An Optimization Approach to Single-Bit Quantization

This paper presents an optimization approach to single-bit quantization. The paper starts by redefining single-bit quantization as a maximum-likelihood sequence detection problem and by showing that the Viterbi algorithm is its optimal solution. It also shows that the conventional ???? converter implements a greedy solution to the same optimization problem. There is, moreover, a continuum of solutions with different degrees of complexity between the ????s and the Viterbi solution. The paper details one such intermediate-complexity solution (based on the M-algorithm) and demonstrates that with an appropriate noise shaping filter it achieves a performance very close to the optimal Viterbi solution. The paper concludes by presenting two procedures for designing effective noise shaping filters.