Bit error rate analysis of multilevel coding scheme and optimum error‐correcting capability assignment for impulsive noise

Abstract

AbstractThe advantage of the multilevel coding scheme is that the coding can be performed independently for each level, and the optimal coding can easily be determined for the channel with superposed noise with arbitrary probability density distribution. To evaluate the performance of this coding scheme, an approximate formula for the bit error rate after decoding is derived. As an example, the channel with the impulsive noise is considered. Using the approximate formula, the error‐correcting capability is assigned optimally to the levels and the coding gain of 20 dB is obtained for the BCH code of code length 31. The foregoing result is confirmed by a computer simulation. A report has already been proposed for the case where the errors of the decoder outputs are randomized except for the top level, by interleaving among the levels. However, a problem arises in that the delay as well as the circuit scale is increased. From such a viewpoint, this paper discusses the case without inter‐leaving. Finally, the performances are compared between the cases with and without interleaving among levels.