BER vs PER

This article explores the concepts of Bit Error Rate (BER) and Packet Error Rate (PER), two crucial metrics for evaluating the performance of digital communication systems, both wired and wireless. These systems often face challenges like noise, jitter, interference, and I/Q imbalances that can degrade signal quality. BER and PER help us quantify these degradations and assess the reliability of our data transmission.

What is Bit Error Rate (BER)?

BER is defined as the ratio of the number of received bits in error to the total number of bits transmitted during a specific test period. It’s a unitless measure, often expressed as a percentage. BER tester (BERT) is used to measure the Bit Error Rate. BER measurements are conducted over both short and long durations to evaluate the system’s stability and performance in the short-term and long-term before actual deployment.

BER can be improved by using more robust modulation schemes and applying forward error correction (FEC) codes, such as Convolutional encoding and CTC. For instance, Binary Phase Shift Keying (BPSK) is more robust than Quadrature Phase Shift Keying (QPSK), which in turn is more robust than Quadrature Amplitude Modulation (QAM).

Let’s say we transmit a sequence of bits: [1 1 1 0 1 0 1 0 1 1 0]

If the received bits are [1 1 0 0 1 1 1 0 0 1 0], there are 3 errors.

Therefore:

• BER = 3 / 11 = 0.27 (approximately)
• BER (%) = 0.27 * 100 = 27% (approximately)

What is Packet Error Rate (PER)?

Packets or frames consist of multiple bytes (e.g., 8 bits per byte). For example, an Ethernet packet, as per IEEE 802.3, can carry up to 1518 bytes. Evaluating system performance at the packet level helps determine if errors occur at the bit level or the entire packet level. Packet Error Rate (PER) is defined as the ratio of the number of packets received in error to the total number of transmitted packets. A packet is considered to be in error if even a single bit within the packet is received incorrectly.

The figure below represents a plot of PER vs SNR (Signal-to-Noise Ratio) for a wireless system using various modulation schemes.

Relationship Between BER and PER

The following equation demonstrates the mathematical relationship between BER and PER, assuming an ideal communication system over a binary symmetric channel with uncorrelated noise:

In the formula:

• ‘n’ represents the number of bits in a packet.
• ‘Pb’ is the bit error rate (BER).
• ‘Pn’ is the packet error rate (PER).

PER is determined by the BER and the number of bits within a packet’s data payload. It does not depend on data encoding methods or the transmit-receive process. The relationship can be expressed as:

$$ PER = 1 - (1 - BER)^n $$

Conclusion

In summary, the fundamental difference between BER and PER is that BER focuses on individual bits, while PER is concerned with entire packets. However, both are interrelated, as shown in the formula above, and they are both important measures for assessing the quality and reliability of digital communication systems.