edVirtus Reference

What Is Linear Predictive Coding?

How Does Linear Predictive Coding Work?

Linear Predictive Coding (LPC) is a speech-coding technique that represents speech by modelling the way it is produced by the human vocal system rather than by transmitting the speech waveform directly. Instead of sending every speech sample, LPC estimates the characteristics of the speaker's vocal tract and transmits only the parameters needed to recreate the speech at the receiver. This allows intelligible speech to be transmitted at remarkably low bit rates, making LPC one of the most influential techniques in the history of digital speech coding.

LPC is based on the source-filter model of speech production. In this model, the lungs provide an airflow, the vocal cords generate an excitation signal, and the vocal tract acts as a resonant filter that shapes the sound into speech. Rather than reproducing the speech waveform directly, LPC analyses the speech to estimate the filter characteristics and the excitation that produced it.

The term linear prediction refers to the mathematical process used to estimate each speech sample from a weighted combination of previous samples. Because speech changes relatively smoothly over short time intervals, the current sample can usually be predicted with reasonable accuracy from a small number of earlier samples. The encoder therefore needs to transmit only the prediction parameters and the small difference between the predicted and actual speech, greatly reducing the amount of information required.

A useful analogy is describing the shape of a musical instrument rather than recording every sound it produces. Once the instrument's characteristics are known, only the notes being played need to be specified. Similarly, LPC describes the characteristics of the vocal tract while transmitting only the information needed to reproduce the speech.

An LPC encoder periodically analyses short segments of speech, typically 10–30 milliseconds long, to determine parameters such as the vocal tract filter coefficients, pitch, signal gain, and whether the speech is voiced or unvoiced. These parameters are transmitted to the receiver, where a speech synthesizer reconstructs an approximation of the original speech by exciting the same vocal tract model with an appropriate excitation signal.

LPC represented a major advance over earlier waveform coders because it achieved intelligible speech at bit rates of only a few kilobits per second. However, the synthetic quality of early LPC speech led to the development of more sophisticated techniques such as Code-Excited Linear Prediction (CELP), Mixed Excitation Linear Prediction (MELP), Regular Pulse Excitation (RPE), and Multipulse Excitation (MPE). These methods retain the same predictive modelling principles while producing much more natural-sounding speech.

It is important to distinguish Linear Predictive Coding from Pulse Code Modulation (PCM). PCM transmits sampled speech waveforms directly, requiring relatively high bit rates to preserve quality. LPC transmits only a mathematical description of the speech-production process, dramatically reducing the required transmission rate while sacrificing some naturalness of the reconstructed speech.

Today, LPC remains one of the foundational techniques of digital speech coding. Although modern speech codecs generally employ more advanced predictive algorithms, most continue to build upon the principles established by LPC. Its introduction transformed digital voice communications and laid the foundation for the low-bit-rate speech coders used in mobile telephony, satellite communications, secure voice systems, and Voice over IP (VoIP).