RS码的编译码算法及DSP实现
|
摘要
RS码作为一种多进制BCH码,具有同时纠正突发错误和随机错误的能力,因而被广泛地应用于数据通信和数据存储系统的差错控制中。本文研究了RS码的编译码理论,在译码算法中重点对step-by-step译码和频域译码算法进行了探讨,将素因子分解的算法应用在IDFT过程中,理论分析和在CCS环境中的仿真结果表明这样做确实减少了有限域乘法和加法的次数,节省了所用的时钟周期数。完成了基于TMS320VC5402系列DSP的RS码编译码器的硬件电路的设计,调试结果表明编译码器工作正常。最后对RS码频域译码的性能进行了MATLAB仿真,结论是RS码能有效地纠正码字中的随机错误和突发错误。
As a kind of non-binary code,RS codes can correct burst errors and random errors. They are widely used in data communication and data storage systems. In this paper,the theory of the RS codes encoding and decoding are studied,especially in the algorithm of step-by-step and the decoding in frequency domain. The prime factor algorithm is used in the IDFT, which decreases the times of multiplication and addition in the Finite Field and saves the CPU cycles showed in the theory analysis and simulation in CCS. The encoder/decoder of the RS codes based on TMS320VC5402 is designed to test the algorithm and after debugging, it works well. At last,the performance of RS decoding in frequency domain is simulated in MATLAB and the conclusion is RS codes can effectively correct random errors and burst errors.
As a kind of non-binary code,RS codes can correct burst errors and random errors. They are widely used in data communication and data storage systems. In this paper,the theory of the RS codes encoding and decoding are studied,especially in the algorithm of step-by-step and the decoding in frequency domain. The prime factor algorithm is used in the IDFT, which decreases the times of multiplication and addition in the Finite Field and saves the CPU cycles showed in the theory analysis and simulation in CCS. The encoder/decoder of the RS codes based on TMS320VC5402 is designed to test the algorithm and after debugging, it works well. At last,the performance of RS decoding in frequency domain is simulated in MATLAB and the conclusion is RS codes can effectively correct random errors and burst errors.
引文
[1]王新梅,肖国镇,纠错码,西安:西安电子科技大学出版社,2001
[2]曾晓洋等,一种新的脉动阵列RS码编码方法,通信学报,2002,23(7):76～82
[3]Youshi Xu,A modified Euclidean algorithm and the VLSI implementation. Electrotechnical Conference, 1996. MELECON '96., 8th Mediterranean,1996,1324～1327
[4]Truong,T.-K.,Jeng,J.-H.,Cheng,T.C.,A new decoding algorithm for correcting both erasures and errors of Reed-Solomon codes,IEEE Transactions on Communications, 2003,51(3):381～388
[5]Hanho Lee,A VLSI design of a high-speed Reed-Solomon decoder. ASIC/SOC Conference,2001. Proceedings. 14th Annual IEEE International,2001,316～320
[6]王进祥,张乃通等,流水线结构RS(255,223)译码器的VLSI设计,计算机研究与发展,2000,37(1):61～65
[7]徐元欣,夏芳,采用软/硬件协同设计的RS译码器,电路与系统学报,2002,7(3):39～44
[8]李云鹏,王新梅等,基于FPGA自适应高速RS编译码器的IP核设计,重庆邮电学院学报,2003,15(1):25～29
[9]Branka VUCETIC,Vishakan PONAMPALAM,Low Complexity Soft Decision Decoding Algorithms for Reed-Solomon Code,IEICE TRANS COMMUN,2001,E84-B(3):392～399
[10]牛兰奇,刘高辉,基于多元符号可信信息的RS码的软判决译码算法,西安理工大学学报,2002,18(2):159～162
[11]朱起悦,RS码编码和译码的算法,电讯技术,1999,39(2):63～67
[12] T.K.TRUONG,A Pipeline Design of Fast Prime Factor DFT on a Finite Field,IEEE Transaction On Communication,1988,37(3):266～273
[13]聂红光,李永茂等,基于费马素数域高基FFT的RS码快速译码算法,武汉大学学报,2000,46(3):362～364
[14]T.-C.Chen,C.-H.Wei,S.-W.Wei,Step-by-step decoding algorithm for Reed-Solomon code,IEEE Proc-Commun,2000,147(1):8～12
[15]候正信,胡浩,RS码的时域编码/频域译码技术,电视技术,2002,(1): 32～34
[16]TMS320VC5402 Fixed-Point Digital Signal Processor Data Sheet ,Texas Instruments Incorporated,2000
[17]TMS320C54x DSP Reference Set,Volume 1:CPU and Peripherals,Texas Instruments Incorporated,1999
[18]TMS320C54x DSP Reference Set,Volume 5:Enhanced Peripherals,Texas Instruments Incorporated,1999
[19]TMS320VC5501/5502 DSP Universal Asynchronous Receiver/Transmitter(UART) Refenence Guide ,Texas Instruments Incorporated,2003
[20]ST16C550 Data Sheet,EXAR Corporation,2000
[21]MAX3232 3-V to 5-V Multichannel RS-232 Line Driver/Receiver Data Sheet,Texas Instruments Incorporated,2002
[22]邓勇,施文康,TMS320C50与PC机高速串行通信的实现,计算机自动测量与控制,2000,8(5):23～25
[23]夏晓华,姜建国,基于闪烁存储器的TMS320VC5409 DSP并行引导装载方法,电子技术应用,2002,28(7):78～80
[24]SST39VF400A Data Sheet,SST Inc. 2001
[25]TPS767D318 Data Sheet,Texas Instruments Incorporated,2002
[26]郑红,吴冠, TMS320C54xDSP应用系统设计,北京: 北京航天航空大学出版社, 2002
[27]张雄伟,陈亮,DSP集成开发与应用实例,北京: 电子工业出版社, 2002
[2]曾晓洋等,一种新的脉动阵列RS码编码方法,通信学报,2002,23(7):76～82
[3]Youshi Xu,A modified Euclidean algorithm and the VLSI implementation. Electrotechnical Conference, 1996. MELECON '96., 8th Mediterranean,1996,1324～1327
[4]Truong,T.-K.,Jeng,J.-H.,Cheng,T.C.,A new decoding algorithm for correcting both erasures and errors of Reed-Solomon codes,IEEE Transactions on Communications, 2003,51(3):381～388
[5]Hanho Lee,A VLSI design of a high-speed Reed-Solomon decoder. ASIC/SOC Conference,2001. Proceedings. 14th Annual IEEE International,2001,316～320
[6]王进祥,张乃通等,流水线结构RS(255,223)译码器的VLSI设计,计算机研究与发展,2000,37(1):61～65
[7]徐元欣,夏芳,采用软/硬件协同设计的RS译码器,电路与系统学报,2002,7(3):39～44
[8]李云鹏,王新梅等,基于FPGA自适应高速RS编译码器的IP核设计,重庆邮电学院学报,2003,15(1):25～29
[9]Branka VUCETIC,Vishakan PONAMPALAM,Low Complexity Soft Decision Decoding Algorithms for Reed-Solomon Code,IEICE TRANS COMMUN,2001,E84-B(3):392～399
[10]牛兰奇,刘高辉,基于多元符号可信信息的RS码的软判决译码算法,西安理工大学学报,2002,18(2):159～162
[11]朱起悦,RS码编码和译码的算法,电讯技术,1999,39(2):63～67
[12] T.K.TRUONG,A Pipeline Design of Fast Prime Factor DFT on a Finite Field,IEEE Transaction On Communication,1988,37(3):266～273
[13]聂红光,李永茂等,基于费马素数域高基FFT的RS码快速译码算法,武汉大学学报,2000,46(3):362～364
[14]T.-C.Chen,C.-H.Wei,S.-W.Wei,Step-by-step decoding algorithm for Reed-Solomon code,IEEE Proc-Commun,2000,147(1):8～12
[15]候正信,胡浩,RS码的时域编码/频域译码技术,电视技术,2002,(1): 32～34
[16]TMS320VC5402 Fixed-Point Digital Signal Processor Data Sheet ,Texas Instruments Incorporated,2000
[17]TMS320C54x DSP Reference Set,Volume 1:CPU and Peripherals,Texas Instruments Incorporated,1999
[18]TMS320C54x DSP Reference Set,Volume 5:Enhanced Peripherals,Texas Instruments Incorporated,1999
[19]TMS320VC5501/5502 DSP Universal Asynchronous Receiver/Transmitter(UART) Refenence Guide ,Texas Instruments Incorporated,2003
[20]ST16C550 Data Sheet,EXAR Corporation,2000
[21]MAX3232 3-V to 5-V Multichannel RS-232 Line Driver/Receiver Data Sheet,Texas Instruments Incorporated,2002
[22]邓勇,施文康,TMS320C50与PC机高速串行通信的实现,计算机自动测量与控制,2000,8(5):23～25
[23]夏晓华,姜建国,基于闪烁存储器的TMS320VC5409 DSP并行引导装载方法,电子技术应用,2002,28(7):78～80
[24]SST39VF400A Data Sheet,SST Inc. 2001
[25]TPS767D318 Data Sheet,Texas Instruments Incorporated,2002
[26]郑红,吴冠, TMS320C54xDSP应用系统设计,北京: 北京航天航空大学出版社, 2002
[27]张雄伟,陈亮,DSP集成开发与应用实例,北京: 电子工业出版社, 2002