Annex J to Recommendation G.728 defines a 40 kbit/s extension optimized for voiceband data signals of the existing Annex G/G.728 - 16 kbit/s fixed point specification. The main difference between the codec described hereby and the codec described in Annex G/G.728 is the application of a Trellis-Coded Quantization (TCQ) approach to codebook search. The TCQ approach replaces the analysis-by-synthesis approach to codebook search of Recommendation G.728 only in voiceband data (VBD) mode. The backward adaptation of the predictor achieved in VBD mode is almost identical to the backward adaptation achieved in speech mode (Recommendation G.728). Additionally, the same adaptation cycle is used for both speech mode (Recommendation G.728) and VBD mode. In speech mode, the 40 kbit/s reverts to the LD-CELP of Recommendation G.728. This annex includes an electronic attachement containing test vectors for implementation verification of Annex J/G.728.