On Secrecy Rate Analysis of MIMO Wiretap Channels Driven by Finite-Alphabet Input

Abstract

This work investigates the effect of finite-alphabet input constraint on the secrecy rate of a multi-antenna wiretap channel. Most existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. For practical considerations, we study the effect of finite discrete-constellation on the achievable secrecy rate of multipleantenna wire-tap channels. Our proposed precoding scheme converts the underlying multi-antenna system into a bank of parallel channels. Based on this precoding strategy, we develop a decentralized power allocation algorithm based on dual decomposition to maximize the achievable secrecy rate. In addition, we analyze the achievable secrecy rate for finite-alphabet inputs in low and high SNR regions. Our results demonstrate substantial difference in secrecy rate between systems given finite-alphabet inputs and systems with Gaussian inputs.Index Terms-Wiretap channel, eavesdropping, informationtheoretic security, secrecy rate, finite-alphabet input.

On the Binary Input Gaussian Wiretap Channel with/without Output Quantization

“…SS and C (6) SS are plotted as an upper and a lower bound on C SS , respectively. Moreover, Figure 4 also depicts the approximations on (C HS ) lower and (C SH ) lower by m = 6, 7.…”

“…Following the numerical evaluations in the previous subsection, we use C (6) B (γ) and C (6) SS to approximate C B (γ) and C SS , respectively. Figure 5 consists of two sub-figures to illustrate how the crossing point occurs as ∆γ = γ 1 /2.…”

“…Recently, the Gaussian wiretap channel with constrained/finite inputs has attracted increasing research attention [4][5][6][7][8]. The closed-form expression of the secrecy capacity of the Gaussian wiretap channel with continuous input signal was given in [9].…”

“…The closed-form expression of the secrecy capacity of the Gaussian wiretap channel with continuous input signal was given in [9]. The work in [4] considered the Gaussian wiretap channel with M-ary pulse amplitude modulation (M-PAM) inputs and established the necessary conditions for the input power allocation and the input distribution in order to maximize So far, all the known works about BI-GWC [4][5][6] focus on Case 1, where the classical results in [2,3,9] were used to optimize the input power and the input distribution. However, no closed-form expression was derived.…”

Achievable secrecy rate of bit-interleaved coded modulation schemes

“…finite-size signal constellations [3]. Substantial differences have been found between the secrecy rate curves obtained with the schemes relying on finite-alphabet inputs and infinitealphabet inputs.…”