Search

Sampling above the Nyquist rate is at the heart of sigma–delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a low-pass filter at the decoder. The goal of this paper is to characterize the optimal trade-off between the per-sample quantization rate and the resulting mean-squared-error distortion under various restrictions on the feedback filter. To this end, we establish a duality relation between the performance of sigma–delta modulation and the performance of differential pulse-code modulation when applied to (discrete-time) band-limited inputs. As the optimal trade-off for the latter scheme is fully understood, the full characterization for sigma–delta modulation, as well as the optimal feedback filters, immediately follows. [ABSTRACT FROM AUTHOR]

The recently introduced compressive sensing (CS) framework enables digital signal acquisition systems to take advantage of signal structures beyond bandlimitedness. Indeed, the number of CS measurements required for stable reconstruction is closer to the order of the signal complexity than the Nyquist rate. To date, the CS theory has focused on real-valued measurements, but in practice measurements are mapped to bits from a finite alphabet. Moreover, in many potential applications the total number of measurement bits is constrained, which suggests a tradeoff between the number of measurements and the number of bits per measurement. We study this situation in this paper and show that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement compression (MC) regime, a high SNR favors acquiring fewer measurements with more bits per measurement; in the quantization compression (QC) regime, a low SNR favors acquiring more measurements with fewer bits per measurement. A surprise from our analysis and experiments is that in many practical applications it is better to operate in the QC regime, even acquiring as few as 1 bit per measurement. [ABSTRACT FROM PUBLISHER]

In this paper, we propose low precision BER-optimal analog-to-digital converters (ADC) where quantization levels and thresholds are set nonuniformly to minimize the bit-error rate (BER) in a high data rate communication link. This is in contrast to how ADCs are used today, in which they act as transparent waveform preservers. Simulations for various communication channels show that for 2-PAM modulation, the BER-optimal ADC achieves shaping gains that range from 2.5 dB for channels with low intersymbol interference (ISI) to more than 30 dB for channels with high levels of ISI. Moreover, a 3-bit BER-optimal ADC achieves the same or even lower BER than a 4-bit uniform ADC. With a DFE and a high-ISI channel, a 3-bit BER-optimal ADC achieves lower BER than a 5-bit uniform ADC. [ABSTRACT FROM PUBLISHER]