Code-Based Channel Shortening for Faster-Than-Nyquist Signaling: Reduced-Complexity Detection and Code Design

A novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where special convolutional codes are used to absorb the channel memory. These convolutional codes have a special type of generator matrix that allows previous code symbols to be determined by the current code trellis state and thus been referred to as output-retainable convolutional codes (ORCCs). Different from conventional schemes, the CCS algorithm performs joint detection and decoding (JDD) based only on the code trellis by exploiting the ORCC structure. Therefore, it provides a new view for channel shortening techniques, i.e., absorbing the channel memory by using channel codes. Properties of ORCCs are discussed. Based on these properties, we derive the bit error rate (BER) bound for the CCS algorithm. According to the bound, a code search algorithm is proposed to facilitate the code design. Furthermore, two concatenated codes based on ORCCs are designed. Simulation results show that with a 16-states BCJR algorithm for JDD, the BER performance of the designed self-concatenated convolutional code incorporated with FTN signaling is only 0.75 dB away from the Shannon limit of the shaping pulse, and the required signal-to-noise ratio is below the BPSK limit of Nyquist signaling.