Robust Index Assignment Using Hadamard Transform for Vector Quantization Transmission over Finite-Memory Contagion Channels

This paper presents a new index assignment (IA) method when vector quantization indices are transmitted over a particular class of Markov binary channels, namely the finite-memory contagion channels. (See F. Alajaji and T. Fuja, IEEE Trans. Inform. Theory, 40:2035-2041, 1994.) For this class of binary channels, the Hadamard transform of the vector formed with noise pattern probabilities obeys well-structured recursions, allowing an efficient evaluation of the channel distortion and also revealing a useful approximation based on the dominant terms in the channel distortion expression. The proposed IA method minimizes the distortion approximation and is very robust to changes in the parameters of the channel model. The same technique applies for both maximum likelihood and mean-squared error decoding methods. The IA algorithm is applied to the transmission of line spectral frequency parameters quantized as in the G.729 standard to show the usefulness of the proposed method.