Article thumbnail
Location of Repository

Performance Analysis of Coded $M$-ary Orthogonal Signaling Using Errors-and Erasures Decoding Over Frequency-Selective Fading Channels

By L-L. Yang and L. Hanzo


The performance of $M$-ary orthogonal signaling schemes employing Reed–Solomon (RS) codes and redundant residue number system (RRNS) codes is investigated over frequency-selective Rayleigh fading channels. “Errors-and-erasures” decoding is considered, where erasures are judged based on two low-complexity, low-delay erasure insertion schemes—Viterbi’s ratio threshold test (RTT) and the proposed output threshold test (OTT). The probability density functions (PDF) of the ratio associated with the RTT and that of the demodulation output in the OTT conditioned on both the correct detection and erroneous detection of $M$-ary signals are derived, and the characteristics of the RTT and OTT are investigated. Furthermore, expressions are derived for computing the codeword decoding error probability of RS codes or RRNS codes based on the above PDFs. The OTT technique is compared to Viterbi’s RTT, and both of these are compared to receivers using “error-correction only” decoding over frequency-selective Rayleigh-fading channels. The numerical results show that by using “errors-and-erasures” decoding, RS or RRNS codes of a given code rate can achieve higher coding gain than that without erasure information, and that the OTT technique outperforms the RTT, provided that both schemes are operated at the optimum decision thresholds. Index Terms—“Errors-and-erasures” decoding, $M$-ary orthogonal signaling, Rayleigh fading, redundant residue number system codes, Reed–Solomon codes

Year: 2001
OAI identifier:
Provided by: e-Prints Soton
Sorry, our data provider has not provided any external links therefore we are unable to provide a link to the full text.

Suggested articles


  1. (1992). A coding theory approach to error control in redundant residue number system—Part I: Theory and single error correction,” doi
  2. (1992). A coding theory approach to error control in redundant residue number system—Part II: Multiple errors detection andcorrectiontheory,”IEEETrans.CircuitsSystems,vol.39,pp.18–32,
  3. (1982). A robust ratio-threshold technique to mitigate tone and partial band jamming in coded MFSK systems,” in doi
  4. (1984). A study of Viterbi’s ratio threshold AJ technique,” in doi
  5. (1993). A systolic redundant residue arithmetic error correction circuit,” doi
  6. (1999). arithmetic assisted M-ary modulation,” doi
  7. (1992). Bayesian methods for erasure insertion in frequency-hop communication system with partial-band interference,” doi
  8. (1999). Coding theory and performance of redundant residue number system codes,”IEEE Trans. doi
  9. (1971). Detection of Signals in Noise. doi
  10. (1987). Diversity combining for channels with fading and partial-band interference,” doi
  11. (1995). EIA/TIA-95RevA,“Mobilestation–basestationcompatibilitystandard for dual-mode wideband spread spectrum cellular system,”,
  12. (1973). Error correcting properties of redundant residue number systems,” doi
  13. (1968). Exponential error bounds for erasure, list, and decision feedback scheme,” doi
  14. (1988). Fault-tolerance in a systolic residue arithmetic processor array,” doi
  15. (1993). Fundamentals of Statistical Signal Processing: Detection Theory. Englewood Cliffs,
  16. (1996). generation of dependent erasures for frequency-hop communications and fading channels,” doi
  17. (1993). H.KrishnaandJ.D.Sun,“Ontheoryandfastalgorithmsforerrorcorrection in residue number system product codes,”
  18. (2000). Hanzo,“AReed–Solomon codedDS-CDMA system using noncoherent M-ary orthogonal modulation over multipath fading channels,” doi
  19. (1999). Mobile Radio Communications. doi
  20. (1994). Performance analysis of DS/CDMA with noncoherent M-ary orthogonal modulation in multipath fading channels,” doi
  21. (1998). Performance limits of Reed–Solomon coded CDMA with orthogonal signaling in a Rayleigh-fading channel,” doi
  22. (1998). Performance of residue number system based DS-CDMA over multipath fading channels using orthogonal sequences,” doi
  23. (1966). Self-checking computations using residue arithmetic,” doi
  24. (1983). Theory and Practice of Error Control Codes. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.