Cyclic-Coded Integer-Forcing Equalization

A discrete-time intersymbol interference (ISI) channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of ISI. The proposed approach involves equalizing the channel impulse response to a response with integer-valued coefficients in conjunction with utilizing cyclic block codes. Leveraging the property that a cyclic code is closed under cyclic integer-valued convolution allows us to perform decoding prior to applying decision feedback. Explicit bounds on the performance of the proposed scheme are derived.