# Introduction to LPDC Codes Flashcards

1
Q

What are the advantages of Log-Likelihood Ratios

A

They are used due to their advantages when it comes to hardware implementation; when dealing with probabilities in the real world, we usually deal with high or low probs.

This means that we need a large number of bits to calculate.

We don’t need to normalise as we are dividing .

The log factor becomes additions, which is advantageous in digital circuits; used in encoders

2
Q

Explain the concept of normalising in probability

A

That P(X=0) + P(X=1) = 1

3
Q

What is Lc in LLR?

A

Channel reliability parameter

4
Q

In graph theory, what is an edge?

A

We connect vertex vi to vertex vj

5
Q

What is d(v)?

A

The degree of the vertex connected to v (the number of vertices)

6
Q

What is a bipartite graph?

A

It’s a graph that subdivides the vertex set V into V1 and V2

7
Q

What is a tanner graph?

A

A tanner graph is a bipartite graph i.e. it has two classes of vertices and every edge connects a node of the first class with a node of the second class

The first class of vertices V1 are variable nodes and there are n of them, each corresponding to a code bit xi and therefore a column of H

The second class of vertices V2 are check nodes and there are m of them, each corresponding to a parity-check constraint and therefore a row of H

It’s for binary linear (LPDC) codes

8
Q

What is an LPDC code

A

An LPDC code is one that has a variety of parity check sets which cover a low density.

This allows the fast recovery of erasures while allowing a good coding rate.

9
Q

Discuss the sub-optimality of message passage decoding

A

If the Tanner graph of the LDPC code does not contain any cycles, then the message passing decoder is equivalent to the (bit-wise) MAP decoder.

All practically relevant codes have cycles, thus, message passing decoding is sub-optimal compared to (bit-wise) MAP decoding.

10
Q

When does an error floor occur?

A

Occurs if above a certain channel quality, the bit error rate does not decrease rapidly anymore, but decreases with a smaller slope only

Usually happens due to combinations of cycles (trapping sets) that cannot be recovered by the decoder

11
Q

When do we hit the threshold of LDPC codes?

A

It hits when the BER starts to decrease rapidly