Basic Coding Concepts Flashcards
What is a code?
An error correcting code is a device that adds redundant information to a block of data symbols and uses this information to correct potential transmission errors.
What happens if a code has a high and low rate?
A high rate adds only a small amount of redundant information
A low rate adds a large amount of redundant information
The rate of a code is a measure of what?
The bandwidth effiency
How do we get the hamming weight?
We get the nymber of non-zero symbols (number of ones)
Give an example of how to get the hamming distance
u = (00100)
v = (10101)
d(min)=2
Give the formula for detectable errors (BSC)
d = dmin - 1
Give the formula for correctable errors (BSC)
e = [dmin - 1 / 2]
What’s the disadvantage of BI-AWGN channels
Not good for good dmin
What’s the goal of a decoder?
To maximises the a posteriori probability
Channel Coding Theorem
What’s entropy?
A measure of “unpredictability” of a random variable
What’s the capacity of a channel?
The maximum amount of information (expressed in “information bits per channel use” that a channel can convey)
Explain what the rate should be when finding the best possible code
When the rate is equal to the capacity
What is the absolute communication limit for AWGN and what is it?
- The worst channel we can communicate over and it’s -1.59dB
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Explain what the Hard-Decision BI-AWGN Channel does
It has a decision factor transforms the channel into a BSC channel
