Abstract
Low Density Parity Check (LDPC) codes are considered in many future communication systems for error correction coding. Optimal decoding of LDPC codes is usually too costly to be done in practice. For this reason, sub-optimal algorithms are used. A state-of-the-art algorithm for decoding of LDPC codes is called belief propagation (BP). For short LDPC codes and for codes with an implementation efficient structure, the performance of this algorithm can be far from optimum.
We present a graphical model for representing the decoding problem, called configuration graph. We show the construction of a configuration graph and describe how the decoding problem can be represented as maximum weighted vertex problem (VP) on a configuration graph. We describe decoding approaches utilizing this representation and show the improvements in terms of decoding performance as well as the complexity/performance trade-offs possible with these algorithms.
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References
Gallager, R.G.: Low-Density Parity-Check Codes. MIT Press, Cambridge (1963)
Joint Proposal: High throughput extension to the 802.11 Standard: PHY. IEEE 802.11-05/1102r4 (2006)
Kschischang, F., Frey, B., Loeliger, H.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 51(3), 954–972 (2005)
Chung, S.Y., Forney, G.D., Richardson, T.J., Urbanke, R.: On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit. IEEE Communications Letters 5(2) (2001)
Etzion, T., Trachtenberg, A., Vardy, A.: Which Codes Have Cycle-Free Tanner Graphs. IEEE Transactions on Information Theory 45(6), 2173–2181 (1999)
Lunglmayr, M., Berkmann, J., Huemer, M.: Vertex Packing Decoding. In: Proc. International Conference on Communications (ICC), Dresden, Germany (2009)
Nemhauser, G., Trotter, L.: Vertex Packings: Structural Properties and Algorithms. Mathematical Programming 8(1), 232–248 (1975)
Michalewicz, Z., Fogel, D.: How to Solve It: Modern Heuristics, 2nd edn. Springer, Heidelberg (2004)
Bossert, M.: Channel Coding for Telecommunications. Wiley, Chichester (1999)
MacKay, D.: Encyclopedia of Sparse Graph Codes (hypertext archive), http://www.inference.phy.cam.ac.uk/mackay/codes/data.html
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Lunglmayr, M., Berkmann, J., Huemer, M. (2009). Simulation Based Optimization of Vertex Packing Decoding Algorithms. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2009. EUROCAST 2009. Lecture Notes in Computer Science, vol 5717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04772-5_61
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DOI: https://doi.org/10.1007/978-3-642-04772-5_61
Publisher Name: Springer, Berlin, Heidelberg
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