Algebraic analog decoding of linear binary codes

Rudolph, L.; Hartmann, C.; Hwang, Tai-Yang; Đuc, Nguyen Quang

doi:10.1109/tit.1979.1056073

Cited by 21 publications

(3 citation statements)

References 5 publications

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“…Therefore, in Figure 1, the minimum function is used instead of multiplication, even in the Boolean case. The demand for processing analog channel outputs by digital coding is not new [34]. Our approach is based on fuzzy linear coding [35,36].…”

Section: Decision Methodsmentioning

confidence: 99%

Deep Neural Networks Classification via Binary Error-Detecting Output Codes

Klimo

Tarábek

2021

Applied Sciences

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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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Section: Decision Methodsmentioning

confidence: 99%

Deep Neural Networks Classification via Binary Error-Detecting Output Codes

Klimo

Tarábek

2021

Applied Sciences

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“…In Fig. 6, RS (7,5,3) is used. For comparison, the decoding error rates in harddecision decoding and maximum-likelihood decoding are also shown, D in the proposed decoding is set at 1.…”

Section: Proposed Decoding Methodsmentioning

confidence: 99%

Soft-decision decoding of Reed-Solomon codes

Nara

Tanaka

2000

Electron. Comm. Jpn. Pt. III

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“…Ο αλγόριθμος Viterbi δεν είναι κατάλληλος για την αποκωδικοποίηση των κωδίκων αυτών διότι η έξοδος του είναι δυαδική-(hard) πληροφορία (0 ή 1). Οι πρώτες αρχές της αναλογικής επαναληπτικής υλοποίησης δόθηκαν από τον Rudolph και την ομάδα του το 1979 [32], προτείνοντας έναν αναλογικό soft αποκωδικοποιητή για κυκλικούς κώδικες δομής (cyclic block codes). Αναλογικές υλοποιήσεις βασιζόμενες σε νευρομορφικά δίκτυα για τον αλγόριθμο Viterbi υποδηλώνοντας την υπεροχή τους έναντι των αντιστοίχων ψηφιακών σε θέματα ταχύτητας και κατανάλωσης δημοσιεύτηκαν το 1996 [33] και 2004 [26], αντιστοίχως.…”

Section: τεχνολογικές προκλήσειςunclassified

Αρχιτεκτονικές Και Υλοποίηση Κωδίκων Διόρθωσης Λαθών

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Algebraic analog decoding of linear binary codes

Cited by 21 publications

References 5 publications

Deep Neural Networks Classification via Binary Error-Detecting Output Codes

Deep Neural Networks Classification via Binary Error-Detecting Output Codes

Soft-decision decoding of Reed-Solomon codes

Αρχιτεκτονικές Και Υλοποίηση Κωδίκων Διόρθωσης Λαθών

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