Analysis of LPDC Codes Flashcards
Describe the lemma of monotonicity with respect to channel
We can decode a value for epsilon for bad channels, meaning we can also decode for better channels as well.
Essentially epsilon will converge to zero for all 0 <= epsilon’ <= epsilon
In regular LPDC codes, what happens when we increase the number of variable nodes?
The BEC threshold decreases
Which is the best choice of variable node degree?
Three
What does the threshold tells us, in terms of picking code parameters?
Tells us which values of dv and dc to choose if we want to realise a code design rate rd
What is an EXIT Chart?
We use it to optimise LPDC codes
It tells us the number of steps before it converges
When does EXIT chart get violated?
When v tilda is less than c tilda; when there’s no open tunnel
What’s an extrinsic vector?
A vector which extracts one value
y_2 = (y_1, y_3, y_4)
Describe the inner-workings of the average EXIT function
The mutual information transferred one bit to the other bits except yj
What’s a necessary condition for EXIT functions
The area underneath the variable node EXIT function must be strictly larger than the area above the check node; have an open decoding tunnel
How do you build capacity-achieving codes?
dv, average must go to inf
How do we optimise an LDPC code in a BEC
- Optimise code
- Fix dv, max
- Sweep through dc,avg and dc,min
- Fix threshold
Employ binary search
1, Select dv,avg that leads to the average rate
2. rd,max > r,target; set target higher
3. and then repeat until delta epsilon gets so small until dc,avg is made
Describe when the threshold can be attained
If the code length n becomes asymptotically large and infinite number of iterations can be invested
What’s the density evolution
A method for analysing the asymptotic performance of network capability error-correcting codes.
For irregular LPDC codes with message-passing decoding, the density evolution can track the messages ot find out the threshhold, enabling optimisation of the degree distribution.
