Transform coding with integer-to-integer transforms

A new interpretation of transform coding is developed that downplays quantization and emphasizes entropy coding, allowing a comparison of entropy coding methods with different memory requirements. With conventional transform coding, based on computing Karhunen–Loève transform coefficients and then quantizing them, vector entropy coding can be replaced by scalar entropy coding without an increase in rate. Thus the transform coding advantage is a reduction in memory requirements for entropy coding. This paper develops a transform coding technique where the source samples are first scalar-quantized and then transformed with an integer-to-integer approximation to a nonorthogonal linear transform. Among the possible advantages is to reduce the memory requirement further than conventional transform coding by using a single common scalar entropy codebook for all components. The analysis shows that for high-rate coding of a Gaussian source, this reduction in memory requirements comes without any degradation of rate-distortion performance.