Abstract
We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs–most importantly, low-density parity-check (LDPC) codes–exploit randomness in the structure of the code. Our approach is to introduce a similar degree of controlled randomness into the operation of the message-passing decoder, to improve the performance of iterative decoding of classical structured (i.e., non-random) codes for which strong code properties are known. We use ideas similar to Halford and Chugg (IEEE Trans. on Commun., April 2008), where permutations on the columns of the parity-check matrix are drawn from the automorphism group of the code, Aut\(\mathcal{(C)}\). The main contributions of our work are: 1) We maintain a graph-local perspective, which not only gives a low-complexity, distributed implementation, but also suggests novel applications of our work, and 2) we present an operation to draw from Aut\(\mathcal{(C)}\) such that graph isomorphism is preserved, which maintains desirable properties while the graph is being updated. We present simulation results for the additive white Gaussian noise (AWGN) channel, which show an improvement over standard sum-product algorithm (SPA) decoding.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gallager, R.G.: Low-density parity-check codes. IRE Trans. Inform. Theory 8(1), 21–28 (1962)
MacKay, D.J.C., Neal, R.M.: Good codes based on very sparse matrices. In: Cryptography and Coding 5th IMA Conf., December 1995, pp. 100–111 (1995)
Jiang, J., Narayanan, K.R.: Iterative soft-input soft-output decoding of Reed-Solomon codes by adapting the parity-check matrix. IEEE Trans. Inform. Theory 52(8), 3746–3756 (2006)
Jiang, J., Narayanan, K.R.: Iterative soft decision decoding of Reed-Solomon codes. IEEE Commun. Lett. 8(4), 244–246 (2004)
Halford, T.R., Chugg, K.M.: Random redundant iterative soft-in soft-out decoding. IEEE Trans. on Commun. 56(4), 513–517 (2008)
Vontobel, P.O., Koetter, R.: Graph-cover decoding and finite-length analysis of message-passing iterative decoding of LDPC codes. IEEE Trans.Inform.Theory (2005) (submitted for publication)
Di, C., Proietti, D., Telatar, I.E., Richardson, T.J., Urbanke, R.L.: Finite-length analysis of low-density parity-check codes on the binary erasure channel. IEEE Trans. Inform. Theory 48(6), 1570–1579 (2002)
Richardson, T.: Error floors of LDPC codes. In: Proc.41st Annual Allerton Conf.on Commun., Control, and Computing, Monticello, IL, October 2003, pp. 1426–1435 (2003)
Richardson, T.J., Urbanke, R.: The capacity of low-density parity-check codes under message-passing decoding. IEEE Trans. Inform. Theory 47(2), 599–618 (2001)
Bouchet, A.: Isotropic systems. European Journal of Combinatorics 8, 231–244 (1987)
Danielsen, L.E., Parker, M.G.: Edge local complementation and equivalence of binary linear codes. Des. Codes Cryptogr. (to appear, 2008)
Riera, C., Parker, M.G.: On Pivot orbits of Boolean functions, optimal codes and related topics. In: Fourth International Workshop on Optimal Codes and Related Topics, Sofia, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, June 2005, pp. 248–253 (2005)
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE. Trans. on Inform. Theory 47(2), 498–519 (2001)
Knudsen, J.G.: Randomised construction and dynamic decoding of LDPC codes. Master’s thesis, University of Bergen (2006)
Danielsen, L.E., Parker, M.G.: On the classification of all self-dual additive codes over GF(4) of length up to 12. Journ. of Comb. Theory, Series A 113(7), 1351–1367 (2006)
Catherine, C.: Enhancing the error-correction performance of low-density parity-check codes. PhD thesis, University of Mauritius (2008)
Kothiyal, A., Takeshita, O.: A comparison of adaptive belief propagation and the best graph algorithm for the decoding of linear block codes. In: International Symposium on Information Theory, September 2005, pp. 724–728 (2005)
Kou, Y., Lin, S., Fossorier, M.P.C.: Low-density parity-check codes based on finite geometries: A rediscovery and new results. IEEE Trans. Inform. Theory 47(7), 2711–2736 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Knudsen, J.G., Riera, C., Parker, M.G., Rosnes, E. (2008). Adaptive Soft-Decision Iterative Decoding Using Edge Local Complementation. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-87448-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87447-8
Online ISBN: 978-3-540-87448-5
eBook Packages: Computer ScienceComputer Science (R0)