Improved Error Estimation for Wireless QKD

It is essential to estimate the error rate as accurately as possible to avoid possible waste of time and resources. Had the error estimation been done incorrectly and allowed to proceed, it would only be detected when the final Q-MIC values are verified. By then the whole 4-phase handshake would have taken place and they would need to restart the process again.

It is worth investigating how the errors may have distributed within the quantum key. The errors introduced into the key, by environmental, eavesdropping or by any other means, do not

guarantee that they will be evenly distributed within the key itself. The quantum transmission may be subject to impacts that cause errors for a short period of time. If this happens, most of the errors will only be present in a particular segment of the transmission. Hence, when the key bits are mapped into the key string of the classical channel, these errors will continue to occupy the same error distribution. Thus the errors will concentrate in a particular section of the key.

Further, errors may also present in the key at several places.

In the traditional error estimation process, the participants randomly select a subset of key bits for error estimation. This subset of key is obtained in a sequential manner starting from a specific random location chosen by the AP. This method of error estimation is good if the errors are evenly distributed among the key [149]. However, if the errors are concentrated into a specific section or several sections within the key, this error estimation results might be inaccurate.

As a remedy, the best approach is to pick several samples from different places covering the whole key. By this way a sample containing a reasonable rate of error across the whole key can be obtained for error estimation.

For an example, consider below a key string having key length of 40 bits at the receiving party.

These erroneous bits are represented by “underlined bold” characters.

1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 In this particular scenario, the test data has been created in such a way that about 50% of errors to locate towards the last half of the key string.. As mentioned before, this is possible if the environmental or other impacts took place towards a specific section of the key transmission. If the sample bits were taken from the start or middle of the key, the error estimation would not give an actual error rate as more than 50% of total errors are located towards the end of the key.

Thus the traditional error estimation where sample key bits are obtained sequentially from a random location will not give accurate result. However, if several smaller samples covering the whole key are obtained, the error estimation would have been more accurate.

Hence some improvements to the existing method of choosing sample bits have been made under the 4-phase handshake protocol. The existing communication flow that sends the bit sample is in the format:

<Start bit location, length>

This has been changed to:

<Start bit location1, length1>, <Start bit location2, length2>, <Start bit location3, length3> ….

This modification can easily be accommodated in the proposed 4-phase handshake protocol with IEs carrying the additional sample data.

Considering the above example, if the traditional error estimation has taken place, there is a good probability that it will take sample bits from the middle of the key. If this happens, the calculated error rate would have deviated heavily from the actual error rate as most of the errors are concentrated towards the end of the key. With the new proposed method, this can be easily avoided as it would take three samples (say) of 4 bits from 10^th, 20^th and 30^th bit positions.

Figure 51 shows the result of some simulations carried out to compare the traditional error estimation and the proposed error estimation used in 4-phase handshake protocol. During this simulation a key of length 500 bits with 20% actual error rate has been used. Test data has been created such that nearly 12% of its errors are concentrated between 350 to 500 bits, while remaining 8% distributed within the rest of the key length (0 to 350 bits).

This figure shows the data collected by executing both methods (traditional and improved version) on several attempts to estimate the error rate. Using the traditional method, several error estimation cycles have been run with 25 bit length sequential samples taken starting from 50, 100, 150, 200, 250, 300, 350, 400 and 450 bit locations. For each of the sample error rate is calculated and the graph (traditional) is plotted. In comparison, error estimation has been conducted by using the proposed method with small samples of 5 bit lengths taken from different parts covering the whole key. As per the test data in this scenario, the expected error rate is 20%

(0.2). It could be seen that the proposed method always shows near accurate error estimation as its samples are taken from different parts of the key. The calculated error rate is closer to the actual 0.2 mark.

Figure 51 : Comparison of Traditional and Proposed Error Estimation

In contrast, the error estimation results of the traditional method show fluctuating results depending on the location in which the sample is taken. This is obvious since in this particular example, 12% of errors (out of a total 20%) are located between bits 350 to 500. Thus any sample taken from this area would show higher error rates. The error rate for the sample taken, at 450 bit mark went even higher than the actual error rate. This is because the sample test data had several errors located in this particular segment.

The most important advantage of the improved version is, regardless of how the errors are distributed in the key, it gives more accurate error rates than the traditional method.