Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting "LP decoder" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers." The fractional distance d/sub frac/ of a code is introduced, which is a lor bound on the classical distance. It is shown that the efficient LP decoder will correct up to /spl lceil/d/sub frac//2/spl rceil/-1 errors and that there are codes with d/sub frac/=/spl Omega/(n/sup 1-/spl epsi//). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes beten LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.
['Jon Feldman', 'Martin J. Wainwright', 'David R. Karger']
I am writing a research paper on a idea Using linear programming to Decode Binary linear codes
[{"from": "human", "value": "I am writing a research paper on a idea Using linear programming to Decode Binary linear codes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting \"LP decoder\" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including \"stopping sets,\" \"irreducible closed walks,\" \"trellis cycles,\" \"deviation sets,\" and \"graph covers.\" The fractional distance d/sub frac/ of a code is introduced, which is a lor bound on the classical distance. It is shown that the efficient LP decoder will correct up to /spl lceil/d/sub frac//2/spl rceil/-1 errors and that there are codes with d/sub frac/=/spl Omega/(n/sup 1-/spl epsi//). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes beten LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided."}]