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 Modulation 1 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Mridula Sharma February 28, 2011

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

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)

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

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 symbol Due to the interleaving the input bits to the mapper are approx. independent

25. 6 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Introduction Binary to M-ary mapping Binary Encoder Bitwise Interleaver M-ary- modulator Complex flat-fading AWGN Soft-In Binary Decoder LLR Bit Metric Calculation Receiver front end Bitwise Deinterleaver Fig : BICM Overview The combination of binary encoding, bitwise interleaving, and M-ary modulation actually yields better performance in fading than symbol-wise interleaving and trellis-coded modulation (Caire 1998)

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

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

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

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

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)

48. Digital modulation

50. Full channel state information (CSI): rule for the transmitted code sequence

51. No CSI: channel is not memoryless,

52. Also, assuming ideal interleaver: For any KϲƵ with |K|<∞,

54. 18 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Coded Modulation Fig : Performance of coded modulation using convolutional code

55. 19 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Bit Interleaved Coded Modulation Binary Code Ĉ ENC μ π χ Channel

57. Interleaver, π : k  (k‘, i)

58. li(x): ithbit of label Xϵ {0, 1}

65. Since, conditioned on X, Y and b are statistically independent, CCM ≥ CBICM

66. 27 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Fig: CM and BICM capacity for 16QAM in AWGN

68. Was important for comparing channels where finite complexity coding schemes were used

69. Cut off Rate Ȓ oof the discrete-input continuous-outputchannel generated by a CM scheme , perfect CSI , no CSI

73. Hence, cut-off rate Ȓ o for BICM: (resorting to Monte Carlo numerical integration for calculation)Ȓ o= m(1-log2(B+1))

75. gis a scalar complex fading gain

77. 34 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Fig: BICM and CM cutoff rate versus SNR for QAM signal sets with Gray (or quasi-Gray) labeling over Rayleigh fading with coherent detection and perfect CSI

79. No CSI: Choose χ to be N-ary orthogonal (N = 2m).Eg. Hadamard sequences.

81. Time-varying labeling map: In the parallel channel model, to make the channelsymmetric

82. μ’ = compliment of μ

83. For each coded bit bi, let Uibe a binary random variable determining whether μ’ or μis used

86. Pairwise Error Event: {cĉ}

87. Pairwise Error Probability (PEP): P(cĉ)

90. f (d, µ, χ) ≤ Bd

91. BICM Union Bound derived free of Bhattacharyya and Chernoff upper bounds

92. loose but provided basis for tight upper bounds

95. First iteration - Gray labeling optimal here

96. Gray labeling has a lower number of nearest neighbors compared to SP - based labeling.

97. The higher the number of nearest neighbor the higher the chances for a bit to be decoded into wrong region

98. Second iteration

99. The soft information allows to confine the decision region into a pair of constellation points

101. For M=16 and r=⅓ coding, the improvement is 0.7 dB in Rayleigh flat fading

102. The additional complexity is negligible

103. No extra iterations needed

108. system model

109. analyzed in information-theoritical framework

110. error probability analysis

111. BICM-ID

113. 49 Seminar on Signal Processing in Wireless Communications 2011 Bit Interleaved Coded Modulation Thank You!!!