BSTJ 60: 4. April 1981: Subsampling of a DPCM Speech Channel to Provide Two "Self-Contained" Half-Rate Channels. (Jayant, N.S.)

4.7 MB·English

Subsampling of a DPCM Speech Channel
to Provide Two “Self-Contained”
Half-Rate Channels.

By N.S. JAYANT.
(Manure recatved November 12, 1980)

We consider the following channelsplling problem: itis required
to split a B-btsis speech-code sequence into two “self-contained”
‘BiB bits's components, either of which can be used to reproduce
‘acceptable speech; als, sf both components are available at a re
Ceicer, must be possible to repraduce speech with full B-bite/s
‘quality. We propose solution where for intresting value of B, the
Speech quality rewuling from halerate receptions approzimately
‘equals that from conventional fall-rate receptions at B72 bits. In
{he proposed solution, 1-kH2 spocch is sampled at 12 Az and
coded using tex or differentat Fes. ‘The output sequence of cude
itords i pit into odd. and even-word sequences, A ullrate receiver
luith access to both of the subchannels simply reconstitutes the output
Sequence prior to decoding, while a half rate receiver with only the
‘ed for even) subcharnel estimates the even (or odd) componente by
nearest neighbor interpolation.

4. TRODUCTION

‘The channel splitting problem deseribed inthe abstracts redefined
in Fig, 1. The receiving end of a speech communication system ix
supposed to operale in ether a fllzae or alf-zate mode deperiting
fom whether i hs availa vo it both or only one of the speech eub-
Channels, Respective qualities of speech reprodurian are denoted by
Qel Hand Qut2/2). The aonavlaiity of one subchannel sa good
‘model for certain types of tansmiion failure, examples of which ae
tigndl fring in mobile radio and speech sexment losses in packel
Baitching. With apmwiau forms of diversity reception, the second
Eubchannel willbe available with probnbility low te unity when the
fist subchannel isnot. ‘The channelspliting problem has been re

1
extinct le Enea geee daira tel cal a
Serene ih spent gay (hen os poe uf ecw
ear ta “omen ~

cently analyzed for communication aysteme apersting at rate-dstor.
tion limits with binary and Gaussian input signals!”

"The nontrivial nnture of the channel splitting problem can be ap
preciated through the simple example of a uniform quantizer By
combining two appropriately staggered F-bit quantizer (one of ther
‘8 midvie, the other a midteend), one ean resline an (+ I)-bit aster,
but noe a 22-bit ater. For fli-rate speech quality corresponding to
Sit quantization, component quantizers would each need "bit (aot
8/2 = 4 bit) resolution fr the combination to yield bit quality. Thu,
if the subchannels in Fig. 1-were simply uniform quantizers, and it
speech were atmpled at BKH, one woul need ora BObit/ quantizer
systema 0 that a fall-rate combination with 6t-kbiv/s quality can be
realized. By contrast, in te differential pulse code modulation (OPC31)
systom proposed in thia paper, the component receivers that combine
to give Gt-kbit/s qulity are indeed halé-bic rae, 32-kbic/8 systema
“Moreover, with an illustrative cencanco-lengthspoceh input, the all.
ate quali @u(2/2) will be ahown to exceed the fullzale quality
@(4/2) of « conventional urea syevem operating tt B/2 bit’ for
interesting values of B. The quality Qx (82 b/s) i quite aceaplable

S02 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1081
far speech communications although somewhat shore of toll quality
[Note once again that two uniform quantizers opereting st S2-kbit/s
(2 4 bits) ouch oan only give, im combination, 40-Kbit/s (Skike
Xf bite) quality, and not the desired Bt-Kbit/s quality. Similar argu
ments apply to lower bitrates us well

"The avstem of Fig. 1 is x pecinl ease of a communication scenario
‘hac ean be generalized to incite mune than two subchannels, and/or
‘ubchannela that are non-cual-rale.'The system of Pig. T can also be
regarded as a apeck sytnaetrial case of embecled coding with a
berarchy consisting of to equally significant subcodes, vin, she half=
rate sequaees

1 SUBSAMPLING AND INTERPOLATION

"The utility of subsampling and interpultion has heen demonstrated
recently in the context of speech packet losses; speech-encoder out-
Dus are parlitioned into odd-ample and even-saple systems which
fre tronamted a2 separa packets. Ta the event of & lost odd (or
fren) packet, the lore samples are extimated using nearest neighbor
interpolations involving wvailable even (or odd) samples. With the
tusual assumption of S2-KH epeech and @kHs sampling, the 12

sampling (at 4 KH) inplessevious aliasing effets, Iv thene eros
fave mitigated by’ an aduplive interpolation procedure where nearest
eto weighting coeltcients are varie follow speech statistic,
ds elected by appropriate cxira information in packet header.’ The
‘Stem realies cama improvements with packet ls probabilities
Up to about 10 peroent; bul a the component mostngr low peobabilice
tpproaches 100 percent, min the ebannelepiting problem, residual
tliesing occ ave ute unaccepeable, even with adaptive interpola

“Te abuve obvervation ha lod us to the notion of 12-kH sampling
for che problem of Hig, 1, With 12 subearpling. the half-supling rate
‘ll noe be GH, which burs out to e just adequate for the 32H
Smsch inputa in telephony. We lao considered 16-bH» sampling, but
this is lss prferable from the point of wew of quantization noise. In
GAKbIL/s decoding for example 4bit quantisation of 16-KHe spocch
produces more quantization moins than the 5-it quantizer that is
Dorsie with 12-KHe speech,

"A second advantage of 12 KF saenpling is that it permits nonedap-
tive interpolations; adaptive incerplations yielded nearzero gains
With 12:kHz speech, If KH is subsampled, it eannot be adequately
‘econeiguted by moniduplive interpolation even ifthe intorpolatin is
invoked with « probuhiity uch lees than 100 percent”

‘Waveform reconstructions in dhe hall hit-ate Melf-cample rate)

DPCM CHANNEL SPLITTING $03
systems of this paper aru decribed by
Gln) = Avuin 1) + Avan + 1),
Ava Ares. 0

‘The samples u(r) will be quanti pres prediction error samples
in general and more simply, they wil he quantized speech samples in
‘the special eate of nonpredictve, or nondfferential Po

tu, THE pPcM CODEC

Figure 2 shows block diagrams of fallrate and hall-rate DPCM
systems with fixed first-order predictors, In euch case, decoding is
defined by

00) fe hey — D+ gC, °
where q(n) is the quanti prodicilon error signal, and Ay i frt-
‘order predictor Inthe special cave of nondiferential ext (A: ~ 0),
‘9(n) is simply the quantized speech output

14) ou a(n ®

‘Subscripts M and Fin ig. 2 distinguish half and fll-rato versions of
yin) and gn).

cen fomgeea ie ares rant gE
wnt [gocme

fr a

o

2 ok Arama Conventional feat nc (8) Dozer prion
lira nce. a
In conteast wich well-known adaptive nec aystems whore tho
quantizer seep ste is adapted for every sample, tho present paper
tssumes system there the step size i adapted once for each bloc:
(of several ma duration), and held fixed forthe duration ofthe block"
‘A periodically updated, racher than instantaneously adaptive, quan-
zee is usod in anticipation of interpolavion procedures, which are
known from rocint experience to he unreliable when the sep size
exhibits sample-to-semple Nuetustion”

‘The periodically wlaptve quantize ae defined by a lock-apaciic
ep sae & that ie proportional to the root-mean-square value of
teneralized fiaeifference in the form

A lage = KCI Lx0n) ~ he-zt~ Uae 4a)
A Lage = K(RD-Ly(n) ~ hey — Vm (a)
with maximum nd minimum constraints
Baas = 28 Bain= KAR) 12) er

where [A(R], Ki(R)] are bit-ate-speciic constraints with euggested
alwos of (0.25, 108}, (083, OOF (0.58, 012] and [1.0, 0.18] for 5,4,
land 2.bic quanizersreqpectively. Te eubseripes AQF (4a) and AQB
(ab) refer to forward-adaptive and buckwart-adaplive proceiurs,
respective rms valoee in (4a) unl (4) are evaluated over the dueation
of t apooch block to be coded in AQF. and over the duration of the
‘mt recent decode speech block in AQB. The AQN procedure isleas
Cvctive becaune of mesch nonmationarcy os wall ax the effect of
‘quantization nce that ie present in the y(n) eaquenoe iw In (@b)
However, stepesie information in an AQR system need not be sepe
rately cranerited toa receiver itis inberently available inthe decoded
Hin} sequence. AQF procedures, by eonscart, require che explicit
transensson of tep-ize information (spically. about 5 bts worth per
‘lock of 16 ma)-In our experiments, quality lsses in AQB were more
noticeable in full- bit-rate spooch Unnn in halEbitrae speech and in
teach enze the losses were ofa sevond order ofimpertence. With thisin
mind we have elected to cite only AQF resulta in section IV; those
ress oan be regarded as upper bounds a far as quantizer perform
ance is concerned.

nthe context of 12 subsampling, the AQH procaure of (4h) cannot
bbe implemented ac cuch unless 4, = 0 (Pc3). However, step sizes
obtained by setting Ato zero in (4) have been found lo have fairly
tal effects on bpeM performance. Dierences between vcm-optimal
fand pecytoptiml step size are leas significant chan differences among
sep sizes of diferent epesch blocks Moreover, the anboptimality of
Powe-nutehed step aie becomes lees significant ay» "The next

DPCM CHANNEL SPLITTING 505
ction shows that hal bit-rate prea favor values off chat are indeed
‘much smaller than thooe appropriate for conventional fullate DPCM.

Iv, RESULTS AND CONCLUSIONS
Figures # through 6 Mlutrate the performance of the interpolation
procedure for the example uf a S-bil encoder. ‘The waveform segments
fr toto 20-me black fromm 9 12.KHs bandlimited, female utterance
ie chaivan cast threw votes” sampled at 12 KH,

Figure @sthowsfull-rate and interpolated q waveforms (Ay = 05) for
the two segments ic demonstrates that the nonadaptive interpolator
(a) is reasonably adequate even for che fast-varying unvoiced example.
‘This is confirmed in Fig. 4 which ahows corresponding fll-zate and
Ilsa » waveforms Notice thatthe hele-bit-rate output provides a
such bettar reproduction af the voiced segment, bat nevertheless
‘eagonably effective in unvoiced speech reproduction. Perceptually,

i

esd nl rae relied seen gr nd gn = 0 Hh
PELE Rapes Stata tar ae Se ee the pt

[506 THE GEL SYSTEM TECHNICAL JOURNAL, APRIL 1981
(dn waveform degradations inthe hal€-bit coder are indeed fatty able
for R~5,

"The sigaificance of fy ~ 0 ia demonstrated in Fig. 5, which shows
reat performance as a function of predicear coefficient value. The
‘objective quality meesure ured in the segmental signal-to-noiae ratio
Sos defined che average of 101 #/n (B)-vnkues mens ver
Ue cotiy uf 2m lock in be inp, Nove that maxinfzaton of
ful-tate and halérate quill for y =09 anh, = 0.9, respectively,
and notice also that these are aot very sharp msima, suggesting
flenibiity for pracieal implementations The apecal, simple ease of hy
=0 {pes lends to a noticenble quality degradation only for te ful
rate eratem,

‘Figure 6 dopicts the performance of fullate and ballrate nreu
receivers as funtion of ener bitrate, The performance curves (2)
fad Gi) ave for hy values that masienie hal-rate speech quality (2s

DPCM CHANNEL SPLITING 807
IES ea andre ti ste gue ada NE
5 for 5A hits /sample, hy = 0: for 32 bite/sample), The full ate
‘haractorstic shows the expected 6.dB-per-bit behavior, while the
hhalbitvete characters fal more gradually with decreasing
‘Both chaructristics tend to the expected OB limit for no transmis
sions (+ 0). The square dots in Fig 6 ropresent the performance of
1 fullsate receiver in a system designed to maximize full-ate speech
quality (y= 08 t0 09)

‘An important observation from Fig, 6s that for encoder bt ates in
‘he important range of 2 to 8 bits/sumple,

Qu(B/2) = QuIR/2: R= bile/eample @
‘Thin saggeat that che halBhitrnte qualities in the sobenmple-inter

scarf son dasa ons age et ha gay Pe re
{Gisremmseat o lte cde dined fo maxes ui
polate system are extremly gid result, considering the crucial
onsraint tha the Hilf hit-raeystema combine eval to veld the
full-tate performance Qr(). The approximate equality in (5) is borne
‘out very well in pereeplual wsscssnenits of Qo and Qr. In contrast to
(6), enalycical results in Refs, 1 snd 2 ee quite pessimistic. This
tifference in conclusions ie related to the fact that these analytical
results apply a the rate-distortion limit, while the bitrates in this
Paper are nowhere clos i the eatevistorton limit for pooch. In fu,
bur bitrates are ih enough chat there ie suficient redundancy lft in
te eader output to permit sabsampling and high-quality incerpola-

"The relative performance of the bell-bit-riy reeuiver diminishes
with incrensing hi rate, Clearly, as R— =, the quantization nove
contributions @ vanish, Qe =, and Qu tands to finite asymptotic
‘value that showe tho effect of nearert-neighbor interpotion noise.
Fisulls elaewhere® can be used to show that this ayimptoti va, for
a firsorder Markov signal example, is approximately given by the
fexpected value of 10 log [(2 + #2, (11/(1-~ Ra,(011 4B, where Rex)
fa Blockspeciic adjacent sample coreation in the speech input
200.

nally it woud be appropriate tn eaibeace che Qe and Qu values in
Fig. with well-known defritions of cllequslily and communications
‘quality near perfct ineligibility with eoliceable but not obstrusive
Alegradacion} Although siilations and conclusions have cencered on
fs eingle earlieried Goat inj, ie appemts chat fll-bit-rate DecM
Fealias taluaity fo H — Band 4 bite/sarpte and communications
‘wualiy for #3 ad? biby/ennple. The all wate rea receptions in
the proposed system apneic tll quality with A ~ 5 bica/sample and
Inaintem ond romirunicarions quality at A = 4 and 3 bites

REFERENCES

TAH 8 8 mg 2 ae Cis eine Deni
2 MRL PE am oe hn
eee Tika aaron
os Eee ee epi nt

DPCM CHANNEL SPLITTING 500