The description and design of the source-controlled variable-rate multimode wideband (VMR-WB) codec recently selected by the 3/sup rd/ Generation Partnership Project 2 (3GPP2) for the cdma2000/spl reg/ system in Rate-Set II are presented. The paper gives an overview of the codec and the methodologies that enable high quality wideband coding at average data rates ranging from TIA/EIA/IS-733 ADR (average data rate) to that of TIA/EIA/IS-127. The codec has three modes of operation at different average data rates and a fourth mode that is interoperable with 3GPP/AMR-WB (ITU-T G.722.2). Despite the interoperability constraint, the codec is capable of meeting the aggressive performance requirements through the use of novel techniques such as noise suppression, efficient signal classification, new coding types optimized for stable voiced and unvoiced frames, novel post-processing technique for periodicity enhancement in the lower frequency band, and improved frame erasure concealment mechanisms.

Abstract We analyze combinatorial properties of open covers of sets of real numbers by using filters on the natural numbers. In fact, the goal of this paper is to characterize known properties related to ω-covers of the space in terms of combinatorial properties of filters associated with these ω-covers. As an example, we show that all finite powers of a set of real numbers have the covering property of Menger if, and only if, each filter on ω associated with its countable ω-cover is a P+filter.

Abstract We discuss the finite-to-one Rudin-Keisler ordering of ultrafilters on the natural numbers, which we baptize the Rudin-Blass ordering in honour of Professor Andreas Blass who worked extensively in the area. We develop and summarize many of its properties in relation to its bounding and dominating numbers, directedness, and provide applications to continuum theory. In particular, we prove in ZFC alone that there exists an ultrafilter with no Q-point below in the Rudin-Blass ordering.

This paper describes the 8 kb/s speech coding algorithm G.729 which has been standardized by ITU-T. The algorithm is based on a conjugate-structure algebraic CELP (CS-ACELP) coding technique and uses 10 ms speech frames. The codec delivers toll-quality speech (equivalent to 32 kb/s ADPCM) for most operating conditions. This paper describes the coder structure in detail and discusses the reasons behind certain design choices. A 16-b fixed-point version has been developed as part of Recommendation G.729 and a summary of the subjective test results based on a real-time implementation of this version are presented.

In this paper, we describe the enhanced full rate (EFR) speech codec that has recently been standardised for the North American TDMA digital cellular system (IS-136). The EFR codec, specified in the IS-641 standard, has been jointly developed by Nokia and University of Sherbrooke. The codec consists of 7.4 kbit/s speech (source) coding and 5.6 kbit/s channel coding (error protection) resulting in a 13.0 kbit/s gross bit-rate in the channel. Speech coding is based on the ACELP algorithm (algebraic code excited linear prediction). The codec offers speech quality close to that of wireline telephony (G.726 32 kbit/s ADPCM used as a wireline reference) and provides a substantial improvement over the quality of the current speech channel. The improved speech quality is not only achieved in error-free conditions, but also in typical cellular operating conditions including transmission errors, environmental noise, and tandeming of speech codecs.

This paper describes the GSM enhanced full rate (EFR) speech codec that has been standardised for the GSM mobile communication system. The GSM EFR codec has been jointly developed by Nokia and University of Sherbrooke. It provides speech quality at least equivalent to that of a wireline telephony reference (32 kbit/s ADPCM). The EFR codec uses 12.2 kbit/s for speech coding and 10.6 kbit/s for error protection. Speech coding is based on the ACELP algorithm (algebraic code excited linear prediction). The codec provides substantial quality improvement compared to the existing GSM full rate and half rate codecs. The old GSM codecs lack wireline quality even in error-free channel conditions, while the EFR codec provides wireline quality not only for error-free conditions but also for the most typical error conditions. With the EFR codec, wireline quality is also sustained in the presence of background noise and in tandem connections (mobile to mobile calls).

In this paper, we present a new approach to shape the coding noise in speech and audio coders. The approach, called spectral amplitude warping (SAW), consists essentially of a pre- and post-processing which apply a nonlinear transformation to the signal short-term spectrum prior to, and after, encoding. Since it is possible to view SAW as a separate entity from the coder, the noise shaping capability of an existing coder can be improved without modifying the coder itself. Using SAW as a pre- and post-process to the G.722 wideband speech coding standard, it was found in an informal listening test that the quality of the 64 kb/s operating mode can be achieved at only 48 kb/s. The price to be paid is an additional delay.

This paper describes the recently adopted ITU-T Recommendation G.729 Annex A (G.729A) for encoding speech signals at 8 kbit/s with low complexity. G.729A has been selected as the standard speech coding algorithm for multimedia digital simultaneous voice and data (DSVD). G.729A is bitstream interoperable with G.729; i.e., speech coded with G.729A can be decoded with G.729, and vice versa. As G.729, it uses the conjugate structure algebraic code excited linear prediction (CS-ACELP) algorithm with 10 ms frames. However, several algorithmic changes have been introduced into G.729 which resulted in 50% drop in its complexity, enabling a DSP implementation with a complexity of about 10-12 MIPS. This paper describes the algorithmic changes which have been introduced in order to achieve the low complexity goal while meeting the terms of reference. Subjective tests have been performed by ITU-T in both the selection phase and the characterization phase and the results showed that the performance of G.729A is equivalent to both G.729 and G.726 at 32 kbit/s in most operating conditions; however, it is slightly worse in case of three tandems and in the presence of background noise. A breakdown of the complexities of both G.729 and G.729A is given at the end of the paper.

This paper describes the enhanced full rate (EFR) speech codec that has been standardized by ETSI for the GSM mobile communications system in 1996. The codec was developed jointly by Nokia and the University of Sherbrooke. It operates at 12.2 kbit/s speech coding (source coding) bit-rate and provides speech quality equivalent to that of wireline telephony (G.726 32 kbit/s ADPCM). The algorithm is based on the algebraic code-excited linear prediction (ACELP) technology, using 20 ms speech frames. The GSM EFR speech codec provides substantial quality improvement compared to the current GSM full rate (FR) and half rate (HR) codecs. The old GSM codecs lag far behind wireline quality even in error-free conditions, while the EFR codec provides wireline quality also for the most typical error conditions. With the EFR codec, wireline quality is also sustained in the presence of background noise and in tandem connections (mobile-to-mobile calls). The codec was defined using fixed-point basic operators with complexity estimated at 18 WMOPS (below that of the GSM half-rate codec).

This paper presents an algorithm for encoding speech signals at bit rates below 4 kbit/s based on a mixed harmonic and stochastic modeling of the excitation signal. The algorithm uses robust pitch tracking and efficient voicing analysis to determine the ratios of the harmonic and stochastic components. The harmonic component is synthesized using a bank of bandpass filters while the stochastic component is synthesized using inverse STFT with overlap-and-add. Postfiltering is utilized at the decoder to enhance the quality of synthesized speech. A 2.4 kbit/s version of the algorithm was formally tested and the DAM and DRT scores showed that the coder performance is comparable to that of DoD 4.8 kbit/s Federal Standard FS-1016.

Abstract We prove various results on the notion of ordinal ultrafiters introduced by J. Baumgartner. In particular, we show that this notion of ultrafilter complexity is independent of the more familiar Rudin-Keisler ordering.

This paper describes the application of transform coded excitation (TCX) coding to encoding wideband speech and audio signals in the bit rate range of 16 kbits/s to 32 kbits/s. The approach uses a combination of time domain (linear prediction; pitch prediction) and frequency domain (transform coding; dynamic bit allocation) techniques, and utilizes a synthesis model similar to that of linear prediction coders such as CELP. However, at the encoder, the high complexity analysis-by-synthesis technique is bypassed by directly quantizing the so-called target signal in the frequency domain. The innovative excitation is derived at the decoder by inverse filtering the quantized target signal. The algorithm is intended for applications whereby a large number of bits is available for the innovative excitation. The TCX algorithm is utilized to encode wideband speech and audio signals with a 50-7000 Hz bandwidth. Novel quantization procedures including inter-frame prediction in the frequency domain are proposed to encode the target signal. The proposed algorithm achieves very high quality for speech at 16 kbits/s, and for music at 24 kbits/s.>

A toll quality speech codec at 8 kbit/s with a 10 ms speech-frame currently under standardization by the CCITT is presented. The encoding algorithm is based on algebraic code-excited linear prediction (ACELP). Efficient pitch and codebook search strategies, along with efficient quantization procedures, have been developed to achieve toll quality encoded speech with a complexity implementable on current fixed-point DSP chips. Initial subjective tests showed that the codec quality is equivalent to that of G.726 ADPCM at 32 kbit/s in error-free conditions and it outperforms G.726 under error conditions. The codec can support a frame erasure rate up to 3% with slight degradation and performs adequately under tandeming conditions. The algorithm has been implemented on a single fixed-point DSP for the CCITT qualification test. It requires about 24 MIPS.>

The application of algebraic code excited linear prediction (ACELP) coding to wideband speech is presented. An algebraic codebook with a 20 bit address can be used without any storage requirements and, more importantly, with a very efficient search procedure which allows for real-time implementation. The authors describe an efficient procedure for searching such a large codebook deploying a focused search strategy, where less than 0.1% of the codebook is searched with performance very close to that of a full search. High-quality speech at a bit rate of 13 kbps was obtained.>

A general framework is introduced which allows both fast search and freedom in designing codebooks with good statistical properties. Several previously proposed schemes are compared from this viewpoint. A backward filtering formulation is given to show that sparse algebraic codes (SACs) (i.e., with few nonzero components) offer distinct advantages. It is shown that they reduce the optimal-search computation per codeword. They also allow control of the statistical properties of the codebook in the time and frequency domains. This control can be dynamic in the sense that it can be made to evolve as a function of the linear predictive coding model A(z). The algebraic-code excited linear prediction (ACELP) technology which allows full duplex operation on a single TMS320C25 at rates between 4.8 and 16 kb/s and which is based on SAC-driven dynamic codebooks is described.>

It has been proven by Blass [1973] that any two P-points which have a P-point as a common upper bound in the Rudin-Keisler (RK) ordering necessarily have a common lower bound (necessarily a P-point). Hence two nonisomorphic Ramsey ultrafilters have neither a common lower nor a common upper bound which is a P-point. So in a model of CH for example (or MA, P(c),…), the RK ordering restricted to P-points is neither upward nor downward directed, since it is well known that nonisomorphic Ramsey ultrafilters exist in such models. On the other hand, we will see that in the model for “near coherence of filters” (NCF) produced by Blass and Shelah [1985], the RK ordering of P-points is upward, hence downward directed. This shows that the question of directedness of the RK ordering of P-points, upward or downward, cannot be decided in ZFC. There is a related question, asked by Blass in [1973], whether two P-points which have a common lower bound necessarily have a common upper bound which is a P-point. Our main result establishes the independence of this statement relative to ZFC. Its consistency will follow as soon as we show that the RK ordering of P-points is upward directed in the NCF model mentioned above, which we do in §2. But its independence will require a new construction, and will be given in §3.

We use models of set theory described in [2] and [3] to prove the consistency of several combinatorial principles, for example: If ℱ is any filter on N containing all the cofinite sets, then there is a finite-to-one function f: N → N such that f(ℱ) is either the filter of cofinite sets or an ultrafilter. As a consequence of our combinatorial principles, we also obtain the consistency of: The partial ordering P of slenderness classes of abelian groups, denned and studied in [4], is a four-element chain. In the remainder of this Introduction, we shall define our terminology and state the combinatorial principles to be considered. In §2, we shall establish some implications between these principles. In §3, we shall prove our consistency results by showing that the strongest of our principles holds in models of set theory constructed in [2] and [3]. A filter on N will always mean a proper filter containing all cofinite sets; in particular, an ultrafilter will necessarily be nonprincipal. We write N ↗ N for the set of nondecreasing functions from the set N of positive integers into itself. A subset ℐ of N ↗ N is called an ideal if it is closed downward (if f(n) ≤ g(n) for all n and if g ∈ ℐ, then f ∈ ℐ) and closed under binary maximum (if f(n) = max(g(n), h(n)) for all n and if g, h ∈ ℐ then f ∈ ℐ).

An algebra and a logic characterizing the complexity class NC/sup 1/, which consists of functions computed by uniform sequences of polynomial-size, log depth circuits, are presented. In both characterizations, NC/sup 1/ functions are regarded as functions from one class of finite relational structures to another. In the algebraic characterization, upward and downward tree recursion are applied to a class of simple functions. In the logical characterization, first-order logic is augmented by an operator for defining relations by primitive recursion. It is assumed that every structure has an underlying relation giving the binary representations of integers.>