Optimal Binary Coding of Ordered Numbers

A novel high speed and ultra long-haul radio-over-fiber (ROF) system based on Dual Photoelectric Arms Coherent Modulation (DPACM) and Optical Duo-Binary Coding (ODBC) is proposed, and demonstrated. The signal spectrum bandwidth, generated by ODBC based on the first order DPACM, is half of non-return-to-zero (NRZ ) signal spectrum bandwidth. The secondary order DPACM generates a 40-GHz Millimeter-wave (mm-wave) that is transmitted over fiber (ROF). The simulation results show that, the bit rate can be up to 40 Gbps and the transmission distance is over 1500 Km, based on the ROF system with a 0 dBm continuous-wave laser source, multiple stages Er-Doped Fiber Amplifier (EDFA), a standard single mode fiber (SSMF) with a dispersion of 17 ps/nm/Km and a attenuation of 0.2 dB/Km.

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Deep Neural Networks Classification via Binary Error-Detecting Output Codes

Applied Sciences ◽

10.3390/app11083563 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3563

Author(s):

Martin Klimo ◽

Peter Lukáč ◽

Peter Tarábek

Keyword(s):

Neural Networks ◽

Categorical Data ◽

Coding Theory ◽

Hamming Distance ◽

Activation Function ◽

Block Codes ◽

Ease Of Use ◽

Linear Block Codes ◽

Binary Coding ◽

The One

One-hot encoding is the prevalent method used in neural networks to represent multi-class categorical data. Its success stems from its ease of use and interpretability as a probability distribution when accompanied by a softmax activation function. However, one-hot encoding leads to very high dimensional vector representations when the categorical data’s cardinality is high. The Hamming distance in one-hot encoding is equal to two from the coding theory perspective, which does not allow detection or error-correcting capabilities. Binary coding provides more possibilities for encoding categorical data into the output codes, which mitigates the limitations of the one-hot encoding mentioned above. We propose a novel method based on Zadeh fuzzy logic to train binary output codes holistically. We study linear block codes for their possibility of separating class information from the checksum part of the codeword, showing their ability not only to detect recognition errors by calculating non-zero syndrome, but also to evaluate the truth-value of the decision. Experimental results show that the proposed approach achieves similar results as one-hot encoding with a softmax function in terms of accuracy, reliability, and out-of-distribution performance. It suggests a good foundation for future applications, mainly classification tasks with a high number of classes.

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