Vector quantization over a noisy channel using soft decision decoding

A soft decision decoder is presented. The soft decision decoder is optimal in the mean square sense, if the encoder entropy is full. A source vector estimate is obtained as a linear mapping of a soft Hadamard column. The soft Hadamard column is formed as a generally nonlinear mapping of soft information bits. It is shown that the best index assignment, on the encoder, is obtained in the special case of a linear mapping from the soft information bits. Simulations indicate that the jointly trained system performs better than channel optimized VQ with hard decisions. The interesting case, for applications, of using an ordinary VQ codebook as encoder, together with our soft decision decoder, is also investigated. In our examples this approach gives comparable performance to channel optimized VQ with hard decisions