LDPC for MIMO Systems

1. LDPC for MIMO Systems July 8, 2004 Jianuxan Du, du@merl.com Daqing Gu, dgu@merl.com Jinyun Zhang, jzhang@merl.com Mitsubishi Electric Research Lab, Cambridge, MA

2. Outline • Introduction • Quasi-block diagonal LDPC for MIMO systems with layered structure • Simulation comparison with convolutional codes • Simulation comparison with V-BLAST

3. Introduction Advantages of LDPC • Capacity approaching performance • Parallelizability of decoding, suitable for high speed implementation • Flexibility: LDPC is simply a kind of linear block code and its rate can be adjusted by puncturing, shortening, etc.

4. Quasi-Block Diagonal LDPC Space-time Coding for Layered Systems • Feature: The encoding of different layers are correlated as compared with conventional V-BLAST. • Advantage: The space-time LDPC is designed such that the code can be decoded partially, but with the help of other layers (undecoded part) by the introduction of correlation between different layers.

5. Parity Check Structure of QBD-LDPC

6. Encoding of QBD-LDPC Encoding of QBD-LDPC • Qn-1 Hn= [Pn I] by Gaussian elimination. • The parity check bits for subcode n are given by Pnvn+ Qn-1vn-1 , where is vn the input information bit vector for subcode n, and vn-1 is derived from the subcode n-1. • With the given structure, the information about subcode n-1 is also contained in subcode n. Therefore, information from subcode n can help decoding subcode n-1.

7. Decoding of QBD-LDPC

8. Decoding of QBD-LDPC (Cont’) • The decoding is based on zero-forcing and interference cancellation, which is made possible by the lower-triangular structure of the parity check matrix. • The LLR’s of bits in successfully decoded subcodes are set to maximum or minimum value, depending on the output, to avoid ambiguity caused by the introduction of connection matrices.

9. Performance comparison with convolutional coding • 172Mbps • 64QAM • Code rate 0.6 • Channel Model ‘F’

10. Performance Comparison with Conventional V-BLAST • 72Mbps • 64QAM • Code rate 0.5 • Channel model ‘F’

11. Conclusion • LDPC outperforms convolutional coding by about 2dB. • The simulated QBD-LDPC system outperforms conventional LDPC-coded V-BLAST by about 0.5dB.

12. References [1] R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963. [2] B. Lu, X. Wang, and K. R. Narayanan, “LDPC-based space-time coded OFDM systems over correlated fading channels: performance analysis and receiver design,” IEEE Trans. Commun., vol. 50, pp. 74-88, Jan. 2002. [3] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Technical Journal, pp. 41-59, Aug. 1996. [4] S. Y. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inform. Theory, vol. 47, pp. 657-670, Feb. 2001. [5] P. Meshkat and H. Jafarkhani, “Space-time low-density parity-check codes,” Signals, systems and Computers, Conference Record of the Thirty-Sixth Asilomar Conference on, vol. 2, pp. 1117-1121, Nov. 2002.