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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.

Many physical-layer security works in the literature rely on purely theoretical work or simulated results to establish the value of physical-layer security in securing communications. We consider the secrecy capacity of a wireless Gaussian wiretap channel using channel sounding measurements to analyze the potential for secure communication in a real-world scenario. A multi-input, multi-output, multi-eavesdropper (MIMOME) system is deployed using orthogonal frequency division multiplexing (OFDM) over an 802.11n wireless network. Channel state information (CSI) measurements were taken in an indoor environment to analyze time-varying scenarios and spatial variations. It is shown that secrecy capacity is highly affected by environmental changes, such as foot traffic, network congestion, and propagation characteristics of the physical environment. We also present a numerical method for calculating MIMOME secrecy capacity in general and comment on the use of OFDM with regard to calculating secrecy capacity.