Implementation of the Berlekamp-Massey algorithm using a DSP

Shlomo Greenberg; Nir Feldblum; Gal Melamed

Implementation of the Berlekamp-Massey algorithm using a DSP

Shlomo Greenberg, Nir Feldblum, Gal Melamed

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

Reed-Solomon (RS) codes arc error-correcting codes used in many of today's communication systems. RS encoding and decoding are typically implemented using dedicated hardware elements used in ADSL modems and digital TV. In this paper we propose using software in lieu of a hardware-based RS de-coder. This is accomplished using the Berlekamp-Massey algorithm, implemented on a programmable DSP. This software-based RS decoder using Berlekamp-Massey is implemented on Motorola's MSC8101 StarCore DSP. In order to evaluate the algorithm we use the following criteria: computation cost, cycle count, critical paths in the decoding scheme, and error location in the codeword. Furthermore, we examine the effect of changing the RS code's k, t parameters and its primitive polynomial in real-time implementation. The Berlekamp-Massey algorithm operates over finite field arithmetic, whose steps, as applied on the StarCore DSP, are discussed in detail and specifically evaluated using the assembly code for the syndrome search. We conclude that the Berlekamp-Massey algorithm, used for RS decoding, should be implemented using long codewords.

Original language	English
Title of host publication	11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004
Pages	358-361
Number of pages	4
State	Published - 1 Dec 2004
Event	11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004 - Tel Aviv, Israel Duration: 13 Dec 2004 → 15 Dec 2004

Publication series

Name	11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004

Conference

Conference	11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004
Country/Territory	Israel
City	Tel Aviv
Period	13/12/04 → 15/12/04

Keywords

Algorithms
Decoding
Digital signal processors
Reed-Solomon codes

ASJC Scopus subject areas

General Engineering

Cite this

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title = "Implementation of the Berlekamp-Massey algorithm using a DSP",

abstract = "Reed-Solomon (RS) codes arc error-correcting codes used in many of today's communication systems. RS encoding and decoding are typically implemented using dedicated hardware elements used in ADSL modems and digital TV. In this paper we propose using software in lieu of a hardware-based RS de-coder. This is accomplished using the Berlekamp-Massey algorithm, implemented on a programmable DSP. This software-based RS decoder using Berlekamp-Massey is implemented on Motorola's MSC8101 StarCore DSP. In order to evaluate the algorithm we use the following criteria: computation cost, cycle count, critical paths in the decoding scheme, and error location in the codeword. Furthermore, we examine the effect of changing the RS code's k, t parameters and its primitive polynomial in real-time implementation. The Berlekamp-Massey algorithm operates over finite field arithmetic, whose steps, as applied on the StarCore DSP, are discussed in detail and specifically evaluated using the assembly code for the syndrome search. We conclude that the Berlekamp-Massey algorithm, used for RS decoding, should be implemented using long codewords.",

keywords = "Algorithms, Decoding, Digital signal processors, Reed-Solomon codes",

author = "Shlomo Greenberg and Nir Feldblum and Gal Melamed",

year = "2004",

month = dec,

day = "1",

language = "English",

isbn = "0780387155",

series = "11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004",

pages = "358--361",

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note = "11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004 ; Conference date: 13-12-2004 Through 15-12-2004",

}

Greenberg, S, Feldblum, N & Melamed, G 2004, Implementation of the Berlekamp-Massey algorithm using a DSP. in 11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004., TB4.5, 11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004, pp. 358-361, 11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004, Tel Aviv, Israel, 13/12/04.

Implementation of the Berlekamp-Massey algorithm using a DSP. / Greenberg, Shlomo; Feldblum, Nir; Melamed, Gal.
11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004. 2004. p. 358-361 TB4.5 (11th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2004).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Implementation of the Berlekamp-Massey algorithm using a DSP

AU - Greenberg, Shlomo

AU - Feldblum, Nir

AU - Melamed, Gal

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Y1 - 2004/12/1

N2 - Reed-Solomon (RS) codes arc error-correcting codes used in many of today's communication systems. RS encoding and decoding are typically implemented using dedicated hardware elements used in ADSL modems and digital TV. In this paper we propose using software in lieu of a hardware-based RS de-coder. This is accomplished using the Berlekamp-Massey algorithm, implemented on a programmable DSP. This software-based RS decoder using Berlekamp-Massey is implemented on Motorola's MSC8101 StarCore DSP. In order to evaluate the algorithm we use the following criteria: computation cost, cycle count, critical paths in the decoding scheme, and error location in the codeword. Furthermore, we examine the effect of changing the RS code's k, t parameters and its primitive polynomial in real-time implementation. The Berlekamp-Massey algorithm operates over finite field arithmetic, whose steps, as applied on the StarCore DSP, are discussed in detail and specifically evaluated using the assembly code for the syndrome search. We conclude that the Berlekamp-Massey algorithm, used for RS decoding, should be implemented using long codewords.

AB - Reed-Solomon (RS) codes arc error-correcting codes used in many of today's communication systems. RS encoding and decoding are typically implemented using dedicated hardware elements used in ADSL modems and digital TV. In this paper we propose using software in lieu of a hardware-based RS de-coder. This is accomplished using the Berlekamp-Massey algorithm, implemented on a programmable DSP. This software-based RS decoder using Berlekamp-Massey is implemented on Motorola's MSC8101 StarCore DSP. In order to evaluate the algorithm we use the following criteria: computation cost, cycle count, critical paths in the decoding scheme, and error location in the codeword. Furthermore, we examine the effect of changing the RS code's k, t parameters and its primitive polynomial in real-time implementation. The Berlekamp-Massey algorithm operates over finite field arithmetic, whose steps, as applied on the StarCore DSP, are discussed in detail and specifically evaluated using the assembly code for the syndrome search. We conclude that the Berlekamp-Massey algorithm, used for RS decoding, should be implemented using long codewords.

KW - Algorithms

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KW - Digital signal processors

KW - Reed-Solomon codes

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Implementation of the Berlekamp-Massey algorithm using a DSP

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Keywords

ASJC Scopus subject areas

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