A performance analysis of integer-to-integer transforms for lossless coding of vectorial signals

An efficient lossless coding procedure should take advantage of the multichannel aspect of some data standards (such as audio
standards for example). In [6], the instantaneous decorrelation of several quantized scalar signals is shown to be efficiently
realized by a lossless (integer-to-integer) implementation of the Karhunen-Loeve Transform (KLT, unitary transform). The
implementation of this integer-to-integer transform involves a cascade of triangular matrices and truncations. We present in
this paper a lossless coding procedure based on a recently introduced decorrelating scheme (Lower Diagonal Upper factorization,
LDU, causal transform). We define the lossless coding gain for a transformation as the number of bits which are saved
by using the corresponding lossless coding scheme. In a first step, we analyze and compare the effects of the truncations on
the coding gains for the two transformations. In a second step, we analyze the effects of estimation noise uppon the coding
gains : in this case, the transforms are based on an estimate