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

Yang, L-L. and Hanzo, L. (2001) Performance Analysis of Coded $M$-ary Orthogonal Signaling Using Errors-and Erasures Decoding Over Frequency-Selective Fading Channels. IEEE Journal on Selected Areas in Communications, 19 (2), 211-221.

Record type: Article

## Abstract

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.

Text
19jsac02-yang.pdf - Other

Published date: February 2001
Organisations: Southampton Wireless Group

## Identifiers

Local EPrints ID: 255717
URI: http://eprints.soton.ac.uk/id/eprint/255717
PURE UUID: 9707a8ee-c94f-4f54-9492-f1247956519e
ORCID for L-L. Yang: orcid.org/0000-0002-2032-9327
ORCID for L. Hanzo: orcid.org/0000-0002-2636-5214

## Catalogue record

Date deposited: 08 Jan 2004

## Contributors

Author: L-L. Yang
Author: L. Hanzo