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Ellipsoidal lists and maximum-likelihood decoding

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1 Author(s)
Dumer, I. ; Coll. of Eng., California Univ., Riverside, CA, USA

We study an interrelation between the coverings generated by linear (n,k)-codes and complexity of their maximum-likelihood (ML) decoding. First , discrete ellipsoids in the Hamming spaces E1n are introduced. These ellipsoids represent the sets of most probable error patterns that need to be tested in soft-decision ML decoding. We show that long linear (n,k)-codes surrounded by ellipsoids of exponential size 2n-k can cover the whole space E2n. Then it is proven that ML decoding of most long (n,k)-codes needs only about 2n-k most probable error patterns to be tested on any quantized memoryless channel. Finally, ML decoding complexity is bounded from above by 2k(n-k)n/. This substantially reduces the general trellis complexity 2min{n-k,k}

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 2 )