Efficient Berlekamp-Massey based recursive decoder for Reed-Solomon codes

Srivastava, Shraddha; McSweeney, Richard; Spagnol, Christian; Popovici, Emanuel

doi:10.1109/miel.2012.6222879

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…2 Theoretically it can be seen that the classical decoding scheme for SRS uses n s clock cycles for the syndromes computation, 2t for the BM algorithm, n s for the Chien search and 2t for the Forney's formula which results in 2n s + 4t cycles in total. The new evaluation based decoding scheme needs n s clock cycles for the syndromes calculation, 2t for the BM algorithm and k s for the message polynomial calculation resulting in 2n s cycles [4]. In terms of area, the new encoding and the syndrome computation share the same operation and the decoder needs a BM and LFSR blocks (for polynomial division) [12] instead of the traditional decoder (which includes BM, Chien search and Forney formula).…”

Section: Hardware and Software Implementation Resultsmentioning

confidence: 99%

“…Consider an SRS code with parameters [12,4,9] shortened from [15, 7,9] RS code defined over the field F 1 6. The code has an error correction capability, t = 4.…”

Section: Example For Encoding and Decoding Srs Codementioning

confidence: 99%

“…In this paper we concentrate in particular on this aspect of implementation by providing an efficient method for decoding of shortened Reed-Solomon codes. This paper is an extended version of [4] for shortened RS codes.…”

Section: Introductionmentioning

confidence: 99%

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Area efficient evaluation based coding of shortened Reed-Solomon codes for memory constrained applications

Srivastava

McSweeney

Popovici

2012

IET Irish Signals and Systems Conference (ISSC 2012)

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This paper presents an efficient algorithm for encoding and decoding Shortened Reed-Solomon (SRS) codes based on evaluation. The encoding and syndrome computations are performed using polynomial evaluation and the decoding is performed using a recursive extension of the original algorithm. The proposed decoding algorithm initially calculates the error locator polynomial by using the Berlekamp Massey (BM) algorithm and with the recursive computation of discrepancies, it decodes directly the message polynomial. Compared to the traditional decoding algorithm using BM algorithm, Chien search and Forney formula, the proposed algorithm results in area savings for hardware implementations due to hardware re-use and the reduced number of stages. Also, the savings in memory for the software implementation makes it suitable for memory constrained applications such as Wireless Sensor Networks (WSN) applications. For the hardware implementations, the number of clock cycles required are lower for the proposed scheme, which results in time savings. Also, software implementation results of RS (32, 24) for resource constrained WSN application on ATMEL Atmega 128 microcontroller show that the proposed encoder and decoder is only about 52% and 72% of the memory footprint of a traditional encoder and decoder respectively.

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Section: Hardware and Software Implementation Resultsmentioning

confidence: 99%

“…Consider an SRS code with parameters [12,4,9] shortened from [15, 7,9] RS code defined over the field F 1 6. The code has an error correction capability, t = 4.…”

Section: Example For Encoding and Decoding Srs Codementioning

confidence: 99%

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Area efficient evaluation based coding of shortened Reed-Solomon codes for memory constrained applications

Srivastava

McSweeney

Popovici

2012

IET Irish Signals and Systems Conference (ISSC 2012)

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“…An RS decoder is widely used to decode and correct data that have been encoded in various digital communication systems [ 21 ]. An RS decoder is divided into three parts: the calculation of correction factors, the solution of the key equation, and the determination of error location and size [ 70 ], as shown in Figure 11 a. The solution of the key equation is the most complex part of the decoder, and can be implemented by the Berlekamp–Massey (BM) algorithm or the Euclidean algorithm.…”

Section: Decodermentioning

confidence: 99%

The Development and Progress of the UWB Physical Layer

Chen

et al. 2022

Micromachines

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Ultra-wideband (UWB) technology has been applied in many fields, such as radar and indoor positioning, because of its advantages of having a high transmission rate, anti-multipath interference, and good concealment. In the UWB physical layer, the transmitting link, including an encoder and a pulse generator, is used to improve the anti-interference ability of the signal, while the receiving link, including a receiver and a decoder, can correct the error signal. Therefore, the performance of the UWB physical layer can obviously affect the speed and quality of UWB signal transmission. In this paper, the structure and performance of the codec and transceiver of the UWB physical layer are introduced and compared. In addition, some typical architectures and features are summarized and discussed, which provides a valuable reference and suggestions for the design of the UWB physical layer. Finally, the outlook of the UWB physical layer is presented: its development direction mainly includes high speed, low power consumption, and fewer hardware resources.

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