# Development of a Non-Invasive On-Chip Interconnect Health Sensing Method Based on Bit Error Rates
## 3 BER-Based Interconnect Health Sensing  
Bits are determined based on a sampling point at the receiver. Figure 2a shows an example of data transmission on a synchronous bus. A receiver samples the transmitted data at a specific interval; the clock determines the sampling time \(t_{s}\). At a sampling time, the receiver classifies the incoming bits as either 0 or 1 based on a threshold voltage \(V_{s}\). Figure 2b shows a sampling point of a receiver and the manner in which the receiver determines the value of the bits. In particular, the receiver recognizes a bit as a logical one when the signal voltage is over a threshold voltage, or a logical zero when the signal voltage is lower than that threshold voltage.  
In the presence of jitter and noise, the rising and falling edges of the signals may deviate along the time axis, and the voltage may fluctuate along the amplitude axis. Figure 3 shows examples of bit error generation due to jitter, noise, and signal loss. Owing to these issues, correct bit detection might not be achieved, resulting in a bit error, such as a logical one being detected as a logical zero, or vice versa. Furthermore, violations of sampling conditions can occur in the following three scenarios [11]: (1) the crossing time of the rising edge lags behind the sampling time, \(t_{r}>t_{s}\); (2) the crossing time of the falling edge is ahead of the sampling time, \(t_{f}<t_{s}\); and (3) the logical one voltage is below the sampling voltage, or \(V_{1}<V_{s}\), where \(t_{r}\) is the rise time, \(t_{f}\) is the fall time, and \(V_{1}\) is the voltage for the logical one.  
Figure 1: Digital signal transmission: (**a**) conceptual representation (**b**) ideal and real waveforms.  
BER-based interconnect health sensing was developed based on the bit detection mechanism. In order to monitor the degradation of digital signals, the sampling points were moved across the time interval, as well as the voltage interval, of a unit clock. Figure 4 illustrates 32 horizontal and 127 vertical sampling points of a unit clock. The sampling times moved from \(t_{0}\) to \(t_{31}\), and the threshold voltage moved from \(V_{0}\) to \(V_{126}\). Finally, the number of sampling points was 4064. The BER was measured at all the sampling points and the obtained values were arranged in the form of a matrix represented as follows:  
\[\left[\begin{array}{ccccc}BER_{0,126}&BER_{1,126}&BER_{2,126}&\cdots&BER_{31,1 26}\\ &\vdots&&\ddots&\vdots\\ BER_{0,2}&BER_{1,2}&BER_{2,2}&&BER_{31,2}\\ BER_{0,1}&BER_{1,1}&BER_{2,1}&\cdots&BER_{31,1}\\ BER_{0,0}&BER_{1,0}&BER_{2,0}&&BER_{31,0}\\ \end{array}\right], \tag{1}\]  
where \(BER_{a,b}\) is the BER at a sampling point when the sampling time is \(t_{a}\) and the threshold voltage is \(V_{b}\). A digital signal waveform measured using an eye diagram and using the BER of a healthy solder joint showed a good match; this is shown in Figure 5.  
Figure 3: Bit error generation (**a**) by signal loss and (**b**) by timing noise.  
Figure 2: Signal sampling at a receiver. (**a**) data transmission of a synchronous bus (**b**) sampling point at a receiver.  
Figure 7 shows the on-chip health sensing flowchart using BER as a summary. It starts with generating digital signals, transmitting them through the device under test (DUT), and accumulate the transmitted signals to create a BER map. The features, including eye size, are calculated from the BER map, and the health status is determined by comparing the feature with the pre-determined threshold.