Time taken for transmission?

Question

Hi
I have the follow problem:
An essay written in the English language is 3000 words long. Assuming that the English alphbet consists of 26 upper case letters, 10 numerals and 20 punctuation marks, and the average word length si 6 characters, (a) Calculate how long it will take to transmit the whole essay through a channel band limited to 2kHz (b) How can the time calculated in (a) be reduced, without losing any information.

Can anyone please explain this to me? thnx :)

Answer 1

3000 words * 6 characters per word = 18,000 characters

Each character must be encoded into binary bits. Since there are 26 + 10 + 20 = 56 possible characters, the whole set may be encoded by 6-bit binary numbers (2^6 = 64, which is the least power of 2 greater than 56 -- pretty close to 56 actually).

18,000 characters * 6 bits / character = 108,000 bits to transmit in the channel. NOTE: this is based on 'brute force', no error correction, no overhead bits -- just the message bits, only.

If the channel bandwidth is 2 kHz, then Nyquist says we can only pass information at 1/2 that frequency; 1 kHz which is 1000 per second, or 1000 'things' per second. Those things are binary bits., so if we can pass 1000 bits/sec and there are 108,000 bits, then it will take108 seconds to transmit the message.

What can be done to reduce the time? There are non-lossy compression algorithms that could be applied to the 108,000 bits of the message that would probably reduce the message length (and the transmission time).

Another way to reduce the transmission time (that can be used by itself, or in combination with compression): There are techniques in modulating a carrier signal (with the binary bit information) that group 2, 3,or 4 bits together and change the voltage and phase of the carrier based on the number in those 2, 3, or 4 bits and treat that particular voltage/phase combination as a single entity for transmission. This is how Modems work.

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