Shannon’s limit

As promised my second post is about how Claude Shannon’s theory of communications shapes the future of the wireless world. Even though his formula is fairly simple, it will take a number of posts to discuss the relationship among all the factors determining a communications system.

Fundamentally what Shannon developed can be summarized by the following formula:

where C signifies the channel capacity, W denotes the channel bandwidth, P and N stand for power of signal and noise, respectively.

Entire history of wireless communications since the days of Marconi is all about optimizing these parameters so that the channel capacity (C) can be increased to allow richer communication among the users of these devices. A great reference is a Master’s thesis submitted by Mario Amaya to MIT in 2008. Considering wireless communications history has started with sending Morse signals (less than 1 bit/s), we have come some a significant way when commercial systems for handheld devices, with fast mobility have reached channel capacity of 100 Mbit/s. Recent news from Telstra is a good proof of this.  I believe this scale of more than 108 increase in just over 100 years is a testament to human desire for richer communications.

Even though human speech can be faithfully reproduced with less than 12 Kbit/s (AMR codec), there is a lot one can do with 100 Mbit/s. I can quickly think of following forms of communication:

  • High-fidelity voice (music) (less than 256 Kbit/s)
  • High fidelity video (less than 3 Mbit/s)
  • Virtual reality (less than <?> Mbit/s) (Any good numbers?)

I believe one can go on forever to find increasing volumes of information to be transferred to replicate one says, sees, touches, hears, (possibly :)) smells to another over long distances. Even though more efficient ways for this replication can be found to reduce the needed channel capacity, ultimately progress in technology points towards increasing the channel capacity year after year.

In the next post, I will discuss how available channel bandwidth and its location (of the center frequency) within the radio spectrum affect the channel capacity.

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