# Analysis of LPDC Codes Flashcards

1
Q

Describe the lemma of monotonicity with respect to channel

A

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

2
Q

In regular LPDC codes, what happens when we increase the number of variable nodes?

A

The BEC threshold decreases

3
Q

Which is the best choice of variable node degree?

A

Three

4
Q

What does the threshold tells us, in terms of picking code parameters?

A

Tells us which values of dv and dc to choose if we want to realise a code design rate rd

5
Q

What is an EXIT Chart?

A

We use it to optimise LPDC codes

It tells us the number of steps before it converges

6
Q

When does EXIT chart get violated?

A

When v tilda is less than c tilda; when there’s no open tunnel

7
Q

What’s an extrinsic vector?

A

A vector which extracts one value

y_2 = (y_1, y_3, y_4)

8
Q

Describe the inner-workings of the average EXIT function

A

The mutual information transferred one bit to the other bits except yj

9
Q

What’s a necessary condition for EXIT functions

A

The area underneath the variable node EXIT function must be strictly larger than the area above the check node; have an open decoding tunnel

10
Q

How do you build capacity-achieving codes?

A

dv, average must go to inf

11
Q

How do we optimise an LDPC code in a BEC

A
1. Optimise code
2. Fix dv, max
3. Sweep through dc,avg and dc,min
4. 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

12
Q

Describe when the threshold can be attained

A

If the code length n becomes asymptotically large and infinite number of iterations can be invested

13
Q

What’s the density evolution

A

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.