Binary symmetric channel capacity

In summary, the conversation discusses the calculation of a binary symmetric channel denoted as C. The formula for the channel is C=1+plogp+(1-p)log(1-p). The speaker also asks about the meaning of ";" in X;Y and requests for additional resources on the topic. Another person replies to keep the conversation going and invites others to share their knowledge on the subject.
  • #1
dervast
133
1
Hi to our nice community. I want to learn why
in a binary symetric channel the channel is calculated as
C=1+plogp+(1-p)log(1-p)

I only know that the channel is denoted as C=maxI(X;Y)
btw what ; means in X;Y?
Unfortunately my book doesn't mention these things so if u can reply me or provide me with some good links that will be rezlly nicenow i need something more
Why in a binary symetric channel the channel is calculated for
C=1+plogp+(1-p)log(1-p)

I only know that the channel is denoted as C=maxI(X;Y)
btw what ; means in X;Y?
Unfortunately my book doesn't mention these things so if u can reply me or provide me with some good links that will be rezlly nice
 
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  • #2
Replying so that this thread isn't a no-reply, as per Greg's wishes.
If anyone has knowledge on this subject, feel free to reply.
 

1. What is a binary symmetric channel (BSC)?

A binary symmetric channel is a communication channel that transmits binary (two-state) data, where the probability of error is the same for both states. This means that the channel has an equal chance of flipping a transmitted bit from 0 to 1 or from 1 to 0.

2. How is the capacity of a binary symmetric channel calculated?

The capacity of a binary symmetric channel is calculated using Shannon's channel capacity formula, which takes into account the channel's bandwidth and signal-to-noise ratio. It can be represented as C = 1 - H(p), where H(p) is the Shannon entropy of the channel's error probability (p).

3. What factors affect the capacity of a binary symmetric channel?

The capacity of a binary symmetric channel is affected by the channel's bandwidth, signal-to-noise ratio, and error probability. A wider bandwidth and higher signal-to-noise ratio can increase the channel's capacity, while a higher error probability can decrease it.

4. What is the maximum capacity of a binary symmetric channel?

The maximum capacity of a binary symmetric channel is achieved when the error probability (p) is set to 0.5. In this case, the channel's capacity is equal to 1 bit per channel use. This means that the channel can transmit one bit of information with complete accuracy on average.

5. How is the capacity of a binary symmetric channel related to its error correction capability?

The capacity of a binary symmetric channel is inversely related to its error correction capability. This means that as the channel's capacity increases, its ability to correct errors decreases. Therefore, a higher capacity channel may require more advanced error correction techniques to maintain a low error rate.

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