Identifying Discrepant Tags in RFID-enabled Supply Chains

Abstract

Radio Frequency Identification (RFID) technology is becoming a revolutionary element in supply chain management by providing real-time visibility of goods flows. Across supply chains, one-for-one checking is required at each handover point to discover discrepancies between the physical shipped inventory and receiver’s order. This operation is so ubiquitous throughout the product life cycle that its efficiency improvement can prominently optimize the whole supply chain. There are several main challenges, however, in designing efficient solutions for it: inconsistent tag information, high-volume and high-speed RFID data, and high latency in EPCglobal Network. Based on the characteristic polynomial, we propose a tag identification protocol that achieves better almost minimal latency. The most salient feature of our protocol is that its communication complexities scales well with the size of discrepant tags, instead of the size of overall number of tags in traditional methods. Through experimental comparisons, we show that our protocol significantly outperforms previous methods in terms of communication latency.

Appendix:

Lemma 1

Given a level i and a constant $c>1$, the relative error of estimated cardinality of the union of level j or greater is at most $\mathcal {O}(\sqrt{\frac{c2^i}{M}})$ with probability $(1-2^{-c})$, where $j<i$ and M is the size of all tags.

Proof

In hierarchical estimator, we use $Z_j$ to denote the size of union of level j or greater, and $\mu _j$ be its expectation. Thus, we know that

$$\mu _j=\mathrm {E}(Z_j)=\frac{M}{2^j}.$$

Also by chernoff bound, we can get

$$\mathrm {Pr}(Z_j>(1+\varepsilon ))<e^{\frac{-\mu _j\varepsilon ^2}{4}},\mathrm {Pr}(Z_j<(1-\varepsilon ))<e^{\frac{-\mu _j\varepsilon ^2}{4}}.$$

Therefore, if we let $\varepsilon =\sqrt{4(c+2)\frac{2^i}{M}\ln 2}\sim \mathcal {O}(\sqrt{\frac{c2^i}{M}}),$ we can know that the probability that relative error of $Z_j$ is at most $\varepsilon$ is at most $2e^{\frac{-\mu _j\varepsilon ^2}{4}}.$ Then by a union bound, the probability that the relative error of any $Z_j$ is out of $\varepsilon$ is at most

$$\sum _{j=0}^{i}2e^{\frac{-\mu _j\varepsilon ^2}{4}}\le \sum _{j=0}^{i}2^{-(c+1)2^{i-j}}\le 2^{-c}$$

Theorem 1

Given $0<\varepsilon ,\delta <1$, the hierarchical estimator is able to estimate the discrepant tag size with relative error $\varepsilon$ and failure probability $\delta$.

Proof

Let $\alpha$ be the constant in the big-O notation in Lemma 1.

If $d^2\le \alpha ^2\varepsilon ^{-2}\log \delta ^{-1}$, then the level-0 of hierarchical estimator will decode all discrepant tags with probability at least $1-\frac{\delta }{2}.$

Otherwise, we use i to be $\frac{d}{2^i}\approx \alpha ^2\varepsilon ^{-2}\log \delta ^{-1}$. Thus, by Lemma 1, the relative error of the number of tags in the i-th and higher level is at most $\varepsilon$ with probability $1-\frac{\delta }{2}$, if we let $c=\lceil \log \delta ^{-1}\rceil +1$.