This letter presents a method of finding the optimal quantization stepsize that minimizes quantization loss and maximizes coded BER performance. We define 'Information Error Rate'(IER) and obtain the equation of the modified constraint length (Km) to obtain an upper bound of coded BER performance of a l bit quantized soft decision Viterbi decoder. Using IER and Km, we determine the optimal quantization stepsize of a 2 bit and 3 bit quantized soft decision decoding system in an AWGN channl with respect to SNR, and verify our strategies by simulation results.

Improvement of the convergence characteristics of the NLMS algorithm has received attention in the area of adaptive filtering. A new variable stepsize NLMS method, in which the stepsize is updated optimally by using variances of the measured error signal and the estimated noise, is proposed. The optimal control equation of the stepsize has been derived from a convergence characteristic approximation. A new condition to judge convergence is introduced in this paper to ensure the fastest initial convergence speed by providing precise timing to start estimating noise level. And further, some adaptive smoothing devices have been added into the ADF to overcome the saturation problem of the identification error caused by some random deviations. By the simulation, The initial convergence speed and the identification error in precise identification mode is improved significantly by more precise adjustment of stepsize without increasing in computational cost. The results are the best ever reported performanced. This variable stepsize NLMS-ADF also shows good effectiveness even in severe conditions, such as noisy or fast changing circumstances.