Block-LDPC: A Practical LDPC Coding System Design Approach

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 • 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~