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# Channel bandwidth and backup requirement

Consider an organization, which has a rented communications channel between two buildings, A and B. They have a set of servers in building A, and wish to back up critical data on an hourly basis to a set of storage drives in building B. They know that the channel has a bandwidth of 10KHz and a signal-to-noise ratio of 20dB.
(i) If their server system generates an average of 45 MB of data each hour, can they use this channel to implement the back up? Explain your answer.
(ii) The organization anticipates a doubling of generated backup requirement in the next year. What advice would you offer in respect of their back up options?

#### Solution Preview

Decibel value and signal-to-noise ratio (SNR) are related as below.

Hence,
20 dB = 10 * log_base_10 (SNR)
=> SNR = 10 ^ (20/10) = 10 ^ 2 = 100

Given,
Channel bandwidth (B) = 10 KHz
Channel signal-to-noise ratio (SNR) = 100 (i.e. 20 dB)

We can compute channel's capacity (C) by applying Shannon's formula:

C = B * lg(1+SNR), where lg indicates log_base_2.

Hence,
Channel's capacity (C) = 10 KHz * lg(1+100)
= 10 * lg(101) Kbps
= 10 * 6.6582 Kbps (rounding to ...

#### Solution Summary

Detailed explanations accompany step-by-step solution. In case of question (ii), solution suggests two alternatives.

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