Introduction to LPDC Codes

Question 1

What are the advantages of Log-Likelihood Ratios

Answer 1

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

Question 2

Explain the concept of normalising in probability

Answer 2

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

Question 3

What is Lc in LLR?

Answer 3

Channel reliability parameter

Question 4

In graph theory, what is an edge?

Answer 4

We connect vertex vi to vertex vj

Question 5

What is d(v)?

Answer 5

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

Question 6

What is a bipartite graph?

Answer 6

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

Question 7

What is a tanner graph?

Answer 7

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

Question 8

What is an LPDC code

Answer 8

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.

Question 9

Discuss the sub-optimality of message passage decoding

Answer 9

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.

Question 10

When does an error floor occur?

Answer 10

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

Question 11

When do we hit the threshold of LDPC codes?

Answer 11

It hits when the BER starts to decrease rapidly