Evaluating Built-in ECC of FPGA on-chip Memories for the Mitigation of Undervolting Faults

TL;DR

This paper investigates the use of FPGA built-in ECC to mitigate undervolting faults in on-chip memories, enabling significant power savings with minimal impact on neural network accuracy.

Contribution

It demonstrates that FPGA built-in ECC effectively corrects most undervolting-induced faults, allowing aggressive voltage underscaling and energy savings in neural network accelerators.

Findings

Over 90% of faults are correctable by built-in ECC.

40% power savings achieved through undervolting.

Negligible neural network accuracy loss with ECC mitigation.

Abstract

Voltage underscaling below the nominal level is an effective solution for improving energy efficiency in digital circuits, e.g., Field Programmable Gate Arrays (FPGAs). However, further undervolting below a safe voltage level and without accompanying frequency scaling leads to timing related faults, potentially undermining the energy savings. Through experimental voltage underscaling studies on commercial FPGAs, we observed that the rate of these faults exponentially increases for on-chip memories, or Block RAMs (BRAMs). To mitigate these faults, we evaluated the efficiency of the built-in Error-Correction Code (ECC) and observed that more than 90% of the faults are correctable and further 7% are detectable (but not correctable). This efficiency is the result of the single-bit type of these faults, which are then effectively covered by the Single-Error Correction and Double-Error Detection (SECDED) design of the built-in ECC. Finally, motivated by the above experimental observations, we evaluated an FPGA-based Neural Network (NN) accelerator under low-voltage operations, while built-in ECC is leveraged to mitigate undervolting faults and thus, prevent NN significant accuracy loss. In consequence, we achieve 40% of the BRAM power saving through undervolting below the minimum safe voltage level, with a negligible NN accuracy loss, thanks to the substantial fault coverage by the built-in ECC.

Tables

Table 1. TABLE I: Table Type Styles

Table	Table Column Head
Head	Table column subhead	Subhead	Subhead
copy	More table copya
aSample of a Table footnote.

Equations

$$a+b=\gamma$$

Full text

I Introduction

This document is a model and instructions for LaTeX. Please observe the conference page limits.

II Ease of Use

II-A Maintaining the Integrity of the Specifications

The IEEEtran class file is used to format your paper and style the text. All margins, column widths, line spaces, and text fonts are prescribed; please do not alter them. You may note peculiarities. For example, the head margin measures proportionately more than is customary. This measurement and others are deliberate, using specifications that anticipate your paper as one part of the entire proceedings, and not as an independent document. Please do not revise any of the current designations.

III Prepare Your Paper Before Styling

Before you begin to format your paper, first write and save the content as a separate text file. Complete all content and organizational editing before formatting. Please note sections III-A–III-E below for more information on proofreading, spelling and grammar.

Keep your text and graphic files separate until after the text has been formatted and styled. Do not number text heads—LaTeX will do that for you.

III-A Abbreviations and Acronyms

Define abbreviations and acronyms the first time they are used in the text, even after they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, ac, dc, and rms do not have to be defined. Do not use abbreviations in the title or heads unless they are unavoidable.

III-B Units

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Use either SI (MKS) or CGS as primary units. (SI units are encouraged.) English units may be used as secondary units (in parentheses). An exception would be the use of English units as identifiers in trade, such as “3.5-inch disk drive”.

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Use a zero before decimal points: “0.25”, not “.25”. Use “cm3”, not “cc”.)

III-C Equations

Number equations consecutively. To make your equations more compact, you may use the solidus ( / ), the exp function, or appropriate exponents. Italicize Roman symbols for quantities and variables, but not Greek symbols. Use a long dash rather than a hyphen for a minus sign. Punctuate equations with commas or periods when they are part of a sentence, as in:

[TABLE]

Be sure that the symbols in your equation have been defined before or immediately following the equation. Use “(1)”, not “Eq. (1)” or “equation (1)”, except at the beginning of a sentence: “Equation (1) is . . .”

III-D LaTeX*-Specific Advice*

Please use “soft” (e.g., \eqref{Eq}) cross references instead of “hard” references (e.g., (1)). That will make it possible to combine sections, add equations, or change the order of figures or citations without having to go through the file line by line.

Please don’t use the {eqnarray} equation environment. Use {align} or {IEEEeqnarray} instead. The {eqnarray} environment leaves unsightly spaces around relation symbols.

Please note that the {subequations} environment in LaTeX will increment the main equation counter even when there are no equation numbers displayed. If you forget that, you might write an article in which the equation numbers skip from (17) to (20), causing the copy editors to wonder if you’ve discovered a new method of counting.

BibTEX does not work by magic. It doesn’t get the bibliographic data from thin air but from .bib files. If you use BibTEX to produce a bibliography you must send the .bib files.

LaTeX can’t read your mind. If you assign the same label to a subsubsection and a table, you might find that Table I has been cross referenced as Table IV-B3.

LaTeX does not have precognitive abilities. If you put a \label command before the command that updates the counter it’s supposed to be using, the label will pick up the last counter to be cross referenced instead. In particular, a \label command should not go before the caption of a figure or a table.

Do not use \nonumber inside the {array} environment. It will not stop equation numbers inside {array} (there won’t be any anyway) and it might stop a wanted equation number in the surrounding equation.

III-E Some Common Mistakes

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The word “data” is plural, not singular.

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The subscript for the permeability of vacuum $\mu_{0}$, and other common scientific constants, is zero with subscript formatting, not a lowercase letter “o”.

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In American English, commas, semicolons, periods, question and exclamation marks are located within quotation marks only when a complete thought or name is cited, such as a title or full quotation. When quotation marks are used, instead of a bold or italic typeface, to highlight a word or phrase, punctuation should appear outside of the quotation marks. A parenthetical phrase or statement at the end of a sentence is punctuated outside of the closing parenthesis (like this). (A parenthetical sentence is punctuated within the parentheses.)

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A graph within a graph is an “inset”, not an “insert”. The word alternatively is preferred to the word “alternately” (unless you really mean something that alternates).

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Do not use the word “essentially” to mean “approximately” or “effectively”.

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In your paper title, if the words “that uses” can accurately replace the word “using”, capitalize the “u”; if not, keep using lower-cased.

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Be aware of the different meanings of the homophones “affect” and “effect”, “complement” and “compliment”, “discreet” and “discrete”, “principal” and “principle”.

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Do not confuse “imply” and “infer”.

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The prefix “non” is not a word; it should be joined to the word it modifies, usually without a hyphen.

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There is no period after the “et” in the Latin abbreviation “et al.”.

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The abbreviation “i.e.” means “that is”, and the abbreviation “e.g.” means “for example”.

An excellent style manual for science writers is [7].

III-F Authors and Affiliations

The class file is designed for, but not limited to, six authors. A minimum of one author is required for all conference articles. Author names should be listed starting from left to right and then moving down to the next line. This is the author sequence that will be used in future citations and by indexing services. Names should not be listed in columns nor group by affiliation. Please keep your affiliations as succinct as possible (for example, do not differentiate among departments of the same organization).

III-G Identify the Headings

Headings, or heads, are organizational devices that guide the reader through your paper. There are two types: component heads and text heads.

Component heads identify the different components of your paper and are not topically subordinate to each other. Examples include Acknowledgments and References and, for these, the correct style to use is “Heading 5”. Use “figure caption” for your Figure captions, and “table head” for your table title. Run-in heads, such as “Abstract”, will require you to apply a style (in this case, italic) in addition to the style provided by the drop down menu to differentiate the head from the text.

Text heads organize the topics on a relational, hierarchical basis. For example, the paper title is the primary text head because all subsequent material relates and elaborates on this one topic. If there are two or more sub-topics, the next level head (uppercase Roman numerals) should be used and, conversely, if there are not at least two sub-topics, then no subheads should be introduced.

III-H Figures and Tables

Positioning Figures and Tables

Place figures and tables at the top and bottom of columns. Avoid placing them in the middle of columns. Large figures and tables may span across both columns. Figure captions should be below the figures; table heads should appear above the tables. Insert figures and tables after they are cited in the text. Use the abbreviation “Fig. 1”, even at the beginning of a sentence.

Figure Labels: Use 8 point Times New Roman for Figure labels. Use words rather than symbols or abbreviations when writing Figure axis labels to avoid confusing the reader. As an example, write the quantity “Magnetization”, or “Magnetization, M”, not just “M”. If including units in the label, present them within parentheses. Do not label axes only with units. In the example, write “Magnetization (A/m)” or “Magnetization {A[m(1)]}”, not just “A/m”. Do not label axes with a ratio of quantities and units. For example, write “Temperature (K)”, not “Temperature/K”.

Acknowledgment

The preferred spelling of the word “acknowledgment” in America is without an “e” after the “g”. Avoid the stilted expression “one of us (R. B. G.) thanks $\ldots$”. Instead, try “R. B. G. thanks$\ldots$”. Put sponsor acknowledgments in the unnumbered footnote on the first page.