Linear code-based vector quantization for independent random variables

The computationally efficient vector quantization for a discrete time source can be performed using lattices over block linear codes or convolutional codes. For high rates (low distortion) and uniform distribution the performance of a multidimensional lattice depends mainly on the normalized second moment (NSM) of the lattice. For relatively low rates (high distortions) and non-uniform distributions the lattice-based quantization can be non-optimal in terms of achieving the Shannon rate-distortion function H(D). In this paper we analyze the rate-distortion function R(D) achievable using linear codes over GF (q), where q is a prime number. We show that even for q = 2 the NSM of code-based quantizers is close to the minimum achievable limit. If q → ∞, then NSM → 1/(2πe) which is the NSM of the infinite dimension sphere. By exhaustive search over q-ary time-invariant convolutional codes with memory ν ≤ 8, the NSM-optimum codes for q = 2, 3, 5 were found. For low rates (high distortions) we use a non-lattice quantizer obtained from a lattice quantizer by extending the “zero zone”. Furthermore, we modify the encoding by a properly assigned metric to approximation values. Due to such modifications for a wide class of probability distributions and a wide range of bit rates we obtained up to 1 dB signal-to-noise ratio improvement compared to currently known results.