IEEE Computational Intelligence Magazine - November 2021 - 79

results over 100 random tests. It is clear
that the extraction errors without the
correct keys are approximately 0.5 (the
bound of extraction error) for all cases.
This means that additional data would
not be leaked without the correct keys.
On the other hand, additional data can
be extracted correctly (extraction error
is 0) when the given keys are correct.
Therefore, the key security of the proposed
scheme can be guaranteed.
To the best of the authors' knowledge,
the proposed scheme is the first
work focusing on data hiding for multiple
receivers using CapsNets. Despite
this, the authors also compare the proposed
scheme with two methods of
watermarking in deep networks recently
reported in [10] and [15], which are the
methods most related to the proposed
scheme among existing techniques. The
In the real world, the communication channel
is usually lossy.
embedding capacity comparisons
between the proposed scheme and the
methods in [10], [15] are shown in
Table IV. The acronym " DDA " means
decreased detection accuracy compared
with the original network when additional
data are embedded. The results
indicate that the embedding capacity of
the proposed scheme is higher than that
of the methods in [10], [15]. Meanwhile,
the decreased detection accuracy of the
proposed scheme is also lower than that
of the two methods. In addition, the two
methods are not designed for multiple
receivers, while the proposed scheme is
able to transmit different data to multiple
receivers via the same neural network
simultaneously.
C. Robustness
In the real world, the communication
channel is usually lossy, as shown in
Fig. 10. Affected by the lossy channel,
some noise will be contained in the vector
PM
output by the data decoding
networks. Even in this case, additional
data should also be extracted correctly.
To check the robustness of the proposed
scheme, two lossy channels are simulated
by adding noise with Gaussian and uniform
distributions into
P .M The probability
distribution of Gaussian noise x1
Data Hiding Key
Lossy Channels
Network Contains
Additional Data
FIGURE 10 Demonstration of lossy channels in real world.
Processed
Network
Data
Extraction
Additional Data
0.05
0.04
0.03
0.02
0.01
0.1
0.08
0.06
0.04
0.02
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
φ1
(a)
Capacity = 600 bits
Capacity = 700 bits
0 0.05 0.1 0.15 0.2 0.25 0.3
φ2
(b)
Capacity = 800 bits
FIGURE 11 Extraction errors against noise with (a) gaussian distribution; (b) uniform distribution.
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 79
Extraction Error e
Extraction Error e

IEEE Computational Intelligence Magazine - November 2021

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