A Study of Viterbi's Ratio-Threshold AJ Technique

2002

IEEE Trans. Commun.

Abstract-In this paper we propose two novel low-complexity, low-delay erasure insertion schemes, namely, the output threshold test (OTT) and joint maximum output and ratio threshold Test (MO-RTT). The employment of the OTT and MO-RTT is beneficial in the context of the "errors-and-erasures" Reed-Solomon (RS) decoding in a slow frequency-hopping spread-spectrum (SFH/SS) system using -ary frequency-shift keying (MFSK). The statistics of the erasure insertion related decision variables associated with the OTT, MO-RTT as well as with the ratio threshold test (RTT) are investigated, when the channel of each frequency-hopping (FH) slot is modeled as flat Nakagamifading. The transmitted signals also experience both additive white Gaussian noise (AWGN) as well as partial-band Gaussian interference (PBGI). The properties of these erasure insertion schemes are investigated with the aid of their statistics. The performance of the proposed erasure insertion schemes and that of the erasure insertion scheme using the RTT is investigated and compared in the context of RS coded SFH/SS systems using MFSK. Furthermore, the performance of the RS coded SFH/SS systems is also compared both with and without side-information concerning the PBGI.Index Terms-Errors-and-erasures decoding, frequency-hopping, joint maximum output and ratio threshold test, -ary frequency-shift keying, Nakagami fading, output threshold test, partial band interference, ratio threshold test, Reed-Solomon codes, spread-spectrum communications.

Section: System Overview and Statistics Of The Decision Variablesmentioning

confidence: 99%

Low complexity erasure insertion in RS-coded SFH spread-spectrum communications with partial-band interference and Nakagami-m fading

2002

IEEE Trans. Commun.

“…which obey the relationship of (4) According to (3), the erasure probability is constituted by two terms. The first term is based on the hypothesis of , i.e., when a symbol was detected erroneously and hence erasure is required, while the second term accrues from the unintentional erasure of a symbol, which was detected correctly, due to its mapping into .…”

Section: Erasure Insertion Testmentioning

confidence: 99%

Performance analysis of coded M-ary orthogonal signaling using errors-and-erasures decoding over frequency-selective fading channels

IEEE J. Select. Areas Commun.

2001

Abstract-The performance of -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 -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.

“…Hence, the second-stage maximum selection finds the largest one from the set , which can be expressed as (27) Let us now derive the PDFs of . Since the normalized PDF of for was given by (14), the PDF of for can be expressed as…”

Section: B Selection Combiningmentioning

confidence: 99%

A Reed-Solomon coded DS-CDMA system using noncoherent M-ary orthogonal modulation over multipath fading channels

IEEE J. Select. Areas Commun.

2000

Abstract-The performance of Reed-Solomon (RS) coded direct-sequence code division multiple-access (DS-CDMA) systems using noncoherent -ary orthogonal modulation is investigated over multipath Rayleigh fading channels. Diversity reception techniques with equal gain combining (EGC) or selection combining (SC) are invoked and the related performance is evaluated for both uncoded and coded DS-CDMA systems. "Errors-and-erasures" decoding is considered, where the erasures are based on Viterbi's so-called ratio threshold test (RTT). The probability density functions (PDF) of the ratio associated with the RTT conditioned on both the correct detection and erroneous detection of the -ary signals are derived. These PDFs are then used for computing the codeword decoding error probability of the RS coded DS-CDMA system using "errors-and-erasures" decoding. Furthermore, the performance of the "errors-and-erasures" decoding technique employing the RTT is compared to that of "error-correction-only" decoding refraining from using side-information over multipath Rayleigh fading channels. As expected, the numerical results show that when using "errors-and-erasures" decoding, RS codes of a given code rate can achieve a higher coding gain than without erasure information.Index Terms-Direct sequence code division multiple-access, error-correction-only decoding, errors-and-erasures decoding, noncoherent -ary orthogonal signaling, ratio threshold test, Reed-Solomon codes.