Consider a binary memory less channel characterized by the transition probability diagram shown in the figure.a)Losslessb)Noiselessc)Uselessd)DeterministicCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Binary Memoryless Channel

A binary memoryless channel is a communication channel in which the output at any given time depends only on the current input and is independent of all previous inputs. The channel is characterized by the transition probability diagram, which shows the probabilities of transitioning from one input to another output.

Transition Probability Diagram

The given figure represents the transition probability diagram of the binary memoryless channel. It shows the probabilities of transitioning from one input to another output.

Options

Lossless: A lossless channel is one in which there is no loss of information. In other words, the output is an exact replica of the input. This is not the case here, as there are transitions with non-zero probabilities.

Noiseless: A noiseless channel is one in which there is no noise or distortion in the transmission. The output is a perfect replica of the input. This is not the case here, as there are transitions with non-zero probabilities.

Useless: A useless channel is one in which the output does not provide any meaningful information about the input. This is the case here as there are transitions with zero probabilities. These transitions indicate that certain inputs cannot result in certain outputs. Therefore, the channel is useless as it does not provide any useful information.

Deterministic: A deterministic channel is one in which the output is completely determined by the input. This is not the case here, as there are transitions with non-zero probabilities.

Conclusion

Based on the given transition probability diagram, the binary memoryless channel can be categorized as useless because there are transitions with zero probabilities, indicating that certain inputs cannot result in certain outputs. Therefore, the channel does not provide any meaningful information about the input.

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