Measuring Imperfection: Error Rates

In any real-world communication system, the transmitted signal is affected by noise and distortion, which can cause the receiver to misinterpret the data. The quality of a digital transmission is measured by its error rate-the probability that a unit of information will be received incorrectly.

Types of Error Rates

• Bit Error Rate (BER): This is the most common metric. It is the ratio of the number of erroneously received bits to the total number of bits transmitted. For example, a BER of $10^{-6}$ means that, on average, one bit in every million is incorrect.
• Symbol Error Rate (SER): In systems where one symbol represents multiple bits (e.g., QAM), this measures the ratio of incorrectly received symbols to the total number of transmitted symbols.
• Word/Byte Error Rate (WER/ByteER): Measures the ratio of incorrect words or bytes. A word is considered incorrect if even a single bit within it is wrong.

The Signal vs. Noise Battle: Energy Efficiency

The error rate depends directly on the strength of the signal relative to the strength of the noise in the channel. We define a system's energy efficiency as its ability to achieve a low error rate at a low signal-to-noise ratio. To quantify this, we use a normalized metric:

$E_b/N_0$ (Energy per bit to noise power spectral density ratio): This is the fundamental parameter for determining the performance of a digital communication system. It represents the ratio of the energy used to transmit one bit of information ($E_b$) to the power of the noise present in a 1 Hz bandwidth ($N_0$). A higher $E_b/N_0$ value means a cleaner signal and results in a lower BER.

Interpreting the Graph

The graph vividly illustrates the fundamental tradeoff in telecommunications:

• For a fixed BER target (e.g., $10^{-5}$), systems using more complex modulations (like 32-level) require a significantly higher $E_b/N_0$ ratio than simpler ones (like 2-level/BPSK). This means more complex modulations need a much cleaner, stronger signal to perform reliably.
• For a fixed $E_b/N_0$ level (e.g., 14 dB), simpler modulations are far more robust, offering a much lower BER. They are less prone to errors in noisy conditions.

The Efficiency Tradeoff: Bandwidth vs. Power

The choice of a modulation and coding scheme is always a compromise between two competing types of efficiency, as summarized in the table below.

Therefore, an engineer must make a choice: for a channel with limited bandwidth but a strong signal, a spectrally efficient modulation like 16-QAM is ideal. For a power-limited channel (like a deep-space probe) with plenty of bandwidth, an energy-efficient modulation like BPSK is the correct choice.