Permutation modulation for quantization and information reconciliation in CV-QKD systems

This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increases the losses corresponding to a lower effective Signal to Noise Ratio (SNR) exasperating the problem. Here we propose to use Permutation Modulation (PM) as a means of quantization of Gaussian vectors at Alice and Bob over a d-dimensional space with d >> 1. The goal is to achieve the necessary coding efficiency to extend the achievable range of continuous variable QKD by quantizing over larger and larger dimensions. Fractional bit rate per sample is easily achieved using PM at very reasonable computational cost. Ordered statistics is used extensively throughout the development from generation of the seed vector in PM to analysis of error rates associated with the signs of the Gaussian samples at Alice and Bob as a function of the magnitude of the observed samples at Bob.