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Synthesis and Optimization of Asynchronous Dual Rail
Encoded Circuits Based on Partial Acknowledgement
Yu Zhou, Chun Shi, Zhengjie Deng
School of Information Science and Technology
Hainan Normal University
Haikou, China, 571158
Email: {zhouyu,byshichun,zjdeng}@hainnu.edu.cn
Alex Yakovlev
School of Engineering
Newcastle University
United Kingdom, NE1 7RU
Email: alex.yakovlev@ncl.ac.uk
Abstract—In this paper, a systematic design flow for asyn-
chronous dual-rail encoded circuits with a high timing robustness
level is introduced. With this flow, a synchronous Boolean
network can be translated into its asynchronous counterpart
consisting of the so-called dual-rail encoded functional mod-
ules (DRFMs). Each dual-rail encoded variable in the target
asynchronous circuit is partially acknowledged, and the overall
circuit satisfies speed independent requirements. The translation
process is formulated within integer programing framework and
solved with efficient algorithms. In addition, methods for de-
signing DRFMs and characterizing their propagation delays are
discussed, as well as simulation techniques used for performance
analysis of the target asynchronous circuit.
I. INTRODUCTION
As the feature size of semiconductor technology continues
to scale down, process variation has become one of the
most challenging issues for microelectronics design. With the
conventional synchronous design methods relying on global
synchronization, clock margins must be elaborately reserved
for the worst case delay, considering all process corners with
different working temperatures as well as supply voltage fluc-
tuations. Moreover, with the trend of integrating heterogeneous
computation resources in a single die to explore the full
strength of technology scaling, on-chip communication across
different clock domains calls for design paradigms such as
Globally Asynchronous Locally Synchronous (GaLS) [1], [2]
and Network-on-Chip (NOCs) [3], [4], [5], which depend
heavily on asynchronous circuit design techniques [6], [7].
Instead of routing long clock wires for global synchro-
nization, asynchronous circuits resort to local handshaking
signals for coordinating data transfer. When computation is
finished, real-time request signal is raised so that data is safely
latched by the receiver; after the received data is consumed,
an acknowledging signal is sent back and a new round of
data transfer can begin. This closed-loop control based on
measured delay presents a more timing-robust implementation
against process variations as well as fluctuating environment
conditions [8], [9].
For the purpose of indicating completion of data com-
putation in real-time, delay-insensitive codes [10] are often
adopted in asynchronous circuit design, whereas dual-rail code
is presumably the most frequently used one for its straightfor-
wardness in code conversion and completion detection circuit
design [11], [12], [13]. Furthermore, a dual-rail encoded circuit
must embrace particular implementation techniques to ensure
that it operates correctly with arbitrary delays assumed for all
or part of its circuit elements. One design practice with a fairly
high timing robustness level is called speed-independent (or
quasi-delay-insensitive) [14], [15], [16], where all gates and a
subset of wires in the circuit can take arbitrary delays.
Different synthesis and optimization methods have been
proposed for dual-rail encoded speed independent circuits [17],
[13], [18], [19], [20], [21], [22], [23], [24], [25], and invariably
they adopt techniques of “indicating” or “acknowledging”
circuit signal transitions. In [20], the concept of “partial
acknowledgement” is proposed which describes the causal-
ity relation between dual-rail encoded circuit variables, and
techniques of designing dual-rail encoded functional modules
(DRFMs) with different input acknowledgement patterns are
discussed. In addition, the problems of synthesizing speed-
independent dual-rail encoded circuits are formulated as unate
or binate covering problems.
In this paper, an asynchronous dual-rail circuit is synthe-
sized by direct translating of a Boolean network [18], [19],
[20], [22]. This direct translation method is straightforward,
making asynchronous design easy to accept for designers
with synchronous mentality. With the method, each node in
the Boolean network is mapped to a DRFM with the same
functionality and, in addition, one of the many patterns to
acknowledge its inputs. The synthesis process is formulated
as an optimization problem where partial acknowledgement
patterns can be tuned to achieve a particular objective, whilst
satisfying the overall circuit timing-robustness requirements
that each dual-rail encoded circuit variable must be partially
acknowledged. In this paper, the synthesis and optimiza-
tion problem is formulated within an integer programming
framework, which represents a more fine-grained formulation
compared with previous methods[20], [22].
This paper presents a systematic design flow for asyn-
chronous dual-rail encoded circuits: methods of designing
DRFMs, the fundamental building blocks, are introduced with
their areas and propagation delays characterized. Simulation
techniques, both data dependent and independent, are proposed
for analyzing the circuit performance. Further, efficient algo-
rithms are proposed to solve the optimization problem.
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