SELF-ORGANIZING DSP CIRCUITS

Andr´e Stauffer and Jo¨el Rossier

Logic Systems Laboratory, Ecole polytechnique f´ed´erale (EPFL), CH-1015 Lausanne, Switzerland

Keywords:

Bio-inspiration, Conﬁguration, Cloning, Cicatrization, Regeneration.

Abstract:

Living organisms are endowed with three structural principles: multicellular architecture, cellular division,

and cellular differentiation. Implemented in digital according to these principles, our DSP circuits present

self-organizing mechanisms like conﬁguration, cloning, cicatrization, and regeneration. These mechanisms

are made of simple processes such as growth, load, branching, repair, reset, and kill. The description of a con-

ﬁgurable molecule implementing the self-organizing mechanisms and its application to a multiplier function

constitute the core of this paper.

1 INTRODUCTION

Borrowing the structural principles from living organ-

isms, we have already shown how to grow cellular

systems thanks to an algorithm for cellular division

(Mange et al., 2004). These cellular systems are en-

dowed with self-organizing properties like conﬁgura-

tion, cloning, cicatrization, and regeneration (Stauffer

et al., 2005).

In a previous work (Stauffer et al., 2006), the

conﬁguration mechanisms (structural and functional

growth), the cloning mechanisms (cellular and organ-

ismic self-replication), the cicatrization mechanism

(cellular self-repair), and the regeneration mechanism

(organismic self-repair) were already devised as the

result of simple processes like growth, load, branch-

ing, repair, reset, and kill. The goal of this paper is to

implement these mechanisms in DSP circuits.

Starting with the cellular architecture of the DSP

circuits, Section 2 will point out how the bio-inspired

properties like cloning, cicatrization, and regenera-

tion apply to these kind of circuits. Section 3 intro-

duces digital simulations to describe the data and the

signals involved in the corresponding self-organizing

mechanisms and their underlying processes. We de-

ﬁne then the detailed molecular architecture of the cir-

cuits (Section 4) and devise a multiplier as an appli-

cation example (Section 5). A brief conclusion (Sec-

tion 6) summarizes our paper and opens new research

avenues.

2 BIO-INSPIRED PROPERTIES

2.1 Cellular Architecture

DSP circuits are made up of identical slices. They can

be seen as multicellular organisms made up of identi-

cal cells. Each slice processes one data bit and corre-

sponds to a cell made up of functionally conﬁgurable

molecules. The minimal cell consists of two rows of

three molecules with two columns of application spe-

ciﬁc molecules to the left and one column of spare

molecules (SM) to the right (Fig. 1).

Figure 1: DSP slice corresponding to a minimal cell made

up of six molecules.

The minimal multicellular organism is made up of

two identical cells and represents a DSP circuit pro-

cessing two data bits (Fig. 2).

Figure 2: DSP circuit corresponding to a minimal organism

made up of two cells.

The minimal population of organisms is made up

of two identical organisms. The left one consists of

197

Stauffer A. and Rossier J. (2009).

SELF-ORGANIZING DSP CIRCUITS.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 197-203

DOI: 10.5220/0001120401970203

 SciTePress

two speciﬁc application cells while the right one is

composed of two spare cells (SC, Fig. 3).

Figure 3: DSP circuit corresponding to a minimal popula-

tion of organisms made up of two organisms.

2.2 Cloning

The cloning or self-replication can be implemented

at the cellular level in order to build a multicellular

organism and at the organismic level in order to gen-

erate a population of organisms. The cloning of the

minimal cell displayed in Fig. 1 results thus in the or-

ganism of Fig. 2. The cloning of this organism deﬁnes

the population of Fig. 3.

2.3 Cicatrization

The introduction in the cells of the minimal organ-

ism of one column of spare molecules (SM, Fig. 2),

deﬁned by a speciﬁc structural conﬁguration, and the

automatic detection of faulty molecules (by a built-in

self-test mechanism which constantly compares two

copies of the same molecule) allows cicatrization or

self-repair at the cellular level: each faulty molecule is

deactivated, isolated from the network, and replaced

by the nearest right molecule, which will itself be re-

placed by the nearest right molecule, and so on until

a spare molecule (SM) is reached (Fig. 4). The num-

ber of faulty molecules handled by the cicatrization

mechanism is necessarily limited: in the example of

Fig. 2, we tolerate at most one faulty molecule per

row.

Figure 4: Cicatrization of the minimal organism.

2.4 Regeneration

In order to implement regeneration, that is self-repair

at the organismic level, we need at least one spare or-

ganism to the right of the original organism (Fig. 3).

The existence of two faulty molecules in a same row

identiﬁes the faulty organism which is deactivated

(Fig. 5). The functionality of the DSP circuit is now

Figure 5: Regeneration of the minimal organism.

performed by the spare cells (SC) of the organism to

the right.

3 SELF-ORGANIZING

MECHANISMS

3.1 Structural Conﬁguration

The goal of the structural conﬁguration mechanism is

to deﬁne the boundaries of the cell as well as the liv-

ing mode or spare mode of its constituting molecules.

This mechanism is made up of a structural growth

process followed by a load process.

The growth process starts when an external growth

signal is applied to the lower left molecule of the cell

(Fig. 6a) and this molecule selects the corresponding

eastward data input (Fig. 6b). According to the struc-

tural conﬁguration data or structural genome, each

molecule of the cell generates then successively an

internal growth signal and selects an input (Fig. 7),

in order to create a data path among the molecules of

the cell (Fig. 6b-g). When the connection path be-

tween the molecules closes, the lower left molecule

delivers a close signal to the nearest left neighbor cell

(Fig. 6h). The structural conﬁguration data is now

moving around the data path and ready to be trans-

mitted to neighboring cells.

The load process is triggered by the close sig-

nal applied to the lower right molecule of the cell

(Fig. 8a). A load signal propagates then westward

and northward through the cell (Fig. 8b-d) and each of

its molecules acquire a molecular mode (Fig. 9) and a

molecular type (Fig. 10). We ﬁnally obtain an homo-

geneous tissue of molecules deﬁning both the bound-

aries of the cell and the position of its living mode and

spare mode molecules (Fig. 8e). This tissue is ready

for being conﬁgured by the functional conﬁguration

data.

3.2 Functional Conﬁguration

The goal of the functional conﬁguration mechanism

is to store in the homogeneous tissue, which already

contains structural data (Fig. 8e), the functional data

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(e)

(f)

(g)

(a)

(b) (c)

(d)

(h)

Figure 6: Structural growth process of the minimal cell

made up of six molecules. (a) External growth signal ap-

plied to the lower left molecule. (b-g) Generation of internal

growth signals to build the structural data path. (h) Closed

path and close signal delivered to the nearest left neighbor

cell.

(a) (b) (c) (d)

Figure 7: Data input selection. (a) Northward. (b) East-

ward. (c) Southward. (d) Westward.

(b)

(c)

(d)

(e)

Figure 8: Load process. (a) External close signal applied

to the lower right molecule by the nearest right neighbor

cell. (b-e) Generation of internal load signals propagating

westward and northward to store the molecular modes and

types of the cell.

(a) (b) (c) (d)

(e)

Figure 9: Molecular modes. (a) Living. (b) Spare. (c)

Faulty. (d) Repair. (e) Dead.

(b) (c) (d)

(a)

(e) (f)

(g) (h)

(i)

Figure 10: Molecular types. (a) Internal. (b) Top. (c) Top-

left. (d) Left. (e) Bottom-left. (f) Bottom. (g) Bottom-right.

(h) Right. (i) Top-right.

needed by the speciﬁcations of the current applica-

tion. This mechanism is a functional growth process,

performed only on the molecules in the living mode

while the molecules in the spare mode are simply by-

passed. It starts with an external growth signal ap-

plied to the lower left living molecule (Fig. 11a). Ac-

cording to the functional conﬁguration data or func-

tional genome, the living molecules then successively

generate an internal growth signal, select an input,

and create a path among the living molecules of the

cell (Fig. 11b-f). The functional conﬁguration data

is now moving around the data path and ready to be

transmitted to neighboring cells.

(a)

(b) (c)

(d)

(e)

(f)

Figure 11: Functional conﬁguration of the cell per-

formed as a functional growth process applied to the living

molecules. (a) External growth signal applied to the lower

left molecule. (b-e) Generation of internal growth signals in

order to build the functional data path. (f) Closed functional

data path.

3.3 Cloning

The cloning mechanism or self-replication mecha-

nism is implemented at the cellular level in order to

build a multicellular organism and at the organismic

level in order to generate a population of organisms.

This mechanism suppose that there exists a sufﬁcient

number of molecules in the array to contain at least

one copy of the additional cell or of the additional or-

ganism. It corresponds to a branching process which

takes place when the structural and the functionalcon-

ﬁguration mechanisms deliver northward and east-

ward growth signals on the borders of the cell during

the corresponding growth processes (Fig. 12).

3.4 Cicatrization

Fig. 11f, shows the normal behavior of a healthy min-

imal cell, i.e. a cell without any faulty molecule. A

molecule is considered as faulty, or in the faulty mode,

if some built-in self-test detects a lethal malfunction.

Starting with the normal behavior of Fig. 11f, we sup-

pose that two molecules will become suddenly faulty

(Fig. 13a): (1) The lower left molecule, which is in the

living mode. (2) The upper right molecule, which is in

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199

(a)

(b) (c)

(d)

Figure 12: Generation of growth signals triggering the

cloning mechanism. (a) Northward structural branching

process. (b) Eastward structural branching process. (c)

Northward functional branching process. (d) Eastward

functional branching process.

(a)

(b) (c)

(d)

(e)

(f)

(g)

Figure 13: Cicatrization mechanism performed as a repair

process followed by a reset process. (a) Living and spare

molecules becoming faulty. (b-c) Generation of repair sig-

nals propagating eastward. (d-f) Generation of internal re-

set signals propagating westward and northward. (g) Cell,

comprising two faulty and two repair molecules, ready for

functional reconﬁguration.

the spare mode. While there is no change for the up-

per right molecule, which is just no more able to play

the role of a spare molecule, the lower left one trig-

gers a cicatrization mechanism. This mechanism is

made up of a repair process involving eastward prop-

agating repair signals (Fig. 13b-c) followed by a re-

set process performed with westward and northward

propagating internal reset signals (Fig. 13d-g). This

tissue, comprising now two molecules in the faulty

mode and two molecules in the repair mode, is ready

for being reconﬁgured by the functional conﬁguration

data. This implies a functional growth process by-

passing the faulty molecules (Fig. 14).

3.5 Regeneration

Our minimal cell comprises a single spare molecule

per row and tolerates therefore only one faulty

molecule in each row. A second faulty molecule in

the same row will cause the death of the whole cell,

and the start of a regeneration mechanism. Fig. 15 il-

lustrates the repair process and kill process involved

in this mechanism. Starting with the normal behavior

of the cicatrized cell (Fig. 14f), a new molecule, the

upper middle one, becomes faulty. In a ﬁrst step, the

new faulty molecule sends a repair signal eastward,

in order to look for a spare molecule, able to replace

it (Fig. 15b). In a second step, the supposed spare

molecule, which is in fact a faulty one, enters the

lethal dead mode and triggers kill signals which prop-

agate northward, westward and southward (Fig. 15c-

f). Finally in Fig. 15g, all the molecules of the array

are dead as well as our minimal system.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 14: Functional reconﬁguration of the living and re-

pair molecules. (a) External growth signal bypassing the

lower left faulty molecule. (b-e) Generation of internal

growth signals to build a functional data path bypassing the

faulty molecules. (f) Closed functional data path within the

living and repair molecules.

4 CONFIGURABLE MOLECULE

4.1 Control Layer

We will now describe the detailed architecture of the

control layer of our basic conﬁgurable molecule. This

layer, which implements the self-organizing mecha-

nisms and their constituting processes, corresponds

to a data and signals cellular automaton (DSCA) cell

(Stauffer and Sipper, 2004). It results from the inter-

connection of the following resources (Fig. 16):

• An input multiplexer DIMUX, selecting one out

of the four conﬁguration input data NDI, EDI,

SDI or WDI.

• A 2N-level stack organized as N genotypic regis-

ters G1 to GN (for mobile conﬁguration data), and

N phenotypic registers P1 to PN (for ﬁxed conﬁg-

uration data).

• An output buffer DOBUF producing the conﬁgu-

ration output data DO.

• An encoder ENC for the input signals NSI, ESI,

SSI, and WSI.

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(a)

(b) (c)

(d)

(e)

(f)

(g)

Figure 15: Regeneration mechanism performed as a repair

process followed by a kill process. (a) Living molecule be-

coming faulty. (b) Eastward repair signal. (c-f) Genera-

tion of internal and external kill signals propagating north-

ward, westward and southward. (g) Cell made up six dead

molecules.

DIMUX

NDI

WDI

SDI

EDI

G1:N P1:N

DOBUF

ENC

WSI

SSI

ESI

NSI

GEN

PN-1

GN-1

WSO

SSO

ESO

NSO

DEC TPN-1

WSI

Figure 16: Detailed architecture of the control layer of the

molecule.

• A decoder DEC deﬁning the mode and the type of

the molecule.

• A transmission register I for the memorization of

the input selection.

• A signal register S.

• A mode register M.

• A type register T.

• A generator GEN producing the output signals

NSO, ESO, SSO, and WSO.

4.2 Processing Layer

The processing layer implements the logic design of

the DSP application under development as well as its

routing connections between neighboring and distant

molecules. This layer, which is conﬁgured by the

ﬁxed data of the phenotypic registers P1 to PN-1, is

made up of the following resources (Fig. 17):

• An input multiplexer AIMUX, selecting four in-

puts out of the four application data NAI, EAI,

SAI, WAI, and the routing data RO.

• A 16-bit look-up table LUT.

• A D-type ﬂip-ﬂop DFF for the realization of se-

quential circuits.

• An output multiplexer AOMUX selecting the

combinational or the sequential data as applica-

tion output AO.

• An output multiplexer ROMUX selecting the ﬁve

outputs NRO, ERO, SRO, WRO, and RO out of

the four routing input data NRI, ERI, SRI, WRI,

and the application output data AO.

AOMUX

WAI

SAI

EAI

NAI

LUT

DFF

AIMUX

ROMUX

ERI

WRI

SRI

NRI

NRO

ERO

SRO

WRO

Figure 17: Detailed architecture of the processing layer of

the molecule.

5 MULTIPLIER APPLICATION

5.1 Basic Cell

Even if the ﬁnal goal is the self-organization of DSP

circuits, we will use a simpliﬁed application exam-

ple, the multiplication function (Andrejas and Trost,

2000), in order to illustrate its basic mechanisms. The

circuit that multiplies two 4-bit signals X andY can be

considered as a one-dimensional artiﬁcial organism

composed of four identical cells. Each cell is made

up of ten application speciﬁc molecules (Fig. 18):

• Four C molecules computing the carry output of a

1-bit adder.

• Four S molecules computing the sum output of a

1-bit adder.

• One D molecule generating a deactivation signal

in order to bypass the cells of the neighboring

spare organism to the right.

• One R molecule recovering the multiplication re-

sult performed by the living organism.

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Y0 Y1 Y2 Y3

Figure 18: Basic cell of the 4-bit signals X and Y multiplier.

5.2 Structural Conﬁguration,

Functional Conﬁguration and

Cloning

In order to build the multicellular organism of Fig. 19,

the structural conﬁguration mechanism, the func-

tional conﬁguration mechanism, and the cloning

mechanism are applied at the cellular level. Start-

ing with the structural and functional conﬁguration

data of the basic cell, these mechanisms generate

successively the four identical cells of the multiplier

organism. In this implementation, each individual

cell of the organism presents two columns of spare

molecules.

Figure 19: One-dimensional organism composed of four

cells resulting from the structural conﬁguration, functional

conﬁguration and cloning mechanisms applied to the basic

cell.

5.3 Cicatrization and Functional

Reconﬁguration

The cicatrization mechanism (or cellular self-repair)

results from the introduction of the columns of spare

molecules (Fig. 19), deﬁned by the structural conﬁgu-

ration of the basic cell, and the automatic detection of

faulty molecules. Thanks to this mechanism, each of

the two faulty molecules of the lower cell (Fig. 20) is

deactivated, isolated from the network, and replaced

by the nearest right molecule, which will itself be re-

placed by the nearest right molecule, and so on until a

spare molecule is reached. The functional reconﬁgu-

ration mechanism takes then place in order to regener-

ate the multiplier organism. As shown in Fig. 20, the

regenerated organism presents some graphical distor-

tion.

Figure 20: Graphical distortion resulting from the cicatriza-

tion and reconﬁguration mechanisms applied to the lower

cell of the organism.

5.4 Regeneration

Each individual cell of the multiplier having two spare

columns (Fig. 19), this implementation allows at most

two faulty molecules per row. When a third one is

detected, the regeneration mechanism (or organismic

self-repair) takes place and all the cells of the organ-

ism are considered faulty and are deactivated. The

functions of the faulty cells are thus shifted to the

spare cells to the right. Obviously, this process re-

quires at least one spare organism to the right. As

shown in Fig. 21, the repair of the faulty organism

needs the spare organism to the right and leaves a scar

in the implementation.

6 CONCLUSIONS

The self-organizing mechanisms are made of simple

processes like growth, load, branching, repair, re-

set, and kill. They allow the DSP circuits to pos-

sess three bio-inspired properties: (1) Cloning or self-

replication at cellular and organismic levels. (2) Ci-

catrization or self-repair at the cellular level. (3) Re-

generation or self-repair at the organismic level.

Starting with a minimal DSP slice, a cell made of

six molecules, we realized digital simulations in order

to describe the data and signals involved in the self-

organizing mechanisms. These mechanisms are im-

plemented in the control layer of a basic conﬁgurable

molecule. The processing layer of the molecule im-

plements the logic design of the DSP circuit under de-

velopment. A 4-bit multiplier, an organism made of

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202

Figure 21: Scar resulting from the regeneration mechanism

applied to the organism.

four cells, was introduced as an application example

for the simulation of our mechanisms and their under-

lying processes.

The conﬁgurable molecule presented here will be

implemented in the ubichip (Upegui et al., 2007), a

programmable circuit that draws inspiration from the

multi-cellular structure of complex biological organ-

isms. The processing layer of the ubichip molecule is

a conventionalprogrammable block. In order to allow

the conﬁguration of complex DSP circuits, this layer

must include some more speciﬁc DSP features.

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