The Theory and Technology of Error Control Coding

1. Chapter 6 OVCDM (OVCDMA) Technology with High Coding Gain & Spectral Efficiency The Theory and Technology of Error Control Coding

2. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

3. Background - 1 • Trends of wireless communications • Mobile broadbandization • Broadband mobilization • Ongoing 4G-related IMT-Advanced • One of the new standards proposed by ITUexpected 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.

4. 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 anovel 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)

5. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

6. OVCDM(OVCDMA) Technology • Multi-user information theory • Optimum CDM(CDMA) • Existed CDM(CDMA) schemes • Traditional Coding and Modulation • Essence ofOVxDM(OVxDMA) Technology • Comparison between OVCDM and CDM • Comparison between OVCDM and Natural Coding • OVCDM(OVCDMA) Coding • OVCDM(OVCDMA) Detection

7. Multi-user information theory • Channel Capacity C • C 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 (CDMA).

8. Optimum CDM(CDMA) • Parallel sub-encoded channels can share a channel capacity • Although the data rate of each encoded sub-channel can never be grater 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?

9. 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 coding 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 coding 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 coding gain

10. Existed CDM(CDMA) schemes - 2 • Drawbacks of Existed multiplexing (multiple access) schemes • Can never share but only distribute the channel capacity----limited efficiency • No coding gain or limited coding gain(CDMA). • Why? • No overlapping no coding gain! • In essential, the channel coding is just the weighted overlapping among adjacent data symbols

11. Traditional Coding and Modulation • Essence ofchannel coding • Offer a certain constraint relation  coding gain • Drawbacks: limited spectrum efficiency • Essence ofmodulation • Offer a certain constraint relation in one signal constellation  improved spectrum efficiency • Drawbacks: No coding gain; no Gaussion distribution • CM(Coded Modulation) • Offer both spectrum efficiency and coding gain • Drawbacks: with high spectrum efficiency, difficult design or large gap still exists compared with Shannon limit; no Gaussion distribution output

12. Essence ofOVxDM(OVxDMA) Technology • Weighted overlapping among adjacent data symbols • Overlapping  Coding constraint  Coding gain • Overlapping  Parallel transmission  Share channel capacity  Spectrum efficiency • White Gaussion output distribution • Overlapping could be employed in X- domain • X ~ Time, Frequency, Space, Code etc • Forming OVXDM ~ Overlapped X division Multiplex • Examples: OVTDM (X ~ Time), OVFDM (X ~ Frequency), OVSDM (X ~ Space), OVCDM (X ~ Code), OVHDM (X ~ Hybrid of Time, Frequency, Space, Code etc) • In fact, all OVXDM schemes could be called as OVCDM • Overlapping is Coding

13. Comparison between OVCDM and CDM - 1 • Traditional XDM ( X~ time, frequency space or others ) • Employing orthogonal or independent sub-channels

14. 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 symbol mapping relation; • no space for adding coding redundancy.

15. Comparison between OVCDM and Natural Coding • Traditional coding • Add redundancy to the data symbol sequences • Drawback: 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.

16. OVCDM(OVCDMA) Coding - 1 • Weighted overlapping among adjacent data symbols • White Gaussion output distribution • 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 complex value, such as PSK or QAM constellations • V is the output weighted symbol vector with N-tuple

17. OVCDM(OVCDMA) Coding - 2 • Special case: N = 1, K input cause 1 output, constraint length L.

18. OVCDM(OVCDMA) Coding - 3 • 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.

19. OVCDM(OVCDMA) Coding - 4 • 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!

20. OVCDM(OVCDMA) Coding - 5 • 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.

21. OVCDM(OVCDMA) Coding - 6 • All the existed modulation schemes like PAM, PM, QAM, etc. are all the special cases of linear OVCDM • Their input data are all binary {0, 1} • Their code constraint length are all L=1 • Their code matrix are all column ones, corresponding to:

22. 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 (maximum likelihood sequence decoding) method. • Considering MLSD complexity, suboptimal detection method may be employed, such as Sphere decoding method.

23. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

24. OVCDM design rules with code rate greater 1 • All the encoding tap polynomials should be relative 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 capability • The larger the code rate r=N/K the higher the spectral efficiency of the system.

25. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

26. Simulation Results - 1（AWGN） Code matrix： Input data set： Figure 1: K=2, N=1, L=3

27. Simulation Results - 2 （AWGN） Input data set： Code matrix： Figure 2: K=3, N=1, L=3

28. Simulation Results - 3 （AWGN） Input data set：QPSK

29. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

30. 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-OVCDMthat may offer near to Shannon limit performance at high spectral efficiency.

31. Turbo-OVCDM - 1 • Parallel or serial OVCDM  Turbo-OVCDM • Turbo Iterative mechanism: Good coding performance • OVCDM: high spectral efficiency • Interleaver: Construct Turbo mechanism • Serial Turbo-OVCDM model

32. Turbo-OVCDM - 2 • Serial Turbo-OVCDM Example:

33. Turbo-OVCDM - 3 • Turbo-OVCDM1: OVCDM1 OVCDM2

34. Turbo-OVCDM - 4 • Turbo-OVCDM2: OVCDM1 OVCDM2

35. Turbo-OVCDM - 5 • Decoding • Symbol-By-Symbol MAP algorithm for non-binary trellis

36. Turbo-OVCDM - 6 • Simulation results (AWGN) Symbol Interleaver length: 2400; Simulation bits number: 1e7bits

37. Turbo-OVCDM - 7 • Simulation results (Rayleigh) Symbol Interleaver length: 2400; Simulation bits number: 1e7bits Doppler: 460Hz Symbol Rate: 15kbps

38. Turbo-OVCDM - 8 • Turbo-OVCDM & Turbo-TCM (LTE)comparison

39. Outline • Background • OVCDM(OVCDMA) Technology • OVCDM design rules with code rate greater 1 • Simulation Results • Ongoing 4G-related R&D works • Conclusions • References

40. 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 efficiency • The 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

41. 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, Turbo codes, LDPC codes, Coded modulation etc; • All the multiplexing & multiple access schemes like CDM/CDMA, TDM/TDMA, 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 Gaussian • Overlapping can offer both coding gain and spectral efficiency

42. 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.