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Figure 16.9. (A) Healthy ECG segment. (B) Corresponding autocorrelation. (C) Zoomed
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A complexity measure reveals the number of patterns that are hidden in a nite sequence as well as their frequency of appearance. In this manner, the degree of disarrangement of a signal is described. More speci cally, since the autocorrelation of quasiperiodic or repetitive signals (such as healthy ECG windows) has peaks that recur periodically, the CM is expected to capture their frequency of appearance. According to the de nitions provided by Lempel and Ziv [38] to calculate CM, the autocorrelation must be translated into a binary sequence. In such a binary projection, local maxima are represented by ones and all the remaining samples by zeros. In order to detect the peaks, the AC signal is passed through a low-pass lter with cutoff frequency at 5 Hz, so that small localized peaks of less interest are eliminated. It is expected that autocorrelations obtained from arrhythmic ECG segments will have higher complexity measures, since they do not carry any repetitive patterns. According to Lempel and Ziv [38], the algorithm for the computation of the complexity measure proceeds as described in Figure 16.11 along with the following de nitions: r x is the binary autocorrelation sequence. r S and Q are two binary strings. r SQ is the concatenation of S and Q. r SQ is SQ where the last character is deleted.
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16.4 The ECG Biometric for Robust Identi cation
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A. Voltage (mV) 4 2 0 2 200 B. 1 Normalized Power 0.5 0 0.5 1 0 1000 2000 3000 4000 5000 6000 7000 8000 400 600 800 1000 1200 1400 1600 1800
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Figure 16.10. (A) Arrhythmia ECG segment. (B) Corresponding autocorrelation. (C) Zoomed
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r l(SQ) is the length of sequence SQ. r v(SQ ) is the vocabulary of SQ . Initially, the complexity measure (Cm) is assigned to be one. S is de ned to be the rst character of the sequence x, and Q the second one. In the midst of the
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Figure 16.11. Flow chart showing the route of computations for the complexity measure.
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computations, if word Q exists in the v(SQ ) vocabulary, then Q is appended with the next symbol of x, while Cm and S remain the same. However, if Q does not belong to v(SQ ), Cm is augmented by one, SQ is assigned to S, and Q becomes the next character of the x sequence. This process continues until the entire sequence x is scanned. Lempel and Ziv [38] showed the upper limit of Cm for a binary sequense x of length l(x) = n to be
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(16.16)
The complexity measure depends highly on the length of the sequence. In order to eliminate this effect, a normalized complexity measure C is adopted instead: C= Cm(n) log (n) = Cm(n) 2 . b(n) n (16.17)
Therefore, 0 C 1, with values closer to one showing higher complexity.
16.5 THE ECG BIOMETRIC FOR SECURE AND RESOURCE-EFFICIENT COMMUNICATIONS IN A BSN
In this section, we consider the utility of the ECG biometric to reduce the resource consumption and provide data security for a BSN, in a practical and exible manner.
Multipoint Fuzzy Key Management
The single-point fuzzy key management, surveyed in Section 16.3.3.5, represents a signi cant improvement over conventional key distribution systems, such as those based on the Dif e Hellman scheme. However, it is still inef cient with respect to the communication rate: The length of the transmitted sequence needs to be at least as long as that of the required cryptographic key. Indeed, with the concatenation of the check code, its size is even longer. This represents an undesirable overhead, since communication transmissions consume the most energy in a BSN, compared to computational operations. Motivated by the inherent design limitation of the single-point fuzzy management, we seek a more exible and ef cient approach to manage the keys for all sensors. The basic idea is to send only the check-code, and not a modi ed version of the key itself over the channel. In a multipoint scheme, as its name suggests, all nodes would be responsible for generating the key from the obtained biometrics at various sensor points. The utility of this approach is that, unlike in a single-point scheme, a full XOR-ed version of the key no longer needs to be sent over the channel. Instead, only the check-code needs to be transmitted for veri cation.