Deficiency of the Gilbert-Elliot channel in modeling time varying channels

In the research of time varying communication channels, signal amplitude attenuation is considered to be the main cause of channel varying memories. The Gilbert-Elliot channel has been used to model this kind of memories for a long time with a decision-feedback decoder or an equivalent genie-aided decoder being its optimal decoders. In the first part of this paper, we show that the decoders have not performed optimal signal detection for the channel. The expression of the achievable mutual information rate by the genie-aided decoder has been revisited and updated recently. The non-optimality of the decoders can be confirmed by showing the maximum value of the updated expression is smaller than the channel´s information capacity, which is obtained by a system-model-independent algorithm. In the second part of this paper, we argue that the phase change of transmitted signal caused by the Doppler effect plays a much more important role in determining the channel varying memory than their amplitude fading does. The Gilbert-Elliot channel, capturing amplitude fading, is therefore not ideal for modelling the memory. And finding its optimal decoder, which is shown to be very difficult, may have little physical significance.