Bit interleaved coded modulation

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Bit interleaved coded modulation

  1. 1. Bit Interleaved Coded Modulation<br />1<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Mridula Sharma<br />February 28, 2011<br />
  2. 2. 2<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Outline<br /><ul><li> Introduction
  3. 3. System Model: CM(Coded Modulation) and BICM (Bit Interleaved Coded Modulation)
  4. 4. Information-theoritical Framework and Results
  5. 5. Error Probability Analysis
  6. 6. BICM-ID
  7. 7. BICM-OFDM
  8. 8. Summary</li></li></ul><li>3<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Introduction<br /><ul><li> 1982: Ungerboeck: landmark paper on Trellis Coded Modulation (TCM)
  9. 9. highly efficient transmission of information over band-limited channels such as telephone lines
  10. 10. 1992: Zehavi: performance of coded modulation over Rayleigh fading channel can be improved
  11. 11. Bit-wise interleaving at the encoder output
  12. 12. Appropriate soft-decision metric as an input to Viterbi decoder
  13. 13. Modulation + Coding: Single entity for improved performance
  14. 14. Bit Interleaved Coded Modulation (BICM)
  15. 15. 1998: Caire: Information-theoritical view on BICM</li></li></ul><li>4<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Introduction<br /><ul><li>Wireless Fading Channels
  16. 16. Non-recursive non-Systematic Convolutional (NSC) code
  17. 17. Type of Serial Concatenated Code (SCC)
  18. 18. Coded bits are interleaved prior to modulation
  19. 19. increase the diversity order of TCM schemes
  20. 20. uses bit-interleavers for all the bits of a symbol
  21. 21. number of bit-interleavers equals to the number of bits assigned to one non-binary codeword
  22. 22. interleaved bits are collected into Gray labeled non-binary symbols</li></li></ul><li>5<br />Seminar on Signal Processing in Wireless Communications 2011<br />Symbol Mapper<br />Flat fading Channel<br />Bit -Inter<br />leaver<br />Binary Encoder<br />Bit Interleaved Coded Modulation<br />Introduction<br /><ul><li>Purpose of the bit-interleaver:
  23. 23. Disperse the burst errors and maximize the diversity order of the system
  24. 24. Uncorrelate the bits associated with the given transmitted symbol</li></ul>m-bits define a symbol<br />Due to the interleaving the input bits to the mapper are approx. independent<br />
  25. 25. 6<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Introduction<br />Binary<br />to M-ary<br />mapping<br />Binary<br />Encoder<br />Bitwise<br />Interleaver<br />M-ary-<br />modulator<br />Complex flat-fading <br />AWGN<br />Soft-In<br />Binary<br />Decoder<br />LLR<br />Bit Metric<br />Calculation<br />Receiver<br />front<br />end<br />Bitwise<br />Deinterleaver<br />Fig : BICM Overview<br />The combination of binary encoding, bitwise interleaving, and M-ary modulation<br />actually yields better performance in fading than symbol-wise interleaving and<br />trellis-coded modulation (Caire 1998)<br />
  26. 26. 7<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Gray Mapping<br /><ul><li> Let χ denote a signal set of size M=2m with a minimum Euclidean distance dmin
  27. 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</li></ul>Fig : 16QAM Symbol arrangement chart with Gray labeling<br />
  28. 28. 8<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Gray Mapping<br /><ul><li> Key component of a BICM system
  29. 29. Main Function: to produce an equivalent channel that has ʋ parallel, independent, memoryless binary channels
  30. 30. Each channel corresponds to a position in the label of a signal x ϵχ
  31. 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</li></li></ul><li>9<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Set Partitioning<br />
  32. 32. 10<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Set Partitioning<br /><ul><li> As proposed by Ungerboeck:
  33. 33. Errors for bit a1 can easily occur, because adjacent symbols of 8PSK will necessarily have different a1s
  34. 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. 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</li></ul>Fig : 16QAM Symbol arrangement chart with Set Partitioning<br />
  36. 36. 11<br />Seminar on Signal Processing in Wireless Communications 2011<br />Building Blocks<br />Bit Interleaved Coded Modulation<br /><ul><li>Encoder (ENC)
  37. 37. Interleaver π
  38. 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. 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. 40. Demodulator (DEM)
  41. 41. Branch Metric Deinterleaver π -1
  42. 42. Decoder (DEC)</li></li></ul><li>12<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />System Model<br />ENC<br />π<br />µ, χ<br /> pƟ(y|x)<br />DEM<br />π -1<br />DEC<br />Fig: Block diagram of transmission with coded modulation (CM) and bit-interleaved coded modulation (BICM). In the case of CM, πdenotes interleaving<br />at the symbol level. In the case of BICM, π denotes interleaving at the bit level.<br />
  43. 43. 13<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Vector Channel Model<br /><ul><li>Consider a vector channel characterized by a family of transition probability density functions (pdf) </li></ul>{ pƟ(Y|X) : Ɵ ϵ CM; X,Y ϵ CN }<br /><ul><li>Channel state Ɵ: stationary, finite memory random process</li></ul>pƟ(Y|X) = ∏k pƟk (Yk|Xk)<br /><ul><li>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</li></li></ul><li>14<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Vector Channel Model<br /><ul><li>Large number of typical communication channels can be represented
  44. 44. Additive White Gaussian Noise (AWGN) channel (Ɵ = constant)
  45. 45. AWGN channel with random phase (Ɵ is the residual phase due to imperfect carrier phase recovery)
  46. 46. Frequency nonselective slow-fading channels (Ɵ describes the multiplicative fading process)
  47. 47. But Inter-symbol Interference (ISI), or frequency selectivity in</li></ul>fading channels cannot be accounted for <br /><ul><li> Channel state depends on the input sequence</li></li></ul><li>15<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Coded Modulation<br /><ul><li>Non-uniform error correction to non-uniform symbol distances for multiphase/ multi-level modulation
  48. 48. Digital modulation
  49. 49. Error correction</li></li></ul><li>16<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Coded Modulation<br /><ul><li>Detection for CM: (assuming ideal interleaver)
  50. 50. Full channel state information (CSI): rule for the transmitted code sequence
  51. 51. No CSI: channel is not memoryless,
  52. 52. Also, assuming ideal interleaver: For any KϲƵ with |K|<∞,
  53. 53. new average transition pdf: p(Y|X)= EƟ[pƟ(Y|X)]</li></li></ul><li>17<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Coded Modulation<br />Fig : Configuration of an 8PSK modulator using coded modulation<br />Fig : Configuration of an Ungerboeck coded modulator<br />
  54. 54. 18<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Coded Modulation<br />Fig : Performance of coded modulation using convolutional code<br />
  55. 55. 19<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Bit Interleaved Coded Modulation<br />Binary Code Ĉ <br />ENC<br />μ<br />π<br />χ<br />Channel<br />
  56. 56. 20<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Bit Interleaved Coded Modulation(Notation)<br /><ul><li> ĉ π (ĉ)  Break into sub-sequences, m-bits each  μ
  57. 57. Interleaver, π : k  (k‘, i)
  58. 58. li(x): ithbit of label Xϵ {0, 1}
  59. 59. χib = { X ϵχ: li(X) = b}</li></li></ul><li>21<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Bit Interleaved Coded Modulation<br /><ul><li> Assuming Ideal Interleaving,
  60. 60. ML detection: For each signal time k’, DEM produces 2m such metrics:</li></li></ul><li>22<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Bit Interleaved Coded Modulation(Simplified Bit Metrics)<br /><ul><li>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. 61. BICM Branch Metric: </li></li></ul><li>23<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Equivalent Channel Model<br /><ul><li> System can be seen as an equivalent parallel channel model</li></ul>Fig: Equivalent parallel channel model for BICM in the case of ideal interleaving<br />
  62. 62. 24<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Capacity<br /><ul><li>As with CM, BICM Capacity can be computed using a Monte Carlo integration</li></ul>Unlike CM, the capacity of BICM depends on how bits are mapped to symbols<br />
  63. 63. 25<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Capacity<br /><ul><li>CM
  64. 64. BICM</li></li></ul><li>26<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Capacity<br /><ul><li> Also, b X CMY
  65. 65. Since, conditioned on X, Y and b are statistically independent, </li></ul>CCM ≥ CBICM<br />
  66. 66. 27<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Fig: CM and BICM capacity for 16QAM in AWGN<br />
  67. 67. 28<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Cut-off Rate<br /><ul><li>Cut-off Rate:
  68. 68. Was important for comparing channels where finite complexity coding schemes were used
  69. 69. Cut off Rate Ȓ oof the discrete-input continuous-output</li></ul>channel generated by a CM scheme<br />, perfect CSI<br />, no CSI<br />
  70. 70. 29<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Cut-off Rate<br /><ul><li>The cutoff rate of a BICM scheme can be obtained from the</li></ul>Bhattacharyya bound on the average bit-error probability Pb of the parallel channel model in the absence of coding<br /><ul><li>By considering the ML bit metrics with perfect CSI</li></ul>where B denotes the average Bhattacharyya factor of the BICM channel, with perfect CSI<br />
  71. 71. 30<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Cut-off Rate<br /><ul><li>Perfect CSI
  72. 72. No CSI</li></li></ul><li>31<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br /> Information-theoritic view of BICM: Cut-off Rate<br /><ul><li>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. 73. Hence, cut-off rate Ȓ o for BICM: (resorting to Monte Carlo numerical integration for calculation)</li></ul>Ȓ o= m(1-log2(B+1))<br />
  74. 74. 32<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Information-theoretic view of BICM: Numerical results<br /><ul><li>Numerical results are presented for nonselective Rician fading channels (which encompass Rayleigh and AWGN as special cases)</li></ul>Y = g X ejɸ + N<br /><ul><li> N is a complex zero-mean Gaussian i.i.d. random vector with covariance
  75. 75. gis a scalar complex fading gain
  76. 76. ɸis the carrier phase, independent of X and g and uniformly distributed over [-π, π]</li></li></ul><li>33<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Fig: BICM and CM cutoff rate versus SNR for QAM signal sets with Gray (or quasi-Gray) labeling over AWGN with coherent detection<br />
  77. 77. 34<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />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<br />
  78. 78. 35<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Information-theoretic view of BICM: Numerical results<br /><ul><li>BICM is shown to be a more robust choice than CM
  79. 79. No CSI: Choose χ to be N-ary orthogonal (N = 2m).</li></ul>Eg. Hadamard sequences.<br />
  80. 80. 36<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Error Probability Analysis<br /><ul><li> Symmetrization:
  81. 81. Time-varying labeling map: In the parallel channel model, to make the channelsymmetric
  82. 82. μ’ = compliment of μ
  83. 83. For each coded bit bi, let Uibe a binary random variable determining whether μ’ or μis used
  84. 84. Assume U is known to the receiver</li></li></ul><li>37<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Error Probability Analysis<br /><ul><li> Assuming CSI
  85. 85. c and ĉ denoting two distinct sequences stemming from</li></ul>the same state and merging after ɭ ≥ 1 trellis steps<br /><ul><li> Assume c and ĉ differ in d consecutive positions
  86. 86. Pairwise Error Event: {cĉ}
  87. 87. Pairwise Error Probability (PEP): P(cĉ)
  88. 88. P(cĉ)= f (d, µ, χ)</li></li></ul><li>38<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Error Probability Analysis<br /><ul><li> Union Bound for linear binary codes:</li></ul>where WI(d) is the total input weight of error events at distance d<br />
  89. 89. 39<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Upper Bound on f (d, µ, χ)<br /><ul><li>Given earlier by Bhattacharyya Union Bound
  90. 90. f (d, µ, χ) ≤ Bd
  91. 91. BICM Union Bound derived free of Bhattacharyya and Chernoff upper bounds
  92. 92. loose but provided basis for tight upper bounds
  93. 93. Tight upper bound to the PEP of BICM for Rician fading channels with perfect CSI</li></li></ul><li>40<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />BICM with Iterative Decoding (BICM-ID)<br />Binary<br />to M-ary<br />mapping<br />Binary<br />Encoder<br />Bitwise<br />Interleaver<br />M-ary-<br />modulator<br />Complex flat-fading <br />AWGN<br />Soft-In<br />Binary<br />Decoder<br />LLR<br />Bit Metric<br />Calculation<br />Receiver<br />front<br />end<br />Bitwise<br />Deinterleaver<br />Bitwise<br />Interleaver<br />Soft-Output Estimates<br />of Coded Bits<br />
  94. 94. 41<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />BICM-ID<br /><ul><li>Converts a 2m ary signaling scheme into m independent parallel binary schemes
  95. 95. First iteration - Gray labeling optimal here
  96. 96. Gray labeling has a lower number of nearest neighbors compared to SP - based labeling.
  97. 97. The higher the number of nearest neighbor the higher the chances for a bit to be decoded into wrong region
  98. 98. Second iteration
  99. 99. The soft information allows to confine the decision region into a pair of constellation points
  100. 100. We want to maximize the minimum Euclidean distance between any two points in the possible phasor pairs for all the bits</li></li></ul><li>42<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />BICM-ID<br /><ul><li> Feeding back from decoder to demod can improve the performance of noncoherent M-FSK
  101. 101. For M=16 and r=⅓ coding, the improvement is 0.7 dB in Rayleigh flat fading
  102. 102. The additional complexity is negligible
  103. 103. No extra iterations needed
  104. 104. Only need to update demod metrics during each iteration</li></li></ul><li>43<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />BICM in Orthogonal Frequency Division Mutiplexing (OFDM)<br /><ul><li> Employed in the WLAN standard IEEE 802.11a
  105. 105. channel can be considered quasi-static and frequency-selective</li></ul>• Powerful, yet easily implementable scheme <br /><ul><li>channel coherence bandwidth is about the same like the Fourier transmission bandwidth</li></ul>• Random position of coded bits in the subcarrier symbols (assuming an ideal interleaver)<br /><ul><li> good performance of BICM in OFDM schemes</li></li></ul><li>44<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />BICM-OFDM<br />h<br />d<br />c<br />x<br />FEC<br />π<br />Mod<br />IFFT<br />GI<br />b<br />DEC<br />π-1<br />Mod-1<br />FFT<br />GI-1<br />Fig: System Model of an adaptive BICM-OFDM<br />y<br />
  106. 106. 45<br />Seminar on Signal Processing in Wireless Communications 2011<br />802.11a Transmitter<br />Bit Interleaved Coded Modulation<br /><ul><li>Channel encoder (error correcting coding) and QAM symbol mapper are connected through a bit interleaver</li></li></ul><li>46<br />Seminar on Signal Processing in Wireless Communications 2011<br />802.11a Receiver<br />Bit Interleaved Coded Modulation<br />
  107. 107. 47<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Summary<br /><ul><li> BICM
  108. 108. system model
  109. 109. analyzed in information-theoritical framework
  110. 110. error probability analysis
  111. 111. BICM-ID
  112. 112. BICM-OFDM</li></li></ul><li>48<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />References<br />[1] G. Caire, G. Taricco, E. Biglieri, “Bit-interleaved coded modulation”, IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927-946, May 1998<br />[2] Martinez_et_al,“Bit-Interleaved Coded Modulation in the Wideband Regime“,2008 <br />[3] E. Zehavi, “8-PSK trellis codes for a Rayleigh channel”, IEEE Trans. Commun., vol. 40, pp. 873-884, May 1992<br />[4] Bockelmann et al, “Efficient Coded Bit and Power Loading for BICM-OFDM“, IEEE 2009<br />[5] Samahi et al, “Comparative Study for Bit-Interleaved Coded Modulation with Iterative Decoding”, 2009 Fifth Advanced International Conference on Telecommunications<br />
  113. 113. 49<br />Seminar on Signal Processing in Wireless Communications 2011<br />Bit Interleaved Coded Modulation<br />Thank You!!!<br />

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