Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

Fathollahi, Dorsa; Farsad, Nariman; Hashemi, Seyyed Ali; Mondelli, Marco

doi:10.1109/isit45174.2021.9517887

Cited by 15 publications

(5 citation statements)

References 23 publications

(26 reference statements)

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“…1) Computational Complexity: The number of calls to the FOD function is commonly used as a measure to estimate the computational complexity of RPA decoding [24], [25], [26], [27], [28]. In the worst-case scenario, where the maximum number of iterations is performed for every recursive call, the total number of FOD calls can be determined as:…”

Section: Ipa Decoding and Implementationmentioning

confidence: 99%

“…Although both simplified RPA and CPA reduce the overall algorithmic complexity, they make the projection and aggregation steps more involved as they employ more complex operations. Sparse RPA (SRPA) [27] is another modification of the RPA decoder that consists of multiple sparse RPA decoders. Each sparse RPA decoder uses only a random subset of projections.…”

Section: Introductionmentioning

confidence: 99%

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Pipelined Architecture for Soft-Decision Iterative Projection Aggregation Decoding for RM Codes

Hashemipour-Nazari,

Ren,

Goossens

et al. 2023

IEEE Trans. Circuits Syst. I

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Section: Ipa Decoding and Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pipelined Architecture for Soft-Decision Iterative Projection Aggregation Decoding for RM Codes

Hashemipour-Nazari,

Ren,

Goossens

et al. 2023

IEEE Trans. Circuits Syst. I

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“…Recently, a recursive projection-aggregation (RPA) algorithm was proposed in [10] for decoding RM codes. Despite its explicit structure and excellent decoding performance, the RPA algorithm (in its general form) requires a complexity of O(n r log n) for an RM code of length n and order r. Building upon the projection pruning idea in [10], there has been some recent attempts at reducing the complexity of the RPA algorithm [11], [12], and also applying it in other contexts than communication [13]. Moreover, building upon the computational tree of RM (and polar) codes, a class of neural encoders and decoders has been proposed in [14] via deep learning methods.…”

Section: Introductionmentioning

confidence: 99%

Low-Complexity Decoding of a Class of Reed-Muller Subcodes for Low-Capacity Channels

Jamali¹,

Fereydounian²,

Mahdavifar³

et al. 2022

Preprint

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We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array, and the encoding over each dimension is done separately via a smaller RM encoder. Similarly, the decoding is performed over each dimension via a low-complexity decoder for smaller RM codes. The proposed construction is of particular interest to low-capacity channels that are relevant to emerging low-rate communication scenarios. We present an efficient soft-input softoutput (SISO) iterative decoding algorithm for the product of RM codes and demonstrate its superiority compared to hard decoding over RM code components. The proposed coding scheme has decoding (as well as encoding) complexity of O(n log n) and latency of O(log n) for blocklength n. This research renders a general framework toward efficient decoding of RM codes.

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“…It then recursively decodes the projected codes to, finally, construct the decoded codeword by properly aggregating them. Very recently, building upon the projection pruning idea in [15], a method for reducing the complexity of the RPA algorithm has been explored in [16].…”

Section: Introductionmentioning

confidence: 99%

Reed-Muller Subcodes: Machine Learning-Aided Design of Efficient Soft Recursive Decoding

Jamali¹,

Liu²,

Makkuva³

et al. 2021

Preprint

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Reed-Muller (RM) codes are conjectured to achieve the capacity of any binary-input memoryless symmetric (BMS) channel, and are observed to have a comparable performance to that of random codes in terms of scaling laws. On the negative side, RM codes lack efficient decoders with performance close to that of a maximum likelihood decoder for general parameters. Also, they only admit certain discrete sets of rates. In this paper, we focus on subcodes of RM codes with flexible rates that can take any code dimension from 1 to n, where n is the blocklength. We first extend the recursive projection-aggregation (RPA) algorithm proposed recently by Ye and Abbe for decoding RM codes. To lower the complexity of our decoding algorithm, referred to as subRPA in this paper, we investigate different ways for pruning the projections. We then derive the soft-decision based version of our algorithm, called soft-subRPA, that is shown to improve upon the performance of subRPA. Furthermore, it enables training a machine learning (ML) model to search for good sets of projections in the sense of minimizing the decoding error rate. Training our ML model enables achieving very close to the performance of full-projection decoding with a significantly reduced number of projections. For instance, our simulation results on a (64, 14) RM subcode show almost identical performance for full-projection decoding and prunedprojection decoding with 15 projections picked via training our ML model. This is equivalent to lowering the complexity by a factor of more than 4 without sacrificing the decoding performance.

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Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

Cited by 15 publications

References 23 publications

Pipelined Architecture for Soft-Decision Iterative Projection Aggregation Decoding for RM Codes

Pipelined Architecture for Soft-Decision Iterative Projection Aggregation Decoding for RM Codes

Low-Complexity Decoding of a Class of Reed-Muller Subcodes for Low-Capacity Channels

Reed-Muller Subcodes: Machine Learning-Aided Design of Efficient Soft Recursive Decoding

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