le. Conversely, the lower the signal power relative to noise power, the dirtier the channel becomes and therefore communication becomes less reliable. This equates to the experience that one has to speak more slowly to get a message across when the channel is not clean enough (or the receiver is hard of hearing - reduced received signal power). Shannon theorem also implies that any channel where signal power exists (i.e. the power of the signal is larger than zero) can be used for telecommunications. Capacity is always positive and more than zero SO long as bandwidth (B) and signal power (S) are not zero. (By definition bandwidth and power do not have negative values.) Example 4.7 If a DSL system uses a signal bandwidth of 1 MHz in its downstream communications, and the signal power to noise power ratio at a subscriber's home is 7, what is the maximum information transmission rate this system can support? Broadband Telecommunications Technologies and Management Answer What if we can increase the SNR at the subscriber's home to 15? Answer If a deep space probe uses a signal bandwidth of 100 MHz for its communications, and the SNR at the Earth's receiver antenna is 10-6, what is the maximum information transmission rate the system can support? Answer Shannon capacity is also known as Shannon limit since it calculates the maximum possible information transmission over a telecommunications channel. The limit in bits per second transmission with respect to a unit of bandwidth (1 Hz) is drawn VS SIN in Figure 4.7. Note for small values of SIN: log2(1+SIN)=SIN Shannon limit S/N (dB) Figure 4.7 Normalised capacity VS SIN Information Theory Therefore the Shannon limit increases linearly as the signal power to noise power ratio increases. In contrast at large SIN: log.(1+SIN)=log.(S/N) Therefore the Shannon limit increases logarithmically as the signal power to noise power ratio increases. The normalised capacity VS SIN is drawn in Figure 4.7. Example 4.8 Considering the Voyager's channel bandwidth of 340 kHz to 1.35 MHz, 