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Confusion about channel capacity definition and units

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Why can the channel capacity C of the additive white gaussion noise (AWGN) channel be denoted in different ways and how do they relate to each other? Examples:

C = (1/2) * log2(1 + SNR)   [bit?]

source: wikipedia: Additive_White_Gaussian_Noise#Channel_Capacity

C = B * log2(1 + SNR)   [bit/s] with bandwidth B in Hz.

source: wikipedia: Channel_capacity#Example_application

SNR is the signal to noise ratio in both formulas and B is the bandwidth of the used channel in Hz.

awgn channel-capacity shannon-limit shannon-hartley-theorem

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Too many undefined variables, abbreviations, and missing context. (3 comments)