Compressed Two's Complement Data Formats Provide Greater Dynamic Range and Improved Noise Performance [exploratory DSP]

Compressed fixed-point data formats with non-standard compression factors

“…A few even focus on sign bit compression (Koyama et al, 2012) similar to the formats shown in this paper. It has also been shown that compressed two's complement data formats outperform both traditional fixed-point and floating-point data formats in terms of noise performance for signal processing applications (Richey and Saiedian, 2011). In this paper, we have demonstrated that non-standard compression factors (i.e.…”

“…Techniques for compressing the fixed-point data format are broadly applicable to most fixed-point formats, but we will illustrate compression for the two's complement format due to the traditional advantages it has over the other fixed-point data formats (Parhami, 1999;Goldberg, 1991). The compressed two's complement data format has been described in some detail by the authors in previous publications (Richey and Saiedian, 2009;Richey and Saiedian, 2011). Here, we will provide a brief description of the format to introduce the new material provided in this paper.…”

“…This will noticeably improve round-off noise performance and allow about five times as much dynamic range in decibels without giving up anything more than a single bit of word width. Of course, IEEE 754 floating point achieves over twice this improvement in dynamic range in dB, but at the cost of doubling the word width to 32 bits (Richey and Saiedian, 2011).…”

“…To verify the asserted performance improvements of irregular compression factors, a data format with a compression factor of 3 was implemented and tested against previously coded formats with compression factors of 1 and 2 (Richey and Saiedian, 2011). Note that a compression factor of 1 results in standard two's complement.…”