Homomorphic Computation in Reed-Muller Codes
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DOI: 10.1109/access.2020.3001120
Abstract: With the ongoing developments in artificial intelligence (AI), big data, and cloud services, fully homomorphic encryption (FHE) is being considered as a solution for preserving the privacy and security in machine learning systems. Currently, the… read more here.
Keywords: muller codes; addition; homomorphic computation; reed muller ... See more keywords
Reed–Muller Network Coded-Cooperation With Joint Decoding
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DOI: 10.1109/lcomm.2018.2879101
Abstract: This letter proposes a Reed–Muller network coded-cooperative (RMNCC) scheme with the joint decoding. The Kronecker product (KP) construction is utilized to construct RM codes. The KP construction is effectively employed to accomplish network coded-cooperation between… read more here.
Keywords: network coded; coded cooperation; reed muller; muller network ... See more keywords
Optimization and Simplification of PCPA Decoder for Reed-Muller Codes
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Communications Letters"
DOI: 10.1109/lcomm.2022.3163622
Abstract: The collapsed projection-aggregation (CPA) decoder reduces the computational complexity of the recursive projection-aggregation (RPA) decoder by removing the recursive structure. From simulations, the CPA decoder has similar error-correction performance as the RPA decoder, when decoding… read more here.
Keywords: muller codes; decoder; reed muller; pcpa decoder ... See more keywords
Dynamic Frozen-Function Design for Reed-Muller Codes With Automorphism-Based Decoding
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DOI: 10.1109/lcomm.2022.3230202
Abstract: In this letter, we propose to add dynamic frozen bits to underlying polar codes with a Reed-Muller information set with the aim of maintaining the same sub-decoding structure in Automorphism Ensemble (AE) and lowering the… read more here.
Keywords: function design; dynamic frozen; reed muller; frozen function ... See more keywords
On Decoding of Reed-Muller Codes Using a Local Graph Search
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Communications"
DOI: 10.1109/tcomm.2021.3128541
Abstract: We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by… read more here.
Keywords: muller codes; decoding reed; reed muller; graph ... See more keywords
Information Sets From Defining Sets for Reed–Muller Codes of First and Second Order
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2018.2817539
Abstract: Reed–Muller codes belong to the family of affine-invariant codes. As such codes, they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper, we identify those… read more here.
Keywords: sets defining; information; muller codes; first second ... See more keywords
Reed–Muller Codes: Theory and Algorithms
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DOI: 10.1109/tit.2020.3004749
Abstract: Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their… read more here.
Keywords: tex math; reed muller; inline formula; muller codes ... See more keywords
Almost-Reed–Muller Codes Achieve Constant Rates for Random Errors
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2021.3116663
Abstract: This paper considers “ $\delta $ -almost Reed–Muller codes”, i.e., linear codes spanned by evaluations of all but a $\delta $ fraction of monomials of degree at most $d$ . It is shown that for… read more here.
Keywords: tex math; reed muller; inline formula;