LDPC Codes for the Two-User GMAC
Keywords:
GMAC, LDPCAbstract
The capacity region of Gaussian Multiple Access Channels (GMACs) has been known since 1971. The efficient design of powerful codes that can achieve points near the dominant face of the capacity region, where the sum-rate is maximal, is an interesting problem. Significant progress has been made in this direction using time sharing, rate-splitting, as well as joint iterative decoding. Joint iterative decoding seems to be the most promising path, especially for codes that have low-complexity decoders, like Low-Density Parity-Check (LDPC) codes. LDPC codes are capacity-approaching over a wide variety of channels. Additionally, elegant tools, such as Density Evolution and EXIT charts, can be used to accurately predict the asymptotic performance of an LDPC code ensemble. These tools can be used for the design of optimal LDPC codes, allowing for transmission over many types of channels with vanishingly small probability of error. In this paper, we focus on the two-user GMAC. To the best of our knowledge, there exist two LDPC code design frameworks for this channel. We provide simulation results that demonstrate the excellent finite length performance of codes designed using the proposed method.
References
T. M. Cover and A. A. E. Gamal, “Capacity theorems for the relay channel,” IEEE Transactions on Information Theory, vol. 25, no. 5, pp. 572-584, Sep. 1979.
R. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory,pp. 21(28, Jan. 1962.
D. MacKay and R. Neal, “Good codes based on very sparse matrices,” in Lecture Notes in Computer Science, pp. 100-111, Cryptography and Coding, 5th IMA Conference, Springer,1995.
T. Richardson and R. Urbanke, “E_cient encoding of low-density parity-check codes,”IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 638-656, Feb. 2001.
M. R. Tanner, “A recursive approach to low complexity codes,” IEEE Transactions on Information Theory, vol. 27, pp. 533-547, Sept. 1981.
T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008.
T. Cover and J. Thomas, Elements of Information Theory, John Wiley & Sons, Inc., 2006.
A. D. Wyner, “Recent results in the Shannon theory,” IEEE Transactions on Information Theory, vol. IT-20, pp. 4?10, Jan. 1974.
P. P. Bergmans and T. M. Cover, “Cooperative broadcasting,” IEEE Transactions on Information Theory, vol. IT-20, pp. 317{324, May 1974.
B. Rimoldi and R. Urbanke, “A rate splitting approach to the Gaussian multiple-access channel,” IEEE Transactions on Information Theory, vol. 42, no. 2, pp. 364{375, Mar. 1996.
A. Amraoui, S. Dusad, and R. Urbanke, “Achieving general points in the 2-user Gaussian MAC without time-sharing or rate-splitting by means of iterative decoding,” in Proceedings of the IEEE International Symposium on Information Theory, 2002, p. 334, July 2002.
A. Roumy and D. Declercq, “Characterization and optimization of LDPC codes for the 2-user Gaussian multiple access channel,” EURASIP Journal on Wireless Communications and Networking., vol. 2007, June 2007.
J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, 1988.
Downloads
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
