The bit rate for the speech and channel coder for the half-rate GSM channel is 11400 bps. A 5600 bps VSELP speech coder designed for this application is described. This speech coder is one of two candidates being considered by GSM for the half-rate channel. It employs a novel strategy for vector quantization of the reflection coefficients (ri), which combines high coding efficiency, low codebook search complexity, and low storage requirements. A computationally streamlined version of a zero-pole spectral noise weighting function is implemented. An adaptive pitch prefilter and an adaptive spectral postfilter are used to improve the speech coder's performance for both the tandemed and non-tandemed cases.