Title :
Ellipsoidal lists and maximum-likelihood decoding
Author_Institution :
Coll. of Eng., California Univ., Riverside, CA, USA
fDate :
3/1/2000 12:00:00 AM
Abstract :
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}
Keywords :
computational complexity; error statistics; linear codes; maximum likelihood decoding; memoryless systems; quantisation (signal); Hamming spaces; ML decoding complexity; coverings; discrete ellipsoids; ellipsoidal lists; error probability; exponential size; linear codes; maximum-likelihood decoding; most probable error patterns; quantized memoryless channel; soft-decision ML decoding; trellis complexity; Clustering algorithms; Concatenated codes; Ellipsoids; Error correction codes; Galois fields; Maximum likelihood decoding; Memoryless systems; Tensile stress; Testing;
Journal_Title :
Information Theory, IEEE Transactions on