Noise-Shaping Binary-to-Stochastic Converters for Reduced-Length Bit-Streams

Stochastic computations have attracted significant attention for applications with moderate fixed-point accuracy requirements, as they offer minimal complexity. In these systems, a stochastic bit-stream encodes a data sample. The derived bit-stream is used for processing. The bit-stream length determines the computation latency for bit-serial implementations and hardware complexity for bit-parallel ones. Noise shaping is a feedback technique that moves the quantization noise outside the bandwidth of interest of a signal. This article proposes a technique that builds on noise shaping and reduces the length of the stochastic bit-stream required to achieve a specific Signal-to-Quantization-Noise Ratio (SQNR). The technique is realized by digital units that encode binary samples into stochastic streams, hereafter called as binary-to-stochastic converters. Furthermore, formulas are derived that relate the bit-stream length reduction to the signal bandwidth. First-order and second-order converters that implement the proposed technique are analyzed. Two architectures are introduced, distinguished by placing a stochastic converter either inside or outside of the noise-shaping loop. The proposed bit-stream length reduction is quantitatively compared to conventional binary-to-stochastic converters for the same signal quality level. Departing from conventional approaches, this article employs bit-stream lengths that are not a power of two, and proposes a modified stochastic-to-binary conversion scheme as a part of the proposed binary-to-stochastic converter. Particularly, SQNR gains of 29.8 dB and 42.1 dB are achieved for the first-order and second-order converters compared to the conventional converters for equal-length bit-streams and low signal bandwidth. The investigated converters are designed and synthesized at a 28-nm FDSOI technology for a range of bit widths.