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-Loeve 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