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Designing scalar quantizers with secrecy constraints

We consider the design of channel-optimized scalar quantizers for secure communications. We derive necessary conditions for an optimal system for which the eavesdropper's minimum achievable distortion is higher then a prescribed threshold. Moreover, we present an iterative optimization scheme for the quantizer design, which follows the spirit of the Lloyd-Max algorithm. Our quantizer design offers secrecy gains when the channel to the eavesdropper is worse than that of the legitimate receiver. When the channel to the eavesdropper is better than that of the legitimate receiver we are able to mitigate the eavesdropper's advantage by increasing its distortion above the prescribed level.