### Abstract

Suppose a binary linear block code C with weight profile W is used for error control over the AWGN channel. A codeword c is mapped into the BPSK sequence x. Let r denote the received noisy vector and z=(z_{1}, ⋯,z_{N}) denote the corresponding bit-by-bit hard decoded sequence. Let V^{N} represent the set all binary N-tuples. For u=(u _{1},⋯,u_{N}) in V^{N}, we define D _{1}(u)={i:u_{i}≠z_{i},i≤N}, n(u)=|D _{1}(u)| and D_{o}(u)={1,⋯,N}-D_{1}(u). Then the maximum likelihood decoding (MLD) solution is the codeword c/sub opt/ which minimize the correlation discrepancy L(c)=Σ_{iεD1(c)}|Ti|. Consequently if for c*εC and α(c*)=min _{εC,c≠c*}{L(c)}, L(c*)≤α(c*), then c*=c_{opt}. Therefore any lower bound on alpha/(c*) will provide a sufficient condition on the optimality of a candidate codeword.

Original language | English |
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Title of host publication | Proceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997 |

Number of pages | 1 |

DOIs | |

Publication status | Published - Dec 1 1997 |

Externally published | Yes |

Event | 1997 IEEE International Symposium on Information Theory, ISIT 1997 - Ulm, Germany Duration: Jun 29 1997 → Jul 4 1997 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Conference

Conference | 1997 IEEE International Symposium on Information Theory, ISIT 1997 |
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Country | Germany |

City | Ulm |

Period | 6/29/97 → 7/4/97 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

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## Cite this

*Proceedings - 1997 IEEE International Symposium on Information Theory, ISIT 1997*[613367] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.1997.613367