wireless mobile communication and transmission lab. the theory and technology of error control...

Wireless Mobile Communication and Transmission Lab.

The Theory and Technology of Error Control Coding

Chapter 6

OVCDM (OVCDMA) Technology with High Coding Gain & Spectral Efficiency

2/42Wireless Mobile Communication and Transmission Lab.

Outline

BackgroundBackgroundOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1Simulation ResultsOngoing 4G-related R&D worksConclusionsReferences


Background - 1

Trends of wireless communicationsMobile broadbandizationBroadband mobilization

Ongoing 4G-related IMT-AdvancedOne of the new standards proposed by ITU expected to be

completed in the year around 2010. For high mobility and worse propagation environment, A

peak date rate up to 100Mbps should be achieved;For low mobility and best propagation environment, A

peak date rate up to 1Gbps should be achieved.


Background - 2

There exists a huge contradiction between the explosive growing of radio traffic requirements and the extremely limited spectrum resources

Existed key techniques:MIMO, OFDM ： high spectral efficiency, low coding

gain;Turbo, LDPC, CM: high coding gain, low spectral efficiency

Questions? ： Any other new & better techenologies?

OVCDM is a novel multiplexing (multiple access) technology That may offer both high coding gain & spectral efficiency with code

rate > 1:Proposed by Prof. Daoben Li from Beijing University of Posts and

Telecommunications(BUPT)OVCDM (OVCDMA) — Overlapped Code Division Multiplexing

(Overlapped Code Division Multiple Access)


Outline

BackgroundOVCDM(OVCDMA) TechnologyOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1Simulation ResultsOngoing 4G-related R&D worksConclusionsReferences


OVCDM(OVCDMA) Technology

Multi-user information theory

Optimum CDM(CDMA)

Existed CDM(CDMA) schemes

Traditional Coding and Modulation

Essence of OVxDM(OVxDMA) Technology

Comparison between OVCDM and CDM

Comparison between OVCDM and Natural Coding

OVCDM(OVCDMA) Coding

OVCDM(OVCDMA) Detection


Multi-user information theory

Channel Capacity CC is the maximum date rate that can only be approached

and can never be exceeded. However, C is calculated under single-resource-single-

destination case. Multi-user information theory

More users can share a common channel, Parallel transmission is one of the key solutions for improving system capacity and spectral efficiency

Waveform division multiplexing (multiple access) is the only optimal alternative, as waveforms are usually generated by coding, people usually call it CDM CDM (CDMA).(CDMA).


Optimum CDM(CDMA)

Parallel sub-encoded channels can share a channel capacityAlthough the data rate of each encoded sub-channel can never be grate

r than C, the summation of them can be grater than C

The optimum CDM (CDMA) is the only way that may share the channel capacity.

The best encoded output distribution white Gaussian

Question: How about existed multiplexing (multiple access) schemes?


Existed CDM(CDMA) schemes - 1

Traditional CDM/CDMA In code domain by employing orthogonal codes with code rate<1 Can never share but only distribute the channel capacity

Traditional TDM/TDMA In time domain by employing different time slot Can never share but only distribute the channel capacity with completely no c

oding gain

Traditional FDM/FDMA/OFDM/OFDMA In frequency domain by employing different/orthogonal frequency slot Can never share but only distribute the channel capacity with completely no c

oding gain

Traditional SDMA In space domain by employing orthogonal or independent sub-spatial channels Can never share but only distribute the channel capacity with completely no c

oding gain


Existed CDM(CDMA) schemes - 2

Drawbacks of Existed multiplexing (multiple access) schemesCan never share but only distribute the channel ca

pacity----limited efficiencyNo coding gain or limited coding gain(CDMA).

Why?No overlapping no coding gain!No overlapping no coding gain!In essential, the channel coding is just the weighte

d overlapping among adjacent data symbols


Traditional Coding and Modulation

Essence of channel codingOffer a certain constraint relation coding gainDrawbacks: limited spectrum efficiency

Essence of modulationOffer a certain constraint relation in one signal constellatio

n improved spectrum efficiencyDrawbacks: No coding gain; no Gaussion distribution

CM(Coded Modulation)Offer both spectrum efficiency and coding gainDrawbacks: with high spectrum efficiency, difficult design

or large gap still exists compared with Shannon limit; no Gaussion distribution output


Essence of OVxDM(OVxDMA) Technology

Weighted overlapping among adjacent data symbolsOverlapping Coding constraint Coding gainOverlapping Parallel transmission Share channel capacity Sp

ectrum efficiency

White Gaussion output distribution Overlapping could be employed in X- domain

X ~ Time, Frequency, Space, Code etcForming OVXDM ~ Overlapped X division Multiplex Examples: OVTDM (X ~ Time), OVFDM (X ~ Frequency), OVSDM (X ~ S

pace), OVCDM (X ~ Code), OVHDM (X ~ Hybrid of Time, Frequency, Space, Code etc)

In fact, all OVXDM schemes could be called as OVCDMOverlapping is Coding


Comparison between OVCDM and CDM - 1

Traditional XDM ( X~ time, frequency space or others )

Employing orthogonal or independent sub-channels

X1 X X2 X3 X4 X X

1 2 3 4 Sub- slot

X


Comparison between OVCDM and CDM - 2

OVXDM ( X~ time, frequency space or others )

Overlapping among adjacent data symbols

Obviously, the system spectral efficiency will be higher

Drawbacks ： losing one-to-one sym

bol mapping relation;no space for adding co

ding redundancy.

A

B

X

C

D

E

F

G

H

I

J

K

X

X

X

X

X

X

X

X

X

X

A B C

+ + +

A B C

+ + -

A B C

+ - +

A B C

+ - -

A B C

- + +

A B C

- + -

A B C

- - +

A B C

- - -

Xs

Xs

Xs/

3

Xs/3

+

+

Xs


Comparison between OVCDM and Natural Coding

Traditional codingAdd redundancy to the data symbol sequencesDrawback: low spectrum efficiency

Is it real necessary to add redundancy to the adjacent data symbols ?not real necessary !“Overlapping between data symbols” is the

only necessary condition from information theory.


OVCDM(OVCDMA) Coding - 1

Weighted overlapping among adjacent data symbols White Gaussion output distribution

( , 1)

0

{[ ]}Min n L

T Tn n l l

l

F

V U B

F(•) is a monotonic function, When F(•) = •, OVCDM becomes a linear code B is weighted coefficient matrix with K row and L column U is the input symbols vector with K-tuple and the input symbols is any comple

x value, such as PSK or QAM constellations V is the output weighted symbol vector with N-tuple

0,

1,

1,

Tl

Tl

l

TK l

b

bB

b



Special case: N = 1, K input cause 1 output, constraint length L.

00b 1

0b 10Lb

串/并

...

01b 1

1b 11Lb

...

01Kb

11Kb

11

LKb

...... F



Is just a non-linear/linear vector convolution encoding model with coding rate:R = K/N

When K>N, R>1 ： This is the generalized overlapped code division multiplexing (OVCDM) scheme.



All the existed channel coding codes, e.g. block codes ( L=1, K<N ), convolution codes ( L>1, K<N ), TCM&CM, LDPC and Turbo codes are all the special case of OVCDM

LDPC codes refer to some block OVCDM;

Turbo codes refer to some concatenated OVCDMs + interleaver;

TCM & CM codes refer to some special non-linear OVCDM

However, the existed encoded output can’t be Gaussian.

With Gaussian output, the best OVCDM may offer much better performance than the existed channel coding schemes! Simulation results fully shown that!



Lots of nowadays multiplexing & multiple access schemes like TDM(TDMA), FDM(FDMA), OFDM(OFDMA), SDM(SDMA), MIMO can be looked upon as a special case of linear OVCDM with constraint length L=1 and code rate r>1.

The traditional CDM(CDMA) scheme is also a special case of linear OVCDM with code rate r<1. And each row of B is just the corresponding spread spectrum code of it.



All the existed modulation schemes like PAM, PM, QAM, etc. are all the special cases of linear OVCDMTheir input data are all binary {0, 1}

Their code constraint length are all L=1

Their code matrix are all column ones, corresponding to:

1: 1, 2, ,2 , 1,2,3,TK K PAM

/ ( 1) /: 1, , , , 1,2,3,Tj K j K Ke e K PM

2 / 2 2 / 2: 1,2, ,2 , , 2, , 2 , 2,4,TK Kj j j K QAM


OVCDM(OVCDMA) Detection

Obviously, if r>1, the system spectral efficiency will be higher, Why no one consider such coding?

Losing one-to-one symbol mapping relation;

No space for adding coding redundancy.

But it is only true in the symbol to symbol case, in the sequence to sequence case it is completely wrong!

OVCDM(OVCDMA) detection must use MLSD MLSD (maximum likelihood sequence decoding) (maximum likelihood sequence decoding) method.

Considering MLSD complexity, suboptimal detection method may be employed, such as Sphere decoding method.


Outline

BackgroundOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1OVCDM design rules with code rate greater 1Simulation ResultsOngoing 4G-related R&D worksConclusionsReferences


OVCDM design rules with code rate greater 1

All the encoding tap polynomials should be relative primerelative prime!

Such codes can never be found in “Finite field”, It can only be found in “complex field”;This is really the reason why OVCDM with be better

than traditional channel coding, Modulation, or Multiplex schemes etc.

For a given K,L and N, in general, The larger L, the larger free Euclidean distance of the

OVCDM code, the better the error correction capabilityThe larger the code rate r=N/K the higher the spectral

efficiency of the system.

( )kb x , 0,1,...., 1,k K


Outline

BackgroundOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1Simulation ResultsSimulation ResultsOngoing 4G-related R&D worksConclusionsReferences


Simulation Results - 1 （ AWGN ）

Figure 1: K=2, N=1, L=3

0 2 4 6 8 10 12 14 16 18 2010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

2*3 OVCDM复指数BPSK

{0,1}

0 0

2 4 2

B

Input data set：

Code matrix：



1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

信噪比(dB)

BPSK8PSK8QAM

OVCDM B3, 1OVCDM B3, 2

2 /3 2 /33,1 3,2

2 /3 2 /3

1 1 1 1

1 , 1

1 1 1

j j

j j

j j

j j e e

j e e

B BFigure 2: K=3, N=1, L=3

Input data set：

Code matrix：

{ 1, 1}



Input data set： QPSK


Outline

BackgroundOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1Simulation ResultsOngoing 4G-related R&D worksOngoing 4G-related R&D worksConclusionsReferences


Ongoing 4G-related R&D works

Insisting on employ OVCDM which may truly share the channel capacity. Giving up traditional CDMA which can only distribute the channel capacity.

Insisting on employ OVSDM which is independent on the propagation environment. Giving up traditional SDM and MIMO which can only distribute spatial channel capacity.

Giving up any channel coding, like Turbo, LDPC codes. Only employing Turbo-OVCDM that may offer near to Shannon limit performance at high spectral efficiency.


Parallel or serial OVCDM Turbo-OVCDMTurbo Iterative mechanism: Good coding performance OVCDM: high spectral efficiencyInterleaver: Construct Turbo mechanism

Serial Turbo-OVCDM model

OVCDM 1 OVCDM 2InterleaverS/P

... S/P

...

Turbo-OVCDM - 1


Turbo-OVCDM - 2

Serial Turbo-OVCDM Example:

Schemes K L Coding Matrix

I (4bps/Symbol)

OVCDM1 2 3

OVCDM2 2 2

II(6bps/Symbol)

OVCDM1 3 3

OVCDM2 2 2222

0.7804-1.0412j 0.2210+0.2089j

-0.2307-0.2372j -0.1091+0.3053j

B

122

0.5649+0.2366j 0.5202-0.3271j

0.0461+0.2945j -0.5486-0.9260j

B

2,1,4)1(

0,4,2)1(B

1

3123 s

s

214)1(

042)1(

008

B1

3123

s

s


Turbo-OVCDM - 3

Turbo-OVCDM1:

OVCDM1 OVCDM2


Turbo-OVCDM - 4

Turbo-OVCDM2:

OVCDM1 OVCDM2

Σ

0.7804-1.0412j 0.2210+0.2089j

-0.2307-0.2372j -0.1091+0.3053j

3( 1) 2S 4

1( 1) 4S 1 2

Σ&

F

S1

S2 S3

8


Turbo-OVCDM - 5

DecodingSymbol-By-Symbol MAP algorithm for non-binary trellis


Turbo-OVCDM - 6

Simulation results (AWGN)

0 1 2 3 4 5 6 7 8 9 1010

-5

10-4

10-3

10-2

10-1

100

EbNo( dB)

BE

R

Symbol Interleaver length: 2400;

Simulation bits number: 1e7bits


Turbo-OVCDM - 7

Simulation results (Rayleigh)

Symbol Interleaver length: 2400;

Simulation bits number: 1e7bits

Doppler: 460Hz

Symbol Rate: 15kbps

0 2 4 6 8 10 12 14 16 1810

-5

10-4

10-3

10-2

10-1

100

EbNo(dB)

BE

R


Turbo-OVCDM - 8

Turbo-OVCDM & Turbo-TCM (LTE)comparison

-1 0 1 2 3 4 5 6 7 8 910

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 (dB)

BE

R

AWGN channel, Spectrum efficiency: 4 bit/s/Hz

Turbo 1/2, 256QAM

Turbo-OVCDM, Yang2Shannon Limit


Outline

BackgroundOVCDM(OVCDMA) TechnologyOVCDM design rules with code rate greater 1Simulation ResultsOngoing 4G-related R&D worksConclusionsConclusionsReferences


Conclusions - 1

OVCDM(OVCDMA) is really a novel technology which can offer both coding gain and spectral efficiency:The larger the K/N, the higher the spectral efficiencyThe longer the L, the higher the coding gain

OVCDM can offer close to Shannon limit error correction capability even at high spectral efficiency

OVCDM is not only a channel coding scheme but also a multiple access or multiplexing one


Conclusions - 2

The special case of OVCDM All the modulation schemes like PAM, PM, QAM, etc.; All the channel coding schemes like Convolutional codes, block codes, Turb

o codes, LDPC codes, Coded modulation etc; All the multiplexing & multiple access schemes like CDM/CDMA, TDM/TD

MA, FDM/FDMA, OFDM/OFDMA, SDM/SDMA, MIMO, etc. ISI channel OVXDM (X ~ T, S, F and H)

Theoretically speaking , the performance of OVCDM will be better than the existed modulation schemes, channel coding schemes, multiplexing & multiple access schemes etc. OVCDM’s coding is beyond the “finite field” and the encoded output is Gaus

sian Overlapping can offer both coding gain and spectral efficiency


References

李道本，一种时间分割复用传输方法与技术， PCT 国际专利，申请号： PCT/CN2006/001585;

李道本，一种频率分割复用传输方法与技术， PCT 国际专利，申请号： PCT/CN2006/002012;

李道本，一种分组时间，空间，频率多地址编码方法， PCT 国际专利，申请号： PCT/CN2006/000947;

李道本，一种编码分割复用 ( 多地址 ) 传输方法与技术， PCT 国际专利申请号：PCT/CN2007/000308;

Hui Jiang, Daoben Li, A New Time Division Multiplexing Technique, IEEE WiCOM 2007, pp771~774

G. David Forney, Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference, IEEE Trans.Inform.Theory, May 1972.

P. Robertson and T. Won, Bandwidth-Efficient Turbo Trellis-Coded Modulation Using Punctured Component Codes, IEEE JSAC, Vol. 16, No. 2, Feb., 1998

Benedetto S., Divsalar D., Montorsi G., and Pollara F., (1996a). A Soft-Input Soft-Output MAP module to Decode Parallel and Serial Concatenated Codes, The Telecommunications and Data Acquisition Progress Report 42-127, Jet ropulsion Laboratory, Pasadena, California, November 15, pp. 1-20.

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