Multilevel block coded modulation (BCM) schemes with unequal error protection (UEP) are investigated. These schemes are based on unconventional set partitions that greatly reduce the error coefficients associated with multi-stage decoding of conventional BCM, at the expense of smaller intra-set distances

Fossorier, Marc P. C.

Imai, Hideki

Lin, Shu

Morelos-Zaragoza, Robert H

English

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San Jose State UniversitySJSU ScholarWorksFaculty Publications Electrical Engineering1997Multilevel Block Coded Modulation with UnequalError ProtectionRobert H. Morelos-ZaragozaUniversity of Tokyo, robert.morelos-zaragoza@sjsu.eduMarc P. C. FossorierUniversity of Hawaii at ManoaShu LinUniversity of Hawaii at ManoaHideki ImaiUniversity of TokyoFollow this and additional works at: https://scholarworks.sjsu.edu/ee_pubPart of the Electrical and Computer Engineering CommonsThis Article is brought to you for free and open access by the Electrical Engineering at SJSU ScholarWorks. It has been accepted for inclusion in FacultyPublications by an authorized administrator of SJSU ScholarWorks. For more information, please contact scholarworks@sjsu.edu.Recommended CitationRobert H. Morelos-Zaragoza, Marc P. C. Fossorier, Shu Lin, and Hideki Imai. "Multilevel Block Coded Modulation with UnequalError Protection" Faculty Publications (1997): 441. doi:10.1109/ISIT.1997.613378ISlT 1997, Ulm. Germany, June 29 - July 4 Multilevel Block Coded Modulation with Unequal Error Protection Robert €1. Morelos-Zaragozat, Marc P.C. Fossoriert , Shu Lint and Hideki Imai t  ‘Institute of Industrial Science, The University of Tokyo *Dept. of Electrical Engineering, University of Hawaii at Manoa 7-22-1 Roppongi, Minatoku, Tokyo 106 JAPAN Email: robert@imailab.iis.u-tokyo.ac.jp Abstract - M u l t i l e v e l  block coded modulation (BCM) schemes with unequal error p r o t e c t i o n  (UEP) are inves t iga ted .  These schemes are based on uncon- vent iona l  set p a r t i t i o n s  that greatly reduce the er- ror coefficients assoc ia ted  w i t h  mul t i - s tage  decoding of conventional BCM, at the expense of smaller in t ra -  set d is tances .  I. INTRODUCTION This paper studies bandwidth efficient multi-level coding schemes [l] with unequal error protection (UEP) over AWGN channels. These schemes are useful for the transmission of in- formation with different error performance requirements, such as digital video or speech. The advantages of unconventional partitions for UEP applications are illustrated with 8-PSK sig- naling in the following. A general approach for both PSK and QAM has been derived [2]. 11. UNCONVENTIONAL PARTITIONS FOR $-PSI< Optimum decoding of multi-level codes is often too complex to  be implemented in practical applications. Therefore, vari- ous suboptimum decoding methods have been devised. Since only the error coefficients are increased, multi-stage decoding achieves asymptotically optimum decoding. However, these error coefficients can become very large and therefore, a t  prac- tical bit error rates (BER), the performance degradation is im- portant. For example, in a BCM scheme based on 8-PSK mod- ulation, the number of signal point sequences at  the minimum squared Euclidean distance (MSED) 0.586d1 is multiplied by the factor 2d1, where dl represents the minimum Hamming distance (MHD) of the code used at the first level [3]. As a re- sult, even if the component codes are chosen to  achieve UEP capabilities, the desired UEP levels may not be achieved at  BER of practical interest. A. NON-STANDARD PARTITION Consider the non-standard labeling of an 8-PSK constellation shown in Fig. 1 (a). It is readily seen that the intra-set dis- tances are the same a t  all levels of the underlying partition. Also note that  the first (resp. second) label bit depends on the X-coordinate (resp. Y-coordinate) only. This fact is used to speed up the decoding since a parallel decoding of these stages is possible. In addition, the same correlation metrics as for BPSK transmission can be used. This results in simple soft-decision decoding implementations. Union bounds on the bit error probabilities at the first and second decoding stages show that ,  whereas the minimum error coefficient is scaled by a factor of 2 d ~  with the standard partitioning method, this value is now scaled by 2 - d J ,  where d, is the MHD of the code used at level j ,  j = 1,2. Consequently, for practical values of EbINo, real coding gains can be provided which are even 2540 Dole Street # 483, Honolulu, HI 96822 U.S.A. Email: marc @spectra. eng.hawaii. edu greater than the asymptotic coding gain associated with the first and second decoding stages. This is a very desirable fea- ture for a coded modulation with UEP. On the other hand, the error performance for the last stage is quite poor due the fact that  the intraset distances remain constant. B. HYBRID PARTITION Fig. 1 (b) shows an 8-PSK constellation with labeling of sig- nal points induced by a hybrid partition. The  first partition level is the same as the non-standard partition while the par- titioning method of [l, 41 is applied to  the remaining levels. Therefore, the intra-set distances a t  the second and third par- tition levels are increased with respect to  the non-standard partition. At the second decoding stage, the minimum error coefficient associated with the hybrid partition is smaller than for the standard partition: (3/2)d2 compared to 2 d Z .  111. CONCLUSION Based on these results, a general procedure to  label signal points in any 2M-ary constellation, for a given number (be- tween l and M )  of levels of protection, can be devised. The standard partitioning of [I, 41 simply corresponds to  the spe- cial case where one level of protection (or no UEP) is desired. REFERENCES [I] H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inform. Theory, vol.IT-23, no.3, pp.371-377, May 1977. [2] R.H. Morelos-Zaragoza, M.P.C. Fossorier, S. Lin and H. Imai, “Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding,” submitted to the IEEE Trans. In- form. Theory. [3] Y. Kofman, E. Zehavi and S. Shamai, “Performance Analysis of a Multilevel Coded Modulation System,” IEEE Transac- tions o n  Communications, vol. COM-42, pp. 299-312, February- March-April 1994. “Channel coding with multilevel/phase sig- nals,” IEEE Trans. Inform. Theory, vol.IT-28, pp.55-67, Jan. 1982. [4! G. Ungerboeck, ‘This work was supported in part by the National Science Foun- dation under Grant No. NCR-94-15374. Fig. 1: (a) Non-standard and (b) hybrid labelings of an 8-PSK constellation. 0-7803-3956-8/97/$10.00 01997  I EEE 441 

Multilevel Block Coded Modulation with Unequal Error Protection

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Multilevel Block Coded Modulation with Unequal Error Protection

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