Towards Low-Complexity Linear-Programming Decoding

Konferenz: TURBO - CODING - 2006 - 4th International Symposium on Turbo Codes & Related Topics; 6th International ITG-Conference on Source and Channel Coding
03.04.2006 - 07.04.2006 in Munich, Germany

Tagungsband: TURBO - CODING - 2006

Seiten: 9Sprache: EnglischTyp: PDF

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Vontobel, Pascal O. (Dept. of EECS, MIT, Cambridge, MA 02139, USA)
Koetter, Ralf (CSL and Dept. of ECE, University of Illinois, Urbana, IL 61801, USA)

We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP at hand is equipped with a lot of structure that one should take advantage of. Towards this goal, we study the dual LP and show how coordinate-ascent methods lead to very simple update rules that are tightly connected to the min-sum algorithm. Moreover, replacing minima in the formula of the dual LP with soft-minima one obtains update rules that are tightly connected to the sum-product algorithm. This shows that LP solvers with complexity similar to the min-sum algorithm and the sum-product algorithm are feasible. Finally, we also discuss some sub-gradient-based methods.