Fixed codebook

Description

A fixed codebook is a component of the speech synthesis filter used in analysis-by-synthesis speech codecs. In such codecs, the encoder models the vocal tract with a short-term synthesis filter (derived from linear prediction coefficients) and models the excitation with a long-term predictor (pitch) plus an excitation signal drawn from a codebook. The fixed codebook supplies candidate excitation vectors — often called codevectors — from which the encoder selects the one that, after filtering, best matches the original speech according to a perceptual error criterion. The index of the selected vector is transmitted to the decoder, which retrieves the same vector from an identical codebook.

The defining property of a fixed codebook is that its contents do not change over time. Unlike an adaptive codebook, whose entries are derived from previously reconstructed excitation and therefore evolve with the signal, the fixed codebook is static and known a priori to both encoder and decoder. This makes it possible to transmit only an index rather than the excitation samples themselves, which is the fundamental efficiency gain of codebook-excited linear prediction (CELP) and its variants.

In the Adaptive Multi-Rate (AMR) narrowband codec (TS 26.090) and the Adaptive Multi-Rate Wideband (AMR-WB) codec (TS 26.190), the fixed codebook is implemented as an algebraic codebook. An algebraic codebook does not store vectors explicitly; instead, it defines them by a structured rule, typically placing a small number of unit pulses at positions determined by the transmitted index. This structure allows fast search procedures and requires no memory for storage, while still providing a rich set of excitation vectors. The AMR-WB codec, operating at 6.6 to 23.85 kbit/s, uses this algebraic fixed codebook as a core element of its multi-rate design.

The fixed codebook interacts closely with the adaptive codebook and the gain quantisation stages. The encoder first determines the adaptive (pitch) contribution, then searches the fixed codebook for the best innovation vector, and finally quantises the gains applied to each contribution. The decoder reverses this: it retrieves the adaptive and fixed contributions, scales them by the decoded gains, sums them to form the excitation, and passes the result through the short-term synthesis filter to reconstruct speech. Post-filtering may then be applied to enhance perceptual quality.

The fixed codebook concept also appears in other 3GPP speech codecs, including the Extended Adaptive Multi-Rate Wideband (AMR-WB+) codec (TS 26.290) and the Enhanced Full Rate (EFR) codec referenced in TS 46.060. Across these codecs the principle is the same: a static, structured set of excitation vectors that enables low-bit-rate, high-quality speech transmission. The algebraic construction is particularly important because it balances coding efficiency, search complexity, and memory footprint, which are critical constraints in mobile terminals and network equipment.

Purpose & Motivation

The fixed codebook exists to make high-quality speech coding possible at low bit rates. Speech signals are highly redundant, and codecs exploit this by separating the slowly varying spectral envelope (captured by linear prediction) from the rapidly varying excitation. The excitation still carries significant information, and transmitting it directly would require far too many bits. The fixed codebook solves this by providing a finite, pre-agreed set of excitation vectors so that only a short index needs to be sent.

Earlier speech coding approaches, such as simple waveform coders, achieved good quality only at relatively high bit rates. The introduction of codebook-excited linear prediction in the 1980s and its standardisation in 3GPP codecs from the late 1990s onward allowed a step change in efficiency. The fixed codebook is the component that makes this possible: it turns an apparently continuous excitation signal into a discrete selection problem.

The choice of an algebraic codebook in AMR and AMR-WB was motivated by practical constraints. Storing large explicit codebooks would consume memory and complicate search. An algebraic structure defines the codebook implicitly, enabling fast search and simple implementation while preserving the statistical richness needed for natural-sounding speech. This design choice underpins the widespread deployment of AMR and AMR-WB in mobile networks and remains relevant in later codecs such as AMR-WB+.