Inner products computation using folded waveforms and distributed arithmetic principles

AbstractWe observe that every map between finite-dimensional normed spaces of the same dimension that respects fixed semi-inner products must be automatically a linear isometry. Moreover, we construct a uniformly smooth renorming of the Hilbert space $$\ell _2$$ ℓ 2 and a continuous injection acting thereon that respects the semi-inner products, yet it is non-linear. This demonstrates that there is no immediate extension of the former result to infinite dimensions, even under an extra assumption of uniform smoothness.

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Implementation of Radix-2 Butterfly Using Distributed Arithmetic Algorithm (DAA)

Lecture Notes in Electrical Engineering - VLSI Design: Circuits, Systems and Applications ◽

10.1007/978-981-10-7251-2_20 ◽

2018 ◽

pp. 179-187 ◽

Cited By ~ 1

Author(s):

Ketan Tarkas ◽

Chetan Sharma ◽

Oshin Mehta ◽

P. Augusta Sophy Beulet

Keyword(s):

Distributed Arithmetic ◽

Arithmetic Algorithm

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Source Symbol Purging-Based Distributed Conditional Arithmetic Coding

Entropy ◽

10.3390/e23080983 ◽

2021 ◽

Vol 23 (8) ◽

pp. 983

Author(s):

Jingjian Li ◽

Wei Wang ◽

Hong Mo ◽

Mengting Zhao ◽

Jianhua Chen

Keyword(s):

Posterior Probability ◽

Side Information ◽

Code Rate ◽

Arithmetic Coding ◽

Distributed Arithmetic ◽

Context Model ◽

Error Performance ◽

Codeword Length ◽

Simulation Results ◽

Correlation Strength

A distributed arithmetic coding algorithm based on source symbol purging and using the context model is proposed to solve the asymmetric Slepian–Wolf problem. The proposed scheme is to make better use of both the correlation between adjacent symbols in the source sequence and the correlation between the corresponding symbols of the source and the side information sequences to improve the coding performance of the source. Since the encoder purges a part of symbols from the source sequence, a shorter codeword length can be obtained. Those purged symbols are still used as the context of the subsequent symbols to be encoded. An improved calculation method for the posterior probability is also proposed based on the purging feature, such that the decoder can utilize the correlation within the source sequence to improve the decoding performance. In addition, this scheme achieves better error performance at the decoder by adding a forbidden symbol in the encoding process. The simulation results show that the encoding complexity and the minimum code rate required for lossless decoding are lower than that of the traditional distributed arithmetic coding. When the internal correlation strength of the source is strong, compared with other DSC schemes, the proposed scheme exhibits a better decoding performance under the same code rate.

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