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About 851 papers for “recursive decoding”

Block Recursive MIMO Decoding

Aymen Askri, Ghaya Rekaya-Ben Othman, Mohamed-Achraf Khsiba · SPIRE - Sciences Po Institutional REpository · 2018

Cited by 0

Recursive decoding of Reed-Muller codes

Ilya Dumer, Kirill Shabunov · 2002

We use the Plotkin (u,u+v)-construction for general Reed-Muller codes (m,r) and relegate decoding to the two constituent RM codes. First, we use the better protected code (m-1,r-1) to find a subblock v. Then we proceed with the block u from the code (m-l,r). We repeat this recursion on both halves and recalculate the reliabilities of the received symbols. In the end, we perform maximum likelihood decoding on the biorthogonal codes.

Cited by 20

Enhanced recursive Reed-Muller erasure decoding

Alexandre Soro, Jérôme Lacan, Vincent Roca et al. · arXiv (Cornell University) · 2016

Recent work have shown that Reed-Müller (RM) codes achieve the erasure channel capacity. However, this performance is obtained with maximum-likelihood decoding which can be costly for practical applications. In this paper, we propose an encoding/decoding scheme for Reed-Müller codes on the packet erasure channel based on Plotkin construction. We present several improvements over the generic decoding. They allow, for a light cost, to compete with maximum-likelihood decoding performance, especially on high-rate codes, while significantly outperforming it in terms of speed.

Cited by 3Open access

Recursive Trellis Decoding Techniques of Polar Codes

Peter Trifonov · 2020

Recursive trellis decoding of polar codes is considered. Polar codes are shown to have much lower recursive trellis decoding complexity compared to similar Reed-Muller codes. Furthermore, a low-latency decoding algorithm, which combines recursive trellis and successive cancellation decoding methods, is presented.

Cited by 5

Recursive decoding of projective Reed-Muller codes

Rodrigo San–José · IEEE Transactions on Information Theory · 2026

We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of projective Reed-Muller codes. We determine the degrees for which we can decode up to the error correction capability of these codes, and we compute the order of complexity of the algorithm, given by that of the chosen decoder for affine Reed-Muller codes. We also show how the decoder behaves when increasing the number of variables and the size of the field.

Cited by 0

Recursive decoding of projective Reed-Muller codes

Rodrigo San–José · IEEE Transactions on Information Theory · 2026

We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of projective Reed-Muller codes. We determine the degrees for which we can decode up to the error correction capability of these codes, and we compute the order of complexity of the algorithm, given by that of the chosen decoder for affine Reed-Muller codes. We also show how the decoder behaves when increasing the number of variables and the size of the field.

Cited by 0Open access

Recursive List Decoding for Reed-Muller Codes

Ilya Dumer, Kirill Shabunov · arXiv (Cornell University) · 2017

We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is further enhanced by using intermediate code lists and permutation procedures. For moderate lengths up to 512, near-optimum decoding with feasible complexity is obtained.

Cited by 2Open access

Recursive projection-aggregation decoding of Reed-Muller codes

Min Ye, Emmanuel Abbé · 2019

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms based on list-decoding algorithms and code concatenation. We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.

Cited by 21

A Recursive Soft-Input Soft-Output Decoding Algorithm

Liudmila Karakchieva, Peter Trifonov · IEEE Transactions on Communications · 2023

A reduced complexity symbolwise maximum a posteriori probability (MAP) decoding algorithm for linear block codes is presented. This algorithm is based on the recursive trellises and performs two passes over the recursion tree. Probability-domain and Log-Max implementations are considered. Numeric results show that the proposed method has lower complexity compared to other known recursive algorithms and the classical BCJR algorithm. The complexity analysis for random codes is provided.

Cited by 1

Twin-stack decoding of recursive systematic convolutional codes

Ravi Sivasankaran, Stephen McLaughlin · IEEE Transactions on Communications · 2001

We present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes. The proposed decoder, the twin-stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative "turbo" configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs). Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R=1/3, recursive code, but this difference narrows progressively at higher SNRs. The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques.

Cited by 9

Coset Error Patterns in Recursive Projection-Aggregation Decoding

Fanyun Chen, Bin Zhang, Qin Huang · 2024

The recursive projection-aggregation (RPA) algorithm provides state-of-the-art performance for Reed-Muller (RM) codes. It relies on projecting onto subspaces, decoding projections and voting. This paper explores the error-correction capability of RPA with a limited number of subspaces. By constructing a false vote matrix, it demonstrates that RPA may fail to correct coset error patterns, even when all projections are decoded successfully. These patterns severely degrade the decoding performance due to their small weights. Thus, two rules on the subspace selection are derived to guarantee the error-correction capability of RPA. Simulation results verify that the two rules dominate the decoding performance of RPA.

Cited by 2

Encoding-Decoding-Based Recursive Filtering for Fractional-Order Systems

Bo Jiang, Hongli Dong, Yuxuan Shen et al. · IEEE/CAA Journal of Automatica Sinica · 2022

Dear editor, This letter focuses on the encoding-decoding-based recursive filtering problem for a class of fractional-order systems. For the purpose of protecting security of the wireless communication network, a dynamic-quantization-based encoding-decoding mechanism is introduced to encrypt the transmitted measurement. Specifically, the measurement outputs are first encoded by the encoder into codewords which are then transmitted over the wireless communication network. After received by the decoder, the codewords are decoded and then sent to the filter. In light of the mathematical properties of truncated Gaussian distribution, the variance of the encoding-decoding-induced error between the decoded measurement and the real measurement is derived. An upper bound on the filtering error covariance is first obtained based on the variance of the encoding-decoding-induced error. Then, the minimal upper bound is derived by choosing proper filter gain. Finally, the efficiency and superiority of the proposed algorithm are verified through a simulation example.

Cited by 23Open access

Soft decision decoding of Reed-Muller codes: recursive lists

Ilya Dumer, Kirill Shabunov · arXiv (Cornell University) · 2017

Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed when these recalculations reach the trivial RM codes. In turn, the updated lists of most plausible codewords are used in subsequent decodings. The algorithm is further improved by using permutation techniques on code positions and by eliminating the most error-prone information bits. Simulation results show that for all RM codes of length 256 and many subcodes of length 512, these algorithms approach maximum-likelihood (ML) performance within a margin of 0.1 dB. As a result, we present tight experimental bounds on ML performance for these codes.

Cited by 0Open access

Recursive Decoding for OFDM Systems with Multiple Transmit Antennas

J. KIM · IEICE Transactions on Communications · 2005

In this letter, we propose a recursive space time decoding method for orthogonal frequency division multiplexing (OFDM) systems exploiting multiple transmit antenna diversity when the channels are fast fading. We first develop a computationally efficient space-time decoding method involving a matrix inversion to mitigate the channel variation effect. We then further reduce the computational complexity of the matrix inversion decoding method via a recursive formulation. Computer simulation results show that the proposed recursive decoding has much better BER performance than Alamouti decoding, requiring much less computation than the matrix inversion decoding. Moreover, the relative advantage in BER performance of the proposed scheme over Alamouti decoding stands out as the Doppler frequency increases.

Cited by 2