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參數(shù)資料
| 型號： | AN2407 |
| 廠商： | 飛思卡爾半導(dǎo)體(中國)有限公司 |
| 英文描述： | Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples |
| 中文描述： | 里德所羅門編碼器/的StarCore SC140/SC1400核心解碼器，以擴(kuò)展實(shí)例 |
| 文件頁數(shù)： | 19/48頁 |
| 文件大小： | 306K |
| 代理商： | AN2407 |
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Summary
Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples, Rev. 1
Freescale Semiconductor
19
Notice the syndromes calculation and the root search. The theoretical lower bounds for syndromes calculation and
root search for
T
= 8 are 5664 and 3968 cycles, respectively. As
Table 2
and
Table 3
show, the actual cycle count
in this implementation is very close to the lowest theoretical bound.
6
Summary
This application note demonstrates the implementation of the Reed-Solomon encoder and decoder on the SC140
core. The implementation is in accordance with the standard for ADSL systems, using Galois field GF(256) and
T
equal to 8. Encoding and decoding is performed by the Petersen-Gorenstein-Zierler (PGZ) algorithm. The
algorithm consists mainly of polynomial evaluations over a set of Galois field points, which is equivalent to a
sequence of MAC operations in the framework of Galois arithmetic. The emphasis is on efficient implementation
of MAC operations on the DSP, under the constraint of reasonable memory requirements. The two most cycle-
intensive routines, syndromes calculation and roots search, perform straightforward polynomial evaluations for
which full parallelization is possible. Thus, we conclude that since most of the cycle-intensive algorithms can be
parallelized, the architecture of the SC140 can be very efficiently employed in the Reed-Solomon application.
7
References
[1]
C. E. Shannon, “A Mathematical Theory of Communication,”
Bell System Technical Journal
, vol. 27,
1948, pp. 379–423 and pp. 623–656.
[2]
E. R. Berlekamp, R.E. Peile and S.P. Pope, “The Application of Error Control to Communications,”
IEEE
Communications Magazine
, vol.25, no 4, 1987, pp.44–57.
[3]
V. Bhargava, “Forward Error Correction Schemes for Digitized Communications,” I
EEE Communications
Magazine
, vol.21, no 1, 1983, pp.11–19.
[4]
I.S. Reed and G. Solomon,
Polynomial Codes Over Certain Finite Fields,
Journal of Soc. Ind. Appl. Math,
vol.8, p.300-304 and Math. Rev., vol23B, p.510, 1960.
[5]
S. Lin and D.J. Costello,
Error Control Coding: Fundamentals and Applications
, Prentice Hall:
Englewood Cliffs, NJ, 1983.
[6]
R.E. Blahut,
Theory and Practice of Error Control Codes
, Addison Wesley: Reading, MA, 1984.
[7]
SC140 DSP Core Reference Manual
, Freescale Semiconductor, (MNSC140CORE/D).
[8]
ITU standard G.992.1.
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