Bit interleaved coded modulation

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  • 1. Bit Interleaved Coded Modulation
    1
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Mridula Sharma
    February 28, 2011
  • 2. 2
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Outline
    • 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. Summary
  • 3
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Introduction
    • 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 BICM
  • 4
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Introduction
    • Wireless 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 symbols
  • 5
    Seminar on Signal Processing in Wireless Communications 2011
    Symbol Mapper
    Flat fading Channel
    Bit -Inter
    leaver
    Binary Encoder
    Bit Interleaved Coded Modulation
    Introduction
    • Purpose 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 symbol
    m-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)
  • 26. 7
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Gray 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 dmin
    Fig : 16QAM Symbol arrangement chart with Gray labeling
  • 28. 8
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Gray 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 bits
  • 9
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Set Partitioning
  • 32. 10
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Set 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 obtained
    Fig : 16QAM Symbol arrangement chart with Set Partitioning
  • 36. 11
    Seminar on Signal Processing in Wireless Communications 2011
    Building Blocks
    Bit Interleaved Coded Modulation
    • Encoder (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)
  • 12
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    System Model
    ENC
    π
    µ, χ
    pƟ(y|x)
    DEM
    π -1
    DEC
    Fig: Block diagram of transmission with coded modulation (CM) and bit-interleaved coded modulation (BICM). In the case of CM, πdenotes interleaving
    at the symbol level. In the case of BICM, π denotes interleaving at the bit level.
  • 43. 13
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Vector Channel Model
    • Consider 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 process
    pƟ(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 independent
  • 14
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Vector Channel Model
    • Large 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 in
    fading channels cannot be accounted for
    • Channel state depends on the input sequence
  • 15
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Coded Modulation
    • Non-uniform error correction to non-uniform symbol distances for multiphase/ multi-level modulation
    • 48. Digital modulation
    • 49. Error correction
  • 16
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Coded Modulation
    • Detection for CM: (assuming ideal interleaver)
    • 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|<∞,
    • 53. new average transition pdf: p(Y|X)= EƟ[pƟ(Y|X)]
  • 17
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Coded Modulation
    Fig : Configuration of an 8PSK modulator using coded modulation
    Fig : Configuration of an Ungerboeck coded modulator
  • 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
  • 56. 20
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Bit Interleaved Coded Modulation(Notation)
    • ĉ π (ĉ)  Break into sub-sequences, m-bits each  μ
    • 57. Interleaver, π : k  (k‘, i)
    • 58. li(x): ithbit of label Xϵ {0, 1}
    • 59. χib = { X ϵχ: li(X) = b}
  • 21
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Bit Interleaved Coded Modulation
    • Assuming Ideal Interleaving,
    • 60. ML detection: For each signal time k’, DEM produces 2m such metrics:
  • 22
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Bit Interleaved Coded Modulation(Simplified Bit Metrics)
    • Sub-optimal branch metrics can be obtained by the log sum approximation which is good as long as the sum in the LHS is dominated by a single term as typically occurs in channels with high SNR
    • 61. BICM Branch Metric:
  • 23
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Equivalent Channel Model
    • System can be seen as an equivalent parallel channel model
    Fig: Equivalent parallel channel model for BICM in the case of ideal interleaving
  • 62. 24
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Capacity
    • As with CM, BICM Capacity can be computed using a Monte Carlo integration
    Unlike CM, the capacity of BICM depends on how bits are mapped to symbols
  • 63. 25
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Capacity
  • 26
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Capacity
    • Also, b X CMY
    • 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
  • 67. 28
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Cut-off Rate
    • Cut-off Rate:
    • 68. Was important for comparing channels where finite complexity coding schemes were used
    • 69. Cut off Rate Ȓ oof the discrete-input continuous-output
    channel generated by a CM scheme
    , perfect CSI
    , no CSI
  • 70. 29
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Cut-off Rate
    • The cutoff rate of a BICM scheme can be obtained from the
    Bhattacharyya bound on the average bit-error probability Pb of the parallel channel model in the absence of coding
    • By considering the ML bit metrics with perfect CSI
    where B denotes the average Bhattacharyya factor of the BICM channel, with perfect CSI
  • 71. 30
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Cut-off Rate
  • 31
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoritic view of BICM: Cut-off Rate
    • Note: A single channel use of the BICM channel is equivalent to m-channel uses of a binary-input channel with average Bhattacharyya factor B
    • 73. Hence, cut-off rate Ȓ o for BICM: (resorting to Monte Carlo numerical integration for calculation)
    Ȓ o= m(1-log2(B+1))
  • 74. 32
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoretic view of BICM: Numerical results
    • Numerical results are presented for nonselective Rician fading channels (which encompass Rayleigh and AWGN as special cases)
    Y = g X ejɸ + N
    • N is a complex zero-mean Gaussian i.i.d. random vector with covariance
    • 75. gis a scalar complex fading gain
    • 76. ɸis the carrier phase, independent of X and g and uniformly distributed over [-π, π]
  • 33
    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 AWGN with coherent detection
  • 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
  • 78. 35
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Information-theoretic view of BICM: Numerical results
    • BICM is shown to be a more robust choice than CM
    • 79. No CSI: Choose χ to be N-ary orthogonal (N = 2m).
    Eg. Hadamard sequences.
  • 80. 36
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Error Probability Analysis
    • Symmetrization:
    • 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
    • 84. Assume U is known to the receiver
  • 37
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Error Probability Analysis
    • Assuming CSI
    • 85. c and ĉ denoting two distinct sequences stemming from
    the same state and merging after ɭ ≥ 1 trellis steps
    • Assume c and ĉ differ in d consecutive positions
    • 86. Pairwise Error Event: {cĉ}
    • 87. Pairwise Error Probability (PEP): P(cĉ)
    • 88. P(cĉ)= f (d, µ, χ)
  • 38
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Error Probability Analysis
    • Union Bound for linear binary codes:
    where WI(d) is the total input weight of error events at distance d
  • 89. 39
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Upper Bound on f (d, µ, χ)
    • Given earlier by Bhattacharyya Union Bound
    • 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
    • 93. Tight upper bound to the PEP of BICM for Rician fading channels with perfect CSI
  • 40
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    BICM with Iterative Decoding (BICM-ID)
    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
    Bitwise
    Interleaver
    Soft-Output Estimates
    of Coded Bits
  • 94. 41
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    BICM-ID
    • Converts a 2m ary signaling scheme into m independent parallel binary schemes
    • 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
    • 100. We want to maximize the minimum Euclidean distance between any two points in the possible phasor pairs for all the bits
  • 42
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    BICM-ID
    • Feeding back from decoder to demod can improve the performance of noncoherent M-FSK
    • 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
    • 104. Only need to update demod metrics during each iteration
  • 43
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    BICM in Orthogonal Frequency Division Mutiplexing (OFDM)
    • Employed in the WLAN standard IEEE 802.11a
    • 105. channel can be considered quasi-static and frequency-selective
    • Powerful, yet easily implementable scheme
    • channel coherence bandwidth is about the same like the Fourier transmission bandwidth
    • Random position of coded bits in the subcarrier symbols (assuming an ideal interleaver)
    • good performance of BICM in OFDM schemes
  • 44
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    BICM-OFDM
    h
    d
    c
    x
    FEC
    π
    Mod
    IFFT
    GI
    b
    DEC
    π-1
    Mod-1
    FFT
    GI-1
    Fig: System Model of an adaptive BICM-OFDM
    y
  • 106. 45
    Seminar on Signal Processing in Wireless Communications 2011
    802.11a Transmitter
    Bit Interleaved Coded Modulation
    • Channel encoder (error correcting coding) and QAM symbol mapper are connected through a bit interleaver
  • 46
    Seminar on Signal Processing in Wireless Communications 2011
    802.11a Receiver
    Bit Interleaved Coded Modulation
  • 107. 47
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Summary
  • 48
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    References
    [1] G. Caire, G. Taricco, E. Biglieri, “Bit-interleaved coded modulation”, IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927-946, May 1998
    [2] Martinez_et_al,“Bit-Interleaved Coded Modulation in the Wideband Regime“,2008
    [3] E. Zehavi, “8-PSK trellis codes for a Rayleigh channel”, IEEE Trans. Commun., vol. 40, pp. 873-884, May 1992
    [4] Bockelmann et al, “Efficient Coded Bit and Power Loading for BICM-OFDM“, IEEE 2009
    [5] Samahi et al, “Comparative Study for Bit-Interleaved Coded Modulation with Iterative Decoding”, 2009 Fifth Advanced International Conference on Telecommunications
  • 113. 49
    Seminar on Signal Processing in Wireless Communications 2011
    Bit Interleaved Coded Modulation
    Thank You!!!