Correction to “TCM With Differential Encoding: Set Partitioning, Trellis Designs and Distance Analysis” [Aug 15 2776-2787]

We present a correction to the above-named work. In Table III, $d_{free}^{2}$ for new codes with $L=32$ should be 3.561 (instead of 3.667) and 3.233 (instead of 3.385) for TCM-DE and DTCM, respectively. The corresponding paragraph on the same page, “For $L=32$ , the best $d'^{2}_{free}$ is …… in simulations.” should be modified as “For $L=32$ , the best $d'^{2}_{free}$ is $5\Delta _{1}^{2}+2\Delta _{0}^{2}$ (for instance, two paths (0,0,0,0,0,0) and (0,2,0,1,2,2), so the resulting minimum squared distance is $\min [\Delta _{2}^{2},d'^{2}_{free}=3.233]=3.233$ for 8PSK. There are some codes that have the best $d'^{2}_{free}$ and we choose (C0,C2),(C3,C1),(C3,C1),(C2,C0),(C2,C0),(C1,C3) and (C1,C3) for $\sigma ^{(1)},\cdots ,\sigma ^{(7)}$ in simulations.”. In addition, the trellis diagram in Fig. 12(b) should be corrected to Fig. 1.