Training Sequence-Based VQ Design Algorithm with LBG Implementation

In the context of vector quantization design: Linde, Buzo, and Gray (LBG) developed a VQ algorithm based on training sequences. This approach circumvents complex multidimensional integration by employing empirical training data. The LBG algorithm operates iteratively, with each cycle processing a substantial training vector set. Typically represented as T={x₁, x₂, ..., xₘ}, this training set contains sampled vectors from representative signals destined for joint encoding. Each xᵢ denotes a training vector sample, while M indicates the training set size—significantly larger than the codebook size N.

Implementation-wise, the algorithm initializes a codebook (often via splitting) and iteratively: (1) assigns all training vectors to nearest codewords using Euclidean distance calculation, (2) computes new centroids for each partition, and (3) updates the codebook until distortion convergence. This process ensures locally optimal codebook generation without requiring explicit probability density functions.