In this paper we show that systematic convolutional encoders perform as well as nonsystematic ones when they are used together with M-algorithm decoders. We describe the algorithm and give a brief historical review

Anderson, John B

Johannesson, Rolf

Osthoff, Harro

English

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Systematic feed-forward convolutional encoders are as good as other encoders withan M-algorithm decoderOsthoff, Harro; Johannesson, Rolf; Anderson, John BPublished in:Abstracts, International Symp. on Information Theory1993Link to publicationCitation for published version (APA):Osthoff, H., Johannesson, R., & Anderson, J. B. (1993). Systematic feed-forward convolutional encoders are asgood as other encoders with an M-algorithm decoder. In Abstracts, International Symp. on Information Theory(pp. 268). IEEE - Institute of Electrical and Electronics Engineers Inc..http://ieeexplore.ieee.org/iel4/5602/14996/00748582.pdfTotal number of authors:3General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.SYSTEMATIC FEED-FORWARD CONVOLUTIONAL ENCODERS ARE AS GOOD AS OTHER ENCODERS WITH AN M-ALGORITHM DECODER Harro Os thoP ,  Rolf Johannesson* , and John Anderson** * Department of Information Theory University of Lund S- 221 00 Lund ** Electrical, Computer, and Systems Engineering Department Box 118 Rensselaer Polytechnic Institute Troy, New York 12180-3590 Sweden USA Summary-In this paper we show that systematic convolutional encoders perform as well as nonsystematic ones when they are used together with M-algorithm de- coders [l]. We describe the algorithm and give a brief historical review. The following curves show simulation results for the event error probability of the M-algorithm. We compare an optimum distance profile nonsystem- atic encoder (clfree = 22) and a quick-look-in encoder ( d f r e e  = 18) with a systematic encoder (cifree = 13). All encoders have memory m = 20 and in the decoder 32 states are extended at every time instant (M = 32). Error Event Probability memory 20. M-32 le* terms of the free distance and the distance spectrum. A rapid growth of the column distances is more important than a large free distance. As a bonus when used together with the M-algorithm, systematic encoders outperform nonsystematic encoders in terms of bit error probability as shown in the next pic- ture (framelength = 1024). The reason is that systematic encoders are superior from a correct path loss point of view. Bit Error Probability memory 20, M-32 1e+W . , . , . , . , . , . , . , . 39 4 1  4 3  4 5  4 7  4 9  6 1  53 5 5  I l e a  ’ 2 E-WNO lea3g 4 1  4 3  4 6  4 7  4 9  s i  63 5s E-WNO All curves show the same event error probability per- for mance . References Using criteria for the encoder quality like the optimum distance profile and the optimum profile spectrum [2] any memory. As long as these distance criteria support the decoder performance, the event error probability of the M-algorithm depends only on M .  Therefore, in a range of interesting values of M ,  systematic encoders should be- have like nonsystematic encoders in terms of error event probability as our simulations show. The decoder com- plexity is independent of the memory of the encoder. The free distance does not matter as long i t  is big enough to  correct all paths within the set of extended decoder the Viterbi decoder, code quality cannot be expressed in [l] J .  B. Anderson, “Limited Search Trellis Decoding of encoder is equivalent to a systematic one over the encoder Convolutional Codes”, IEEE Trans. Information The- ory, IT-35, pp. 944-956, Sep. 1989. [2] H. Osthoff, R. Johannesson, B. Smeets and H. Vinck, “On the Linear M-Algorithm” , Proceedings IEEE In- formation Theory Symposium, San Diego, Jan. 1990, pp.85. states. Hence, for M-akoritl1m decoders, in contrat  to This work was supportedin part by the Swedish Research Cow-  cil for Engineering Sciences under Grant 91-91. 268 

Systematic feed-forward convolutional encoders are as good as other encoders with an M-algorithm decoder

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Systematic feed-forward convolutional encoders are as good as other encoders with an M-algorithm decoder

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