Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.Comment: 46 pages (draft version); extended version of the paper with same title, submitted to IEEE Transactions on Communication

Secret key generation scheme from WiFi and LTE reference signals

<p>Physical layer security has emerged as a promising approach to strengthen security of wireless communications. Particularly, extracting secret keys from channel randomness has attracted an increasing interest from both academic and industrial research groups. In this paper, we present a complete implantation of a secret key generation (SKG) protocol which is compliant with existing widespread Radio Access Technologies. This protocol performs the quantization of the channel state information, then information reconciliation and privacy amplification. We also propose an innovative algorithm to reduce the correlation between quantized channel coefficients that significantly improves the reliability and the resilience of the complete SKG scheme. Finally we assess the performance of our protocol by evaluating the quality of secret keys generated in various propagation environments from real single sense LTE signals, and real single and dual sense WiFi signals.</p