Developing a signal compression technique that is able to achieve a low bit rate while maintaining high perceptual signal quality is a classical signal processing problem vigorously studied for audio, speech, image, and video type of signals. Yet, until recently, there has been limited effort directed toward the compression of vibrotactile signals, which represent a crucial element of rich touch (haptic) information. A vibrotactile signal; produced when stroking a textured surface with a tool-tip or bare-finger; like other signals contains a great deal of redundant and imperceptible information that can be exploited for efficient compression. This paper presents PVC-SLP, a vibrotactile perceptual coding approach. PVC-SLP employs a model of tactile sensitivity; called ASF (Acceleration Sensitivity Function); for perceptual coding. The ASF is inspired by the four channels model that mediate the perception of vibrotactile stimuli in the glabrous skin. The compression algorithm introduces sparsity constraints in a linear prediction scheme both on the residual and the predictor coefficients. The perceptual quantization of the residual is developed through the use of ASF. The quantization parameters of the residual and the predictor coefficients were jointly optimized; by means of both squared error and perceptual quality measures; to find the sweet spot of the rate-distortion curve. PVC-SLP coding performance is evaluated using two publicly available databases that collectively comprise 1281 vibrotactile signals covering 193 material classes. Furthermore, we compare PVC-SLP with a recent vibrotactile compression method and show that PVC-SLP perceptually outperforms existing method by a sizable margin. Most recently, PVC-SLP has been selected to become part of the haptic codec standard currently under preparation by IEEE P1918.1.1, aka Haptic Codecs for the Tactile Internet.