NRZ Codes | Teleinf Edu

The Principle of NRZ Coding

Non-Return-to-Zero (NRZ) is one of the simplest and most direct families of . The name describes the rule: the level selected for a bit does not return to zero before that bit period ends. That level, such as a positive or negative voltage, is held for the entire bit duration, denoted by $T$ .

Variant 1: Unipolar NRZ

In the unipolar version, a logical '1' is represented by a positive voltage level, while a logical '0' is represented by a zero-volt level.

Logical '1' → $+V$
Logical '0' → $0V$

The method is simple, but long sequences of '1's produce a positive, data-dependent . This non-zero average is attenuated by AC-coupled components such as transformers and can complicate signal detection.

Variant 2: Polar NRZ

The polar version is a two-level code that uses voltage levels of opposite polarity. In this model the logical symbols occupy the $+V$ and $-V$ levels.

Logical '1' → $+V$
Logical '0' → $-V$

Symmetric positive and negative levels produce an average DC component close to zero when '0's and '1's occur with roughly equal probability in the data stream.

Spectral Analysis and Limitations

NRZ's narrow spectrum is accompanied by synchronization limits. An analysis of the polar NRZ signal's reveals two characteristics:

Spectral Efficiency: For independent, equally likely symbols and rectangular pulses, the main lobe of the polar NRZ spectrum extends from DC to its first null at the clock frequency, $f_{clk} = 1/T$ . It therefore occupies a narrower band than Manchester coding.
Synchronization: For rectangular pulses, the continuous part of the power spectrum has a null at the clock frequency. Long runs of identical bits ( $1111...$ or $0000...$ ) also contain no transitions. The receiver then has difficulty performing and maintaining synchronization. A shifted sampling instant produces incorrect bit decisions.

Summary of NRZ Properties

Advantages

Simplicity: Simple and inexpensive to implement in basic hardware.
Good Bandwidth Efficiency: The main spectral lobe is narrow (extends to $f_{clk}$ ), requiring less bandwidth than many other codes.

Disadvantages

Poor Synchronization: Long strings of '0's or '1's provide no signal transitions, leading to potential loss of synchronization.
Null at Clock Frequency: The null in the continuous spectrum at the clock frequency makes clock recovery difficult and unreliable.
Presence of DC Component: Heavily dependent on data content. Long runs of one bit create a DC level, which is problematic for AC-coupled systems.

NRZ limitations concern the DC component and long intervals without transitions. NRZ remains in use in optical interfaces specified by ITU-T, including the NRZ classes described in G.959.1. Systems that limit long runs can process the stream with a scrambler or another line coding scheme.