Regular Pulse Excited codec with Long Term Prediction

Description

The Regular Pulse Excited codec with Long Term Prediction (RPE-LTP) is a specific speech coding algorithm standardized for the GSM Full-Rate Traffic Channel (TCH/FS). It operates at a bit rate of 13 kbit/s, producing a compressed digital representation of a 20 ms speech frame (260 bits). The codec is based on a hybrid coding scheme combining Linear Predictive Coding (LPC) for modeling the vocal tract, Long Term Prediction (LTP) for modeling pitch (voiced sounds), and Regular Pulse Excitation (RPE) for modeling the residual signal.

Architecturally, the encoding process works in several stages. First, the input speech signal (sampled at 8 kHz) is divided into frames. For each frame, the short-term LPC analysis calculates a set of reflection coefficients (converted to Log Area Ratios, LARs) that model the spectral envelope of the vocal tract. These LARs are quantized and transmitted. Next, the LTP analysis removes the long-term redundancy (pitch periodicity) from the LPC residual signal. This involves finding a delay (pitch lag) and a gain factor that best match the current residual with a past residual. The LTP parameters (lag and gain) are also quantized and sent. Finally, the remaining signal, called the LTP residual, is encoded using the RPE technique. RPE selects one of four interleaved subsequences of regularly spaced pulses that best approximates the residual. The selected subsequence number, pulse positions, and pulse amplitudes are quantized and transmitted.

The decoder performs the inverse process: it reconstructs the excitation signal from the received RPE parameters, uses the LTP parameters to add the long-term periodicity, and then filters this through the LPC synthesis filter (using the received LARs) to reproduce the speech signal. Key components include the LPC analysis/synthesis filter, the LTP adaptive codebook, and the RPE selection and quantization logic. Its role was fundamental in the GSM radio interface, defining the voice quality and capacity of the initial full-rate service. The specification TS 46.008 details the bit-exact algorithmic description and the mapping of parameters to the 260-bit channel frame.

Purpose & Motivation

The RPE-LTP codec was developed to solve the fundamental challenge of transmitting acceptable quality voice over the severely bandwidth-constrained digital radio channels of early GSM networks. Before GSM, analog cellular systems used frequency modulation which was inefficient and poor in quality. The transition to digital required a speech codec that could compress the 64 kbit/s PCM telephone signal into roughly 13 kbit/s to fit the available channel bit rate, while maintaining toll-quality speech and robustness to transmission errors.

The creation of RPE-LTP was motivated by a competitive selection process. It was chosen over other candidates (like the Multi-Pulse Excited codec) for its good compromise between speech quality, computational complexity (important for early mobile hardware), and robustness. It addressed the limitations of simpler waveform codecs (like ADPCM), which could not achieve such high compression, and more complex vocoders, which sounded unnatural. The inclusion of Long Term Prediction was a key innovation that efficiently modeled the quasi-periodic nature of voiced speech, significantly improving quality at the target bit rate. This codec was instrumental in establishing GSM's commercial success by delivering clear digital voice, enabling efficient spectrum use, and setting a benchmark for subsequent codec developments like the Enhanced Full Rate (EFR) and Adaptive Multi-Rate (AMR) codecs.

Key Features

• Operates at 13 kbit/s for GSM Full-Rate channel
• Uses hybrid coding: LPC, LTP, and RPE
• Processes speech in 20 ms frames (260 bits/frame)
• Provides good speech quality with moderate complexity
• Includes error protection through parameter importance ordering
• Bit-exact specification for interoperability

Evolution Across Releases

Defining Specifications