly used model for studying the effects of channel noise.

Explanation:
The capacity of a communication channel is the maximum rate at which information can be reliably transmitted over the channel. In the case of a Binary Symmetric Channel, the capacity can be calculated using the Shannon Capacity formula.

The Shannon Capacity formula for a Binary Symmetric Channel is given by:
C = 1 - H(p)

where C is the channel capacity, and H(p) is the entropy of the cross-over probability, p.

Entropy Calculation:
The entropy of the cross-over probability, H(p), can be calculated using the formula:
H(p) = -p * log2(p) - (1-p) * log2(1-p)

In the case of a cross-over probability of 0.5 (p=0.5), the entropy can be calculated as follows:
H(0.5) = -0.5 * log2(0.5) - (1-0.5) * log2(1-0.5)
= -0.5 * (-1) - 0.5 * (-1)
= 0.5 + 0.5
= 1

Channel Capacity Calculation:
Using the Shannon Capacity formula, we can calculate the channel capacity for a Binary Symmetric Channel with a cross-over probability of 0.5:
C = 1 - H(0.5)
= 1 - 1
= 0

Conclusion:
The capacity of a Binary Symmetric Channel with a cross-over probability of 0.5 is 0. This means that no reliable information can be transmitted over such a channel. The channel is completely noisy, and any transmitted information will be corrupted.

Given the binary symmetric channel (BSC) with crossover probability 0.6. So, we have