Code Based Channel Shortening for Faster-than-Nyquist Signaling

Abstract

In this paper, a novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where a special type of convolutional codes is used to absorb the channel memory. In contrast to conventional schemes, the proposed CCS algorithm performs joint detection and decoding (JDD) based only on the code trellis by exploiting the code structure. Therefore, the proposed CCS algorithm provides a new view for channel shortening (CS) techniques, i.e., absorbing the channel memory by using channel codes. According to the code structure, we derive the path metric of the proposed CCS algorithm. Furthermore, we introduce a design of self-concatenated convolutional codes (SECCCs) for FTN signaling based on the CCS algorithm. Simulation results show that with a 16-states BCJR algorithm for JDD, the bit error rate (BER) performance of the designed SECCC incorporated with FTN signaling is only around 0.75 dB away from the Shannon limit of the shaping pulse, and the required signal-to-noise ratio (SNR) is below the BPSK capacity limit of Nyquist signaling.