# 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.