A Necessary Condition on the Location of Pilot Tones for Maximizing the Correction Capacity in OFDM Systems

This paper presents a new view of the Bose-Chaudhuri-Hocquengem (BCH) code through the addition of some flexibility to the syndromes distribution in the transmitted sequence. In order to get this flexibility, we derive a necessary condition (NC) on the syndromes distribution for decoding BCH codes, which includes the already known Hartmann-Tzeng proposition. This NC is essentially deduced from the decoding process of BCH code, and is related to the locator polynomial and the requested constraints to guarantee a maximal error-correction capacity. The obtained results have the advantage to be applicable for any considered field (finite or not). Furthermore, we prove that when the correction capacity is equal to 2 or 3, the obtained NC becomes also sufficient. This result is very useful in some practical transmission systems such as orthogonal frequency-division multiplexing systems. Once the pilot tones considered in such systems verify the necessary and sufficient condition, it becomes possible to both reduce the peak-to-average-power rate and correct the impulse noise, present in such multicarrier systems. The usefulness of the presented analysis and the exploitation of the derived condition on the pilot tones distribution is illustrated by simulation results in the case of the Hiperlan2 system