### Abstract

It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Rényi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Rényi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes.

Original language | English (US) |
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Title of host publication | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 |

Pages | 811-818 |

Number of pages | 8 |

DOIs | |

State | Published - Dec 1 2009 |

Event | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States Duration: Sep 30 2009 → Oct 2 2009 |

### Publication series

Name | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 |
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### Other

Other | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 |
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Country | United States |

City | Monticello, IL |

Period | 9/30/09 → 10/2/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Control and Systems Engineering
- Communication

### Cite this

*2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009*(pp. 811-818). [5394942] (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394942

}

*2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009.*, 5394942, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, pp. 811-818, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, Monticello, IL, United States, 9/30/09. https://doi.org/10.1109/ALLERTON.2009.5394942

**Interference channels with strong secrecy.** / He, Xiang; Yener, Aylin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Interference channels with strong secrecy

AU - He, Xiang

AU - Yener, Aylin

PY - 2009/12/1

Y1 - 2009/12/1

N2 - It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Rényi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Rényi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes.

AB - It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Rényi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Rényi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes.

UR - http://www.scopus.com/inward/record.url?scp=77949629139&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949629139&partnerID=8YFLogxK

U2 - 10.1109/ALLERTON.2009.5394942

DO - 10.1109/ALLERTON.2009.5394942

M3 - Conference contribution

SN - 9781424458714

T3 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

SP - 811

EP - 818

BT - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

ER -