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Quasi-light Storage for Optical Data Packets

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Optimizing Finite-Blocklength Nested Linear Secrecy Codes: Using the Worst Code to Find the Best Code.

Morteza Shoushtari¹, Willie Harrison¹

¹Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA.

Entropy (Basel, Switzerland)

|October 28, 2023

Summary

This summary is machine-generated.

This study introduces a faster method for finding optimal nested linear secrecy codes, crucial for secure wireless communications. The new algorithm improves efficiency over traditional brute-force searches.

Keywords:

dimension/length profile dual codes equivocation generalized Hamming weights nested linear codes optimal secrecy code two-edge LDPC codes wiretap channel

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Area of Science:

Coding Theory
Wireless Communications
Information Security

Background:

Nested linear codes enhance security and reliability in wireless systems.
Performance is characterized by parameters like relative generalized Hamming weight and rank properties.
Optimizing nested linear secrecy codes in finite-blocklength regimes is computationally challenging.

Purpose of the Study:

To investigate properties of nested linear codes.
To introduce a novel representation for relative generalized Hamming weight.
To propose an efficient algorithm for finding optimal nested linear secrecy codes for the binary erasure wiretap channel.

Main Methods:

Introduced a new representation of the relative generalized Hamming weight.
Developed a novel algorithm that operates in the dual space, starting from the worst-case scenario.
Applied the method to find the best nested linear secrecy code for the binary erasure wiretap channel.

Main Results:

The proposed algorithm significantly outperforms brute-force search in speed and efficiency.
Demonstrated a novel approach to characterizing and optimizing nested linear secrecy codes.
Provided a more effective method for achieving enhanced security in wireless communication.

Conclusions:

The novel method offers a significant improvement for finding optimal nested linear secrecy codes.
This advancement addresses a key challenge in the finite-blocklength regime.
The findings contribute to more secure and efficient wireless communication systems.