Abstract
An explanation is given for the paradoxical fact that, at low signal-to-noise ratios, the systematic feedback encoder results in fewer decoding bit errors than does a nonsystematic feedforward encoder for the same convolutional code, which is the opposite of the situation at high signal-to-noise ratios. The analysis identifies a new convolutional code property, the weight density of distance-d detours for large d. For a given distance-d weight density, the decoding bit error probability depends on the number of taps in the realization of the encoder inverse. Among all encoders for a given convolutional code, the systematic one has the inverse with fewest taps and, hence, gives the smallest bit error probability at low signal-to-noise ratios where decoding error bursts typically result from the decoder following a detour at large distance d from the transmitted codeword.
This research was supported in part by the Foundation for Strategic Research—Personal Computing and Communication under Grant PCC-9706-09.
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© 2002 Springer Science+Business Media New York
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Johannesson, R., Massey, J.L., Ståhl, P. (2002). Systematic Bits are Better and No Buts About It. In: Blahut, R.E., Koetter, R. (eds) Codes, Graphs, and Systems. The Kluwer International Series in Engineering and Computer Science, vol 670. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0895-3_5
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DOI: https://doi.org/10.1007/978-1-4615-0895-3_5
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