Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.

In the letter, two classes of optimal codebooks and asymptotically optimal codebooks in regard to the Levenshtein bound are presented, which are based on mutually unbiased bases (MUB) and approximately mutually unbiased bases (AMUB), respectively.

In this letter, motivated by the research of Tian et al., two constructions of asymptotically optimal codebooks in regard to the Welch bound with additive and multiplicative characters are provided. The parameters of constructed codebooks are new, which are different from those in the letter of Tian et al.

In this letter, as a generalization of Luo et al.'s constructions, a construction of codebook, which meets the Welch bound asymptotically, is proposed. The parameters of codebook presented in this paper are new in some cases.

In this letter, as a generalization of Heng's constructions in the paper [9], a construction of codebooks, which meets the Welch bound asymptotically, is proposed. The parameters of codebooks presented in this paper are new in some cases.

This paper proposes several cepstral statistics compensation and normalization algorithms which alleviate the effect of additive noise on cepstral features for speech recognition. The algorithms are simple yet efficient noise reduction techniques that use online-constructed pseudo-stereo codebooks to evaluate the statistics in both clean and noisy environments. The process yields transformations for both clean speech cepstra and noise-corrupted speech cepstra, or for noise-corrupted speech cepstra only, so that the statistics of the transformed speech cepstra are similar for both environments. Experimental results show that these codebook-based algorithms can provide significant performance gains compared to results obtained by using conventional utterance-based normalization approaches. The proposed codebook-based cesptral mean and variance normalization (C-CMVN), linear least squares (LLS) and quadratic least squares (QLS) outperform utterance-based CMVN (U-CMVN) by 26.03%, 22.72% and 27.48%, respectively, in relative word error rate reduction for experiments conducted on Test Set A of the Aurora-2 digit database.