Nested linear coding is a widely used technique in wireless communication systems for improving both security and reliability. Some parameters, such as the relative generalized Hamming weight and the relative dimension/length profile, can be used to characterize the performance of nested linear codes. In addition, the rank properties of generator and parity-check matrices can also precisely characterize their security performance. Despite this, finding optimal nested linear secrecy codes remains a challenge in the finite-blocklength regime, often requiring brute-force search methods. This paper investigates the properties of nested linear codes, introduces a new representation of the relative generalized Hamming weight, and proposes a novel method for finding the best nested linear secrecy code for the binary erasure wiretap channel by working from the worst nested linear secrecy code in the dual space. We demonstrate that our algorithm significantly outperforms the brute-force technique in terms of speed and efficiency.
Secure computation of linear functions over linear discrete multiple-access wiretap channels
In this paper, a joint source-channel coding approach is taken to the problem of securely computing a function of distributed sources over a multiple-access wiretap channel that is linear with respect to a finite field. It is shown that if the joint source distribution fulfills certain conditions and the function to be computed matches the linear structure of the channel, secrecy comes for free in the sense that the fundamental limit (i.e., the secrecy computation-capacity) is achieved without the need for stochastic encoding. Furthermore, the legitimate receiver does not need any advantage over the eavesdropper, which is in stark contrast to standard physical-layer security results.
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- NSF-PAR ID:
- 10026242
- Date Published:
- Journal Name:
- Proceedings of the 50th Annual Asilomar Conference on Signals, Systems, and Computers
- Page Range / eLocation ID:
- 1670 to 1674
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ACSSC.2016.7869665
