BSTJ 60: 7. September 1981: Digital Signal Processor: Adaptive Differential Pulse-Code-Modulation Coding. (Boddie, J.R.; Johnston, J.D.; McGonegal, C.A.; Upton, J.W.; Berkley, D.A.; Crochiere, R.E.; Flanagan, J.L.)

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Digital Signal Processor:

Adaptive Differential Pulse-Code-Modulation
Coding

By J. RL BODDIE, J.D. JOHNSTON, C. A. McGONEGAL, J. W.
UPTON, D. A. BERKLEY, RE. GROCHIERE, and J. L. FLANAGAN

(Morusenpt rected June 26, 1960)

An adaptive differant! pulse code modulation technique for en
coding and decoding hax Born implemented wsing the Bell Labora
Lorian digital nigaal proceamur integrated vireut. The encoderde-
‘oder operates in realtime and ean accommodate ar 4 bit (8 Rll)
‘enconting, Tn this poner, we discuss details of the tnsplementaton, the
asic algorithm, and the features utilized in the digital signal proc

|. wrRopUCTION

Adaptive differential puse-code-modiuletion (aurea) encoding hos
‘been shown tobe a simple and ffecive method for digitally encoding
speech at bitrates inthe runge of approximately 24 to 48 kbye!* Ata
rile of 24 Rh/'s anrw can provide a god quality reproduction of
Speech that i acceptable for applications auch as computer contelled
digital voice response systema" Ae a rate of 42 Kya, it can provide
essentially 4 telephone handwidch “tranaparent. quality” (a quality
‘that is indistinguishable from the orignal uncoded source) fora single
tandem encoding, Adplive differenti) plse-oode modulation Was
‘been studied for nse in sme types of Iransmion systems and for
message storage anv retrieval systema in which a reduction by a factor
fat two in bitrate aver tha of conventional 6 kh law compandesd
rt in desired

‘Various forms of hardware have been sugxested for che implemen:
lation of aprent enders. Some designs are hased primarily on analog
Ihardoare! where parameters are pairwise tuned between transmit
ters and recrivers ‘Thi eaulls in problems with repeatbilty and
Stability in Une analog design, Bates’ and Adelman, Ching, nnd Goss!
Subvetqurily presented ewo diferent methods of designing alaligital
Aappes voders. The Bates approach uses a'r. logic design with a HOM
based look-up lable forthe edaptivescep-size and an up/down counting
seliee mith digital adder nel subcraters to avoid the use of «digi
taultplier, The hardhwaee requtes a twelee-bie linear rea input and
bans total “package count” of appresimately 80 standard TTL. logic
packages, It was eonsinutes] on own wie-wrapped Augat cards (one
fneader and one decer per hoard) The harwave by Adelman eta
trae 4 ROM based design that accepted a standard 4k law com
panded ent signal

‘Recently, an 1s) digital signal processor (ost) hus been developed
bby Hell Laboratories "The DSP sea pregrammable proceso? capable
ff parforming the entre aDpcs gorithm for sultple channels in &
Single tar device. The abiity of the processor Lo conver! between
‘ouveutional 265 oompanded ew and to's complemenrbinsry code
formats alloms the auPCM lgurith t vee ether formal. The conti
tration of che apecat algorithm chal implemented vn the BSP i
‘decribed in Section TI. Seeron THT diarsien details of how the algo
fichm ie configured "0 ue DSP Iealnees. Sections TW and ¥ describe the
hardware configuncion and rare! performance, reepertively.

1 THE ADPEM ALGORITHM
2.1 Overat coniguaton

Figure | ilusteates the basic configuration of the DeP implementa
tom of uve, The input analog signal (0) ie mpd and a/
converted to en Sit law companded Pest Coral L@ prevluce the
‘sampled dasa signal sin), where mis the discrete time index, These
‘perntions are done externally ty we nee, The s(n) is omer in
the DsP from law Fora co 8 20 bic Linear Pea Fore for incr
proceasing.

‘The abrow enessling is performed enti sithin the wransmiter
use, The output ion 3 chit endewinl, Za, whieh ean be obtained
‘through the normal output chanel of the Hs. Ta the receiver, a

A] | a] Spee | Le

1543 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 196)
second nar is use to decode in el tw an bit yl fort This
Signal is then converted to an analog signal with an exinml D/A.
converter. "The elock and framing signale are carried between Lan
miter and receiver on separate Lines. The transmission protocol fora
fiven application depends on the cata channel in which tv aster ie
lrmplemented

2.2 Block aagram of ADPCM

Figure 2 shows the block diagram of the abvem algorithm that as
implemented on the ASP. The rameter fe shown i Fi. 2a and the
reir ison in ig 2, We asserne hat s(n) in Fig. 2 in 920i
linear tev format, beeaase of direet 20-bit inpul to The Dar oF
beens of a Hci le Ln 20-ilinenr Peat eonversion thal bs been
performed within che sy.

"Tae aye elgorizhm can be persitioned inca chree hari pars see
Fig. 21: the adaptive uss quancizr, the diferencial predictor loop, and
the adaptive guin (tep-size) contol for che quantizer. We discuss
these operations in the sbove order since cis Is the order in which
‘hey mre compe,

2.3 Adaptive quanizer

A predicted value, (a) frst subtencte from the input signal st)
to form the aifenenoe signal

ein) =

(n) ~ pin a

‘The value of pn) ie obcained from the predictor and ie based on
computations performed atthe previous semple time, ~ 1

‘The differenoe signal e(n) is then quantized by the adaptive quan
Lue to proto the abpeM codeword Zn). This adaptive quantization
Is achieved ly fr sealing et to the range af «3-4 Fe le
‘Ste quantize? (see Fig. 2a. The slo! signal i denoted 23

en) @

whoro Vin} is an adaptive seale factor that is also determined from
Ant alle atthe previous sine Game a = 1 The eambination of
eallng by Pn) fallow hy the fae lepine quantize in vn
oa quantizer with an adaptively varying ctep-sie (which e inversely
proportional co Pin

Figure shows the characiorstis fora bit (love! fixed step-size
quantizer, ‘Tho input signal s(n} Ceonsisting of an ineyer plus 8
fraction part) ie converced to one of elgbe quancizeion levels in the
range ~7/2 to +7/2 corresponding respectively to integer coleworts
Toni inthe range —co+3."The output quantized signal ia denoted s
su) and is telaced co the code word Tin) by the relation
1550. THE RELL SYSTEN TECHNICAL JOURNAL, SEPTENBER 108
A similar quannercharseterinic ia urd ae he 4c (18 level) desig

The unsealed, decoded diferonce signal can be obtained from é."]
by rescaling ie by Aim), whore Ai) isinveroclyeclaced to Vin) and is
directly proportional fo the “stops” of the equivalent adepcive
‘auanczer Thus,

40) = atm -Asind «

ig 3 Quanner character for he .8¢ rw quan

‘ADPCM CODING 1661
is the adaptively quantized repreventaion of thesdiferenee signal ef).
"This completes the adaprive quantization par ofthe algorithm.
24 Fiatorder predictor
‘The sum of pln) and éin) also forms the edaptvely quantized
representation ofthe input signal (eee Fig. 22)
40a) = pin) + éimy o
However, the prodicter value p(n + {) and the quantizer cca factors
Bin + 1) and Ain + 1) rool tw The updated for the next sample ime
nel
"The new predictor value i cnnpaced at 8 tunes din}: Le
PIny Y= Bain,
where fis the predictor “leak” factor! A value of 2

Used for speech encoding. The value of pn + 1) is then stored for vse
st the next sample cme + 2

25 Aaaptnve stopiz0 conto!

‘The computation ofthe naw value of fn + 1) and Vin + 1) fo che
‘next tcwe supe mF 1 i none involved. The algorithm used here is
‘based on the robust step-ize adaptation approseh. The details and
sudvantages of this form of che algorithm are dioeuated in considerable
etal in Ref, (0 W, The method i a8 follows The sep-size referred
‘to above is th elective pacing inthe quantizer levela observed inthe
rinecnled quantized signal a(n). Since thie epacing is proportional to
‘im, we wll refer Lo Ain} in the following disussion as the step-ine

Tithe rout adaptation algriton, che neve step-size Siw + 1) is
chosen at

Bon +1) = caine, ©

"That init inthe old stepsize A(n) mised to tho power 7 (0 < y= 1,
ypieally y = 058) and sealed by a factor MC) which is afunetion of
the code word In). If che code word is one of the uppor mageitude
leeds ofthe quantizer [eg fn) = 4, 8,9, oF 3in Fig. 3}, a value of
1M.) greater than one is used to increase the stepsize of the quantizer
for the nextaample tim K'the codeword ie one ofthe lower magnitde
levels (eg, Ln) = ~2,—1, 0, Tit Fig. 3], w value of M(-) Toss than one
fs used to reduee the quantizer stepsie for the next sample time. Tn
this way, the algorithm continually attempts to adapt the step-size
szuch that the dynamic range of the adaptive quantizer is matched (o
‘he range of ce signal etn

‘A more direct approach for implementing chia algorithm is obtainod
by expressing eg (7) in logarithmic form. Let

1852 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1981
in) = logt din, ®

and
rmiTin)) = logit), °

hero the base of Uke logarithm is determined by the choice of
Parameters in the coder, as discussed ler. Then, eq, 7) becomes

din +1) = y-d00) + mitinn, 10)
and it has the form af fir-order difference equation, This isthe
‘equation that is implemented by the upper right-hand part of the
block diagram in Fig 23

‘The driving finetion m{Fln)) is » fetion ofthe code word Jin),
and i is determined in the adaptation logic lgortham which perforin
the funetion

Sifu 4 05] = 25,

forte quota nd
Se Reape or aa

forthe -bit quantizer
“The ontput ofthe step-sive eduptation lo i the signal dn), which
a, (8) shows as the logarichm of the desired siep-size
"Thus to obtain Ain} (and Pn}) we use implement the reac

en} = expidn (29)

and
1

ve
in)

expl—dtnh, 2)

where, epsin, the hate ofthe logarithms and exponentials in eg. (8 to
112) are determined by the ehoice of parameters i the coder, a
discusced ler:

"Tho exponentials in eqs. (124) and (12b) are computed by using
lookup tables that are stored in the program ox as idiated in Pig
24. The integer value of din) i caken Ant vunatesined to the Tange

2 [dn] < 32 for a lookup table siz of 66, Table offer vals are
then added to this value to produce Une appropriate wow allress
locations, The tables ere set up 80 chat value of dim) ~ 0 points to
tho conte of oth tables (9132) snl AII2D, Note tht the bracketed
values V[.] and 8 [-J in the table of Fig, 2a zefer to the contents of
Table loeations addressed by [:] and not uo sample times (hich are
"alered oly Une parenthesis notation Oo} ane Ain)

"The above algorithm nes Ot diferent steps valucs oF S(t) and

ADEM CODNG 1559
Vin) The table values are chosen to span the desired dynamic range
of the inpur signal, f signals of larger or smaller amplitude than this
fre encountered, the slap-size snrates at the upper or lower table
‘ales, respectively:

‘The table addiecs loeations are stored for use st the next sample
ima + 120 accem values re and Vin + 1) as they are newed,
"This completes the operation af the ADPCM encode,

26 Parameter selection for he stop-sie tables

‘The paramecers of the step-ize table wore chosen such that the
1atio of the maxitmim to init mep-sizes in the lable 258, ke,

yey 1] — 258 — 2

and
sven
‘This gives a step-siae adaptation range of 48 dB (# bite) that is
appropriate for speech roaling, Since there are 88 logaeithmically
Spaced stpvsne values in wach cable this vorrspords to a 0.7-€B8
‘resolution Le step-izes increase bya rtio of L080 in the cable,
AT alt -c.0902"
Sal = SIA -.09020-*"
"The maximum stepsize ia chosen thot che maximum range of
fa) tapprunitalcly 17 bits) azalee (a Che waximam quantizer range

{90rd its), This prevent overloading un Uve high end ofthe dynamic
ange, Thus fora bit quantizer

00 ow = A068

258

2

0 fam = 901) = 2%

ora bit quanciaer, values of af-] sould he mereasee by two ard
valius of F[-] should be deermased by txo for best dynamic range
performance

"The manner in which thes table values are sealed! and stored in the
‘gr will be explained more Tully i Section 3

12.7 Decoder or ADPCM

Figure 2b showsa simile block iggem forthe abpem decoder. The
ingnt ence word Jtn) is converted tothe decoded difference signal 1)
by adding 0 (nce Pie 8) and eesling the resll by Bin) The decoded
fnnput signal din} f Bie oitaned by accumulating valle én) inthe
predictor loop in the sane inenner ae in the encoder. ‘The new step

1594 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1981
size ie then computed ian exactly duplicaLe manner to that in the
encoder. Thus, the aurea decoder duplicales a subset of Une encorler
bel ingram.

1M, PROGRAMMING TECHNIQUES UTILIZED IN THE OSP FOR THE
‘ADPCM ALGORITHM

‘The apron algorithm, as it is configured above, is designed ao that
it can be convenienely implamented am the nar. We have already
‘alluded to ways in which the nse a uned in plement the algorithm.
In this section, we poine out some additional aspects of the program
snd discuss how same of the unique feature of the DSP are Used,
‘Diacussione in thie section wee the 4-bic lgorithon as an example

2.1 Memory uteaton

‘The eneuder program and the stepsie tables for Af-] and V[-] are
stared in wont oevupying approximately 170 words of memory. Five
Bax lications ave wud for storing the flowing values 20a} OS
2m), pla en) nel the newer version of en}, Aceas to che stp
sie Lables ina by setting Une RX register in Ue Dak to the eonter
tides of the desized rable. The cable adres for the appropriate
step-size is then obtained by secting the x register co the integer Value
[nt] iaized tothe venge ~22 to 31) and then incrementing RX by
‘the value x using the rsk command. The Wx regieer then contains the
os address for the eppropriece stepsize VJ. ‘The ase instructions
‘that implemen this technique are az follows:

“nate pine to i fled”
“aot rx pointer to C122)

“sat to int (in)
pp=nik's “pointer co eppropriato M-}"

[Nove sha dhs wchniqi only works for (le wines up wo 956, since the
sx register is limited to & bis,

3.2 Quantization

‘The commutation ofthe quantizer input, ein, is accomplished in a
seightloreard manner on the nar by wsing 9 subtraction and a
rmulipliation. The conversion from etn! to & hit integer Tin)
(according tothe quantizer characteristic in Fig 3) i dane by truncat-
ing the fretional part of etn)

“Assuming e( has boon corapuced and stored inthe wvosister and
1x is pointing tothe appropriate sap size, the following Ost instruc
tions compute F'n)

ADPCM CODING 1855
a=p ponies spite ei) = Ben ea
pHa pani mmpute gn) + 0"
pea, truncate to fren Foy

‘The truncation s echieved by using the cturaulatar control statement
a =p & 4, whieh performa sbit-hy-bit AND operation betersen the 7
tnd a repsters in the PsP. in) ie siored in the & register and Lie
(inary) number HLL «++ TELO ++» is staced in he P segs by Oh
inatruntion p = —TI"e fe = 2". The operation seems onthe fretines
Dart of (etn) + 113) and Ienwee the fnleger par until Ts
esl integer Pl) ithe vane tle range “R= Pn) 27
{foe-it quantization} ta form the desited codewnrd f(a). This ie dome
‘sing the sonlional a operation a shown in dhe allowing inmiruee
tions

po 8s
anpha | paite

a0) doa th “tein <a 8
acpta
uapta

if n> OF dow (i if oom > 9) Pood =
a=pta
u=pta eit Tin”

"This yields the 4-bit value Fin) in tho accumulator

3.3 Internat seating of data

At the output of the quantiver a value of 5 ig alded 10 Ten) (xe
Fig. 2 to produoe én), which is then mtipled hy Ai. Ta seve
pls this, dt) anurt be tranalerned from the roger Uo the.
rglster and the inp ofthe multiplier. Since chi transfer fom the A
rw register truncate the feactional pare af the sve in the &
gir, ib Fst sealed hy far of 2 laid Ue Lean af Te
fractional part. Thi arate factor of tro in eatried through the romp
Calon af St) fn She Block dagratn of Pig. 2

3.4 Scaling of stapsize table volves

‘The values scored in the step-ita tables in ROM. axe more conven
tently handled if they are acaled to be ess that? in munya. The
intereul sr arithmeticiseoch that I6-bitvaluee fom Rost areassumed
to have 1 fractional itn. Thier appropriate forthe inverse ecp-sze
tabla YL-Jin which aumbere(e(n) ina 17-bit range are wale town
fa dbit range ela). This able takes on values:

1555 THE BELL SYSIEM TECHNICAL JOURNAL, SEPTEMBER 1951