### IoT Needs and Impact of the Deterministic K-Identification
In addition, deterministic codes often have the advantage of simpler implementation, simulation [29; 30] and explicit construction [31]. As a result, the deterministic K-identification (DKI) considered in this paper may be regarded a promising solution for several IoT applications that do not comprised randomness in their encoding part. **Performance speed:** In the standard identification with deterministic encoding (DI) problem (i.e., \(K=1\)) [32; 33], the receiver performs a series of comparisons between a given goal message and each element of the message set (one-to-one comparison). However, in the DKI problem, the receiver is capable of performing a one-to-set comparison, i.e., an inclusion test. In other words, the receiver is searching for a specific message within an arbitrary set of \(K\) messages (goal message set), and is able to declare reliably whether or not a specific message which is searching for is included in the goal message set. This feature for the DKI problem may be regarded as an advantage in terms of speed in the set-wise search, compared to the DI for identification-based IoT devices. In the following, we explain from a quantitative perspective that why the one-by-one comparison as made in the DI is _slow_, and why the simple inclusion test as made in the DKI is _fast_. In order to evaluate the search performance speed of K-identification against the standard identification, let us define the time complexity that is required in order to exhaust the entire collection of subsets of size \(K\) as a metric. Then, observe that the message set \(\mathcal{M}=\{1,\ldots,M\}\) with size \(M\) has \({M\choose K}\) subsets of size \(K\), referred to as the search space. Now, note that the total search space is the power set of the message set, i.e., the set of all subsets of the message set with size \(2^{M}\). Therefore, ratio of the size of the search space to the size of the power set for the message set, converges exponentially to zero in the message size, \(M\), i.e.,  
\[\frac{(M)}{2^{M}}\leq\frac{2^{MH(K/M)}}{2^{M}}=2^{MH(K/M)-1)}\xrightarrow{n \rightarrow\infty}0, \tag{1}\]  
for \(K\geq 1\) and \(M-K\geq 1\), where the inequality holds by ([34], p. 353), with \(H(z)\triangleq-z\log(z)-(1-z)\log(1-z)\), being the binary entropy function. On the other hand, for the DI problem the sequence of one-to-one comparisons for the asymptotic codeword lengths, \(n\) (i.e., very large message set size) trades a long delay on the receiver's proficiency with an _inverse polynomial_ order in \(M\). More specifically, the receiver searches for a single message among \(M\) different messages; therefore, the ratio of the size of the search space to the size of the whole search space is \(1/M\), which tends to zero for increasing \(M\). **Growing search space:** Some of the envisioned IoT applications may need a K-identification task where size of the goal message set \(K=K(n)\) has to grow in \(n\). For example, where it is required that the size of the goal message set, \(K\), for which the inclusion test (search in a set) is conducted, remains a _fixed_ percentage order of the size of the message set. Therefore, by growing codeword length, \(n\), which implies a growing size of the message set, the corresponding goal message set also grows. To account for these cases, we consider a generalized identification model, whose parameter \(K\geq 1\) can grow exponentially in \(n\). Possible implications of this observation in the context of IoT include locating an malfunctioned server within a network of \(K\) web servers; spotting/detecting a faulty node in a local partition of wireless sensor network with size \(K\); and in data mining within the procedure of sorting data, where some algorithms need to know that a desired data are included to which set of element with size \(K\).