TY - GEN
T1 - On MMSE properties of optimal codes for the Gaussian wiretap channel
AU - Bustin, Ronit
AU - Schaefer, Rafael F.
AU - Poor, H. Vincent
AU - Shitz Shamai, Shlomo
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/6/24
Y1 - 2015/6/24
N2 - This work examines the properties of "good" codes for the scalar Gaussian wiretap channel that achieve the maximum level of equivocation. Specifically, the minimum mean-square error (MMSE) behavior of these codes is explored as a function of the signal-to-noise ratio (SNR). It is first shown that reliable decoding of the codeword at the legitimate receiver and at the eavesdropper, conditioned on the transmitted message, is a necessary and sufficient condition for an optimally secure code sequence. Moreover, it is observed that a stochastic encoder is required for any code sequence with rate below the channel point-to-point capacity. Then, for code sequences attaining the maximum level of equivocation, it is shown that their codebook sequences must resemble "good" point-to-point, capacity achieving, code sequences. Finally, it is shown that the mapping over such "good" codebook sequences that produces a maximum equivocation code must saturate the eavesdropper. These results support several "rules of thumb" in the design of capacity achieving codes for the Gaussian wiretap.
AB - This work examines the properties of "good" codes for the scalar Gaussian wiretap channel that achieve the maximum level of equivocation. Specifically, the minimum mean-square error (MMSE) behavior of these codes is explored as a function of the signal-to-noise ratio (SNR). It is first shown that reliable decoding of the codeword at the legitimate receiver and at the eavesdropper, conditioned on the transmitted message, is a necessary and sufficient condition for an optimally secure code sequence. Moreover, it is observed that a stochastic encoder is required for any code sequence with rate below the channel point-to-point capacity. Then, for code sequences attaining the maximum level of equivocation, it is shown that their codebook sequences must resemble "good" point-to-point, capacity achieving, code sequences. Finally, it is shown that the mapping over such "good" codebook sequences that produces a maximum equivocation code must saturate the eavesdropper. These results support several "rules of thumb" in the design of capacity achieving codes for the Gaussian wiretap.
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U2 - 10.1109/ITW.2015.7133139
DO - 10.1109/ITW.2015.7133139
M3 - Conference contribution
AN - SCOPUS:84938927222
T3 - 2015 IEEE Information Theory Workshop, ITW 2015
BT - 2015 IEEE Information Theory Workshop, ITW 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2015 IEEE Information Theory Workshop, ITW 2015
Y2 - 26 April 2015 through 1 May 2015
ER -