1. Block-LDPC: A Practical LDPC Coding System Design Approach
Hao Zhong and Tong Zhang,
IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 4, pp. 766–775, April 2005
2005 / 8 / 16 Chia-Yu Lin

2. Outline Introduction Block-LDPC Code Construction
Block-LDPC Encoder Design
LDPC Decoder Design
Conclusion

3. Introduction LDPC coding system implementation
Conventional: code-to-encoder/decoder design
 Not appropriate
Block-LDPC: joint code-encoder-decoder design

4. Introduction Questions of a complete joint design solution
What constraints should be used in code construction to facilitate the hardware implementation?
How to preserve the good error-correcting performance under those code construction constraints?
What are the appropriate encoder and decoder architectures?

5. Introduction
Weaknesses of the state-of-the-art LDPC coding system design solutions
Only consider decoder design and left encoder design unconsidered.
Did not address how to further optimize the code error-correcting performance under these constraints.

6. Introduction Block-LDPC code system
Semi-random implementation-oriented code construction approach.
Low-complexity encoding process and pipelined partially parallel encoder hardware architecture.
Partially parallel decoder hardware architecture.

7. Block-LDPC Code Construction
Implementation-Oriented Constraints
Decoder-oriented constraint
The parity check matrix should be block structured with circular block matrices.
Encoder-oriented constraint
The parity check matrix should be lower macro-block triangular.

8. Block-LDPC Code Construction
Performance-Oriented Constraints
Large code length (Determined by applications)
Carefully designed node degree distribution
 Obtained by a standard technique, i.e, density evolution
Not too many small cycles
 Set a constraint on the girth and the degree of a cycle
Widespread bipartite graph connectivity
 Reached by randomness in the overall construction

9. Block-LDPC Code Construction
The degree of a cycle :
The sum of degrees of all variable nodes found along the path of a cycle.

10. Block-LDPC Code Construction
1) Determine the code parity check matrix parameters.
2) Construct a group of code parity check matrices.
3) Select one code from the code group for real application.

11. Block-LDPC Code Construction
Code selection is based on a metric called cycle effect metric.
Ni : the number of cycles with the length of i
a : a value chosen for the sum to converge.
The code with smaller value of cycle effect tends to have less small cycles.

12. Block-LDPC Code Construction
Parity check matrix subject to implementation-oriented constraints

13. Simulation Result

14. Simulation Result

15. Block-LDPC Encoder Design
Encoding process
* H =
Since
And let x=(s,p1,p2), s : systematic part, p1and p2 : parity part
We get
then

16. Block-LDPC Encoder Design

17. Block-LDPC Encoder Design
Block Structured Matrix-Vector Multiplication
inter-vector-parallel/intra-vector-serial computational style

18. Block-LDPC Encoder Design

19. Block-LDPC Encoder Design
Hardware architecture for block structured sparse matrix-vector multiplication

20. Block-LDPC Encoder Design
Pipelined Block-LDPC encoder structure

21. LDPC Decoder Design
Decoder architecture

22. LDPC Decoder Design

23. Conclusion
Present a joint code-encoder-decoder design solution, called Block-LDPC, for practical LDPC coding system implementations.
Present code construction constraints and develop a semi-random approach for Block-LDPC code construction.
Develop a pipelined partially parallel Block-LDPC code encoder and a partially parallel Block-LDPC code decoder.

24. Thank you~