Quaternary codes for partial-response channels

Abstract

Quaternary codes for improving the reliability of baseband data transmission over noisy partial-response channels are proposed. These codes offer the spectral shaping properties of line codes, i.e., they exhibit spectral nulls at the frequencies where the channel transfer function has zeros, together with a significant increase in minimum Euclidean distance between allowed channel output sequences. Simple encoders and decoders for selected quaternary codes with a spectral null at DC are given for the dicode channel. The receiver employs soft-decision maximum-likelihood sequence estimation on the combined channel and FSTD (finite-state transition diagram) trellis followed by block decoding. The code design avoids long runs of identical symbols and limits the path memory of the Viterbi detector by eliminating all undesired sequences. Simulation results on the performance of 5B4Q, 8B6Q, and 9B6Q codes and their power spectral density are presented. Although the Euclidean distance gain of quaternary codes with a first-order null over an uncoded baseline system is 3 dB, the real coding gain has been demonstrated to be higher. This was achieved by a judicious choice of codewords, that is, by discarding those which contribute most to the average transmitted power. Simulation results verified that these codes provide substantial net gains in noise margin ranging approximately from 2.6 dB to 3.8 dB over an uncoded quaternary baseline system.