Proceedings ArticleDOI
Efficient Maximum-Likelihood Decoding of Reed–Muller RM(m−3,m) Codes
Andrew Thangaraj,Henry D. Pfister +1 more
- pp 263-268
TLDR
This work considers the code family RM(m−3,m) and develops a new ML decoder, for transmission over the binary symmetric channel, that exploits their large symmetry group.Abstract:
Reed–Muller (RM) codes, a classical family of codes known for their elegant algebraic structure, have recently been shown to achieve capacity under maximum-likelihood (ML) decoding on the binary erasure channel and this has rekindled interest in their efficient decoding. We consider the code family RM(m−3,m) and develop a new ML decoder, for transmission over the binary symmetric channel, that exploits their large symmetry group. The new decoder has lower complexity than an earlier method introduced by Seroussi and Lempel in 1983.read more
Citations
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Posted Content
Hardware Implementation of Iterative Projection-Aggregation Decoding of Reed-Muller Codes
TL;DR: This work transforms the recursive structure of RPA decoding into a simpler and iterative structure with minimal error-correction degradation, and describes the first fully parallel hardware architecture for simplified RPA decode.
Proceedings ArticleDOI
Sequential Decoding of High-Rate Reed-Muller Codes
TL;DR: In this article, a soft-input sequential decoder for Reed-Muller (RM) codes of length $2^{m}$ and order $m-3$ is proposed, with permutations being selected on-the-fly from the RM codes' automorphism group based on soft information from a channel.
Journal ArticleDOI
Application of Guessing to Sequential Decoding of Polarization-Adjusted Convolutional (PAC) Codes
TL;DR: It is proved that the computational cutoff rate in sequential decoding of pre-transformed polar codes polarizes and the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed Reed-Muller rate-profile construction.
Journal ArticleDOI
Recursive Decoding of Reed-Muller Codes Starting With the Higher-Rate Constituent Code
TL;DR: In this paper , a permutation-based recursive decoding of Reed-Muller (RM) codes was proposed, with permutations being selected on the fly from the automorphism group of the code using soft information from a channel.
Posted Content
Decoding of Reed-Muller Codes Starting With a Higher-Rate Constituent Code.
TL;DR: In this paper, the authors considered non-iterative soft-input decoders for RM codes that, unlike recursive decoding, start decoding with a higher-rate constituent code.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
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TL;DR: A class of multiple-error-correcting codes and their decoding scheme to device a coding scheme which is able to detect and correct such errors.
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Application of Boolean algebra to switching circuit design and to error detection
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Journal ArticleDOI
Simple MAP decoding of first-order Reed-Muller and Hamming codes
Alexei Ashikhmin,Simon Litsyn +1 more
TL;DR: New MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes are presented, which have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size.
Journal ArticleDOI
Matrix Factorization over $GF(2)$ and Trace-Orthogonal Bases of $GF(2^n )$
TL;DR: Every binary, symmetric matrix A can be factored over $GF(2)$ into $A = BB'$, where the number of columns of B is bounded from below by either the rank of A, or by $\rho (A) + 1$, depending on whether at least one, or none, of the main-diagonal entries of A is nonzero.