The document discusses Bit Interleaved Coded Modulation (BICM). It introduces BICM, which combines binary encoding, bitwise interleaving, and M-ary modulation to improve performance over fading channels compared to trellis coded modulation. It describes the system model of BICM, including the use of a binary encoder, bitwise interleaver, Gray mapping, and equivalent parallel channel model. It also discusses the information theoretical framework for analyzing BICM, including its capacity and cut-off rate.

1. Bit Interleaved Coded Modulation1Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationMridula SharmaFebruary 28, 2011

2. 2Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationOutline Introduction

3. System Model: CM(Coded Modulation) and BICM (Bit Interleaved Coded Modulation)

4. Information-theoritical Framework and Results

5. Error Probability Analysis

6. BICM-ID

7. BICM-OFDM

8. Summary3Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationIntroduction 1982: Ungerboeck: landmark paper on Trellis Coded Modulation (TCM)

9. highly efficient transmission of information over band-limited channels such as telephone lines

10. 1992: Zehavi: performance of coded modulation over Rayleigh fading channel can be improved

11. Bit-wise interleaving at the encoder output

12. Appropriate soft-decision metric as an input to Viterbi decoder

13. Modulation + Coding: Single entity for improved performance

14. Bit Interleaved Coded Modulation (BICM)

15. 1998: Caire: Information-theoritical view on BICM4Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationIntroductionWireless Fading Channels

16. Non-recursive non-Systematic Convolutional (NSC) code

17. Type of Serial Concatenated Code (SCC)

18. Coded bits are interleaved prior to modulation

19. increase the diversity order of TCM schemes

20. uses bit-interleavers for all the bits of a symbol

21. number of bit-interleavers equals to the number of bits assigned to one non-binary codeword

22. interleaved bits are collected into Gray labeled non-binary symbols5Seminar on Signal Processing in Wireless Communications 2011Symbol MapperFlat fading ChannelBit -InterleaverBinary EncoderBit Interleaved Coded ModulationIntroductionPurpose of the bit-interleaver:

23. Disperse the burst errors and maximize the diversity order of the system

24. Uncorrelate the bits associated with the given transmitted symbolm-bits define a symbolDue to the interleaving the input bits to the mapper are approx. independent

25. 6Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationIntroductionBinaryto M-arymappingBinaryEncoderBitwiseInterleaverM-ary-modulatorComplex flat-fading AWGNSoft-InBinaryDecoderLLRBit MetricCalculationReceiverfrontendBitwiseDeinterleaverFig : BICM OverviewThe combination of binary encoding, bitwise interleaving, and M-ary modulationactually yields better performance in fading than symbol-wise interleaving andtrellis-coded modulation (Caire 1998)

26. 7Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationGray Mapping Let χ denote a signal set of size M=2m with a minimum Euclidean distance dmin

27. A binary map µ= {0, 1} m  χis a Gray labeling for χ if for all i= 1……..m and bϵ {0, 1}, each x ϵχ bi has at most one z ϵχ bi at distance dminFig : 16QAM Symbol arrangement chart with Gray labeling

28. 8Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationGray Mapping Key component of a BICM system

29. Main Function: to produce an equivalent channel that has ʋ parallel, independent, memoryless binary channels

30. Each channel corresponds to a position in the label of a signal x ϵχ

31. For each codeword at the output of the binary encoder, the interleaver assigns at random a position in the label of the signals to transmit the coded bits9Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationSet Partitioning

32. 10Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationSet Partitioning As proposed by Ungerboeck:

33. Errors for bit a1 can easily occur, because adjacent symbols of 8PSK will necessarily have different a1s

34. If a1 is assumed to be correct, then a2 changes every other symbol of 8PSK and a symbol distance the same as that of QPSK will be obtained

35. If a1 and a2 are assumed to be correct, then a3 can be determined if a decision can be made as to which diagonal symbol has been received, and a symbol distance the same as that of BPSK will be obtainedFig : 16QAM Symbol arrangement chart with Set Partitioning

36. 11Seminar on Signal Processing in Wireless Communications 2011Building BlocksBit Interleaved Coded ModulationEncoder (ENC)

37. Interleaver π

38. Modulator, modeled by a labeling map μand a signal set χ, i.e., a finite set of points in the complex N-dimensional Euclidean space CN

39. A stationary finite-memory vector channel whose transition probability density function pƟ(y|x), x,y ϵCN may depend on a vector parameter Ɵ

40. Demodulator (DEM)

41. Branch Metric Deinterleaver π -1

42. Decoder (DEC)12Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded ModulationSystem ModelENCπµ, χ pƟ(y|x)DEMπ -1DECFig: Block diagram of transmission with coded modulation (CM) and bit-interleaved coded modulation (BICM). In the case of CM, πdenotes interleavingat the symbol level. In the case of BICM, π denotes interleaving at the bit level.

43. 13Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded Modulation Vector Channel ModelConsider a vector channel characterized by a family of transition probability density functions (pdf) { pƟ(Y|X) : Ɵ ϵ CM; X,Y ϵ CN }Channel state Ɵ: stationary, finite memory random processpƟ(Y|X) = ∏k pƟk (Yk|Xk)Finite Memory of Channel State Process : There exists an integer ʋ> 0 such that, for all r-tuplesʋ < k1 < . . . < krand for all n-tuplesj1 < . . . < jn < 0, the sequences (Ɵk1 ; . . . ; Ɵkr) and (Ɵj1 ; . . . ; Ɵjn) are statistically independent14Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded Modulation Vector Channel ModelLarge number of typical communication channels can be represented

44. Additive White Gaussian Noise (AWGN) channel (Ɵ = constant)

45. AWGN channel with random phase (Ɵ is the residual phase due to imperfect carrier phase recovery)

46. Frequency nonselective slow-fading channels (Ɵ describes the multiplicative fading process)

47. But Inter-symbol Interference (ISI), or frequency selectivity infading channels cannot be accounted for Channel state depends on the input sequence15Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded Modulation Coded ModulationNon-uniform error correction to non-uniform symbol distances for multiphase/ multi-level modulation

48. Digital modulation

49. Error correction16Seminar on Signal Processing in Wireless Communications 2011Bit Interleaved Coded Modulation Coded ModulationDetection for CM: (assuming ideal interleaver)