Error Exponent for Gaussian Channels With Partial Sequential Feedback

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction (<formula formulatype="inline"><tex Notation="TeX">$f$</tex></formula>) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds <formula formulatype="inline"><tex Notation="TeX">$fC$</tex></formula>, where <formula formulatype="inline"><tex Notation="TeX">$C$</tex> </formula> is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below <formula formulatype="inline"> <tex Notation="TeX">$fC$</tex></formula>, the error probability can decrease faster than exponentially with the block length, as with full feedback (<formula formulatype="inline"><tex Notation="TeX">$f=1$</tex></formula>). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages.

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