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seminar on BICM
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Seminar on Signal Processing in Wireless Communications 2011
1
Bit Interleaved Coded Modulation
Bit Interleaved Coded Modulation
Mridula Sharma
February 28, 2011
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Outline• Introduction
• System Model: CM(Coded Modulation) and BICM (Bit
Interleaved Coded Modulation)
• Information-theoritical Framework and Results
• Error Probability Analysis
• BICM-ID
•BICM-OFDM
•Summary
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Introduction• 1982: Ungerboeck: landmark paper on Trellis Coded Modulation (TCM)
• highly efficient transmission of information over band-limited channels such as telephone lines
• 1992: Zehavi: performance of coded modulation over Rayleigh fading channel can be improved
• Bit-wise interleaving at the encoder output• Appropriate soft-decision metric as an input to Viterbi decoder
• Modulation + Coding: Single entity for improved performance
• Bit Interleaved Coded Modulation (BICM)
• 1998: Caire: Information-theoritical view on BICM
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Introduction•Wireless Fading Channels
• Non-recursive non-Systematic Convolutional (NSC) code
• Type of Serial Concatenated Code (SCC)
• Coded bits are interleaved prior to modulation
• increase the diversity order of TCM schemes
• uses bit-interleavers for all the bits of a symbol
• number of bit-interleavers equals to the number of bits assigned
to one non-binary codeword
• interleaved bits are collected into Gray labeled non-binary
symbols
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Introduction•Purpose of the bit-interleaver:
• Disperse the burst errors and maximize the diversity order of the system• Uncorrelate the bits associated with the given transmitted symbol
Binary Encoder
Bit -Interleaver
Symbol Mapper
Flat fading Channel
m-bits define a symbol
Due to the interleaving the input bits to the mapper are approx. independent
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Introduction
Fig : BICM Overview
The combination of binary encoding, bitwise interleaving, and M-ary modulationactually yields better performance in fading than symbol-wise interleaving andtrellis-coded modulation (Caire 1998)
BinaryEncoder
BitwiseInterleaver
Binaryto M-arymapping
M-ary-modulator
Soft-InBinary
Decoder
BitwiseDeinterleaver
LLRBit Metric
Calculation
Receiverfrontend
AWGN
Complex flat-fading
ku kc kc' ms )(ts
)(ta
)(tn
)(trrk'kku
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Gray Mapping• Let χ denote a signal set of size M=2m with a minimum Euclidean distance dmin
• A binary map µ= {0, 1} m χ is a Gray labeling for χ if for all i= 1……..m and bϵ {0, 1}, each x ϵ χ b
i has at most one z ϵ χ bi at
distance dmin
Fig : 16QAM Symbol arrangement chart with Gray labeling
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Gray Mapping• Key component of a BICM system
• Main Function: to produce an equivalent channel that has ʋ parallel, independent, memoryless binary channels
• Each channel corresponds to a position in the label of a signal x ϵ χ
• 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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Set Partitioning
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Set Partitioning• As proposed by Ungerboeck:
• Errors for bit a1 can easily occur, because adjacent symbols of 8PSK will necessarily have different a1s
• 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
• 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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Building Blocks• Encoder (ENC)
• Interleaver π
• Modulator, modeled by a labeling map μ and a signal set χ, i.e., a finite set of points in the complex N-dimensional Euclidean space CN
• A stationary finite-memory vector channel whose transition probability density function pƟ(y|x), x,y ϵ CN may depend on a vector parameter Ɵ
• Demodulator (DEM)
• Branch Metric Deinterleaver π -1
• Decoder (DEC)
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
System Model
Fig: Block diagram of transmission with coded modulation (CM) and bit-interleaved coded modulation (BICM). In the case of CM, π denotes interleavingat the symbol level. In the case of BICM, π denotes interleaving at the bit level.
ENC π µ, χ pƟ(y|x) DEM π -1 DEC
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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 processpƟ(Y|X) = ∏k pƟk (Yk|Xk)
• Finite Memory of Channel State Process : There exists an integer ʋ > 0 such that, for all r-tuples ʋ < k1 < . . . < kr and for all n-tuples j1 < . . . < jn < 0, the sequences (Ɵk1 ; . . . ; Ɵkr) and (Ɵj1 ; . . . ; Ɵjn) are statistically independent
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Vector Channel Model• Large number of typical communication channels can be represented
• Additive White Gaussian Noise (AWGN) channel (Ɵ = constant)• AWGN channel with random phase (Ɵ is the residual phase due to
imperfect carrier phase recovery) • Frequency nonselective slow-fading channels (Ɵ describes the
multiplicative fading process)
• But Inter-symbol Interference (ISI), or frequency selectivity infading channels cannot be accounted for
• Channel state depends on the input sequence
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Coded Modulation
•Non-uniform error correction to non-uniform symbol distances for multiphase/ multi-level modulation
• Digital modulation• Error correction
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Coded Modulation
• Detection for CM: (assuming ideal interleaver)• Full channel state information (CSI): rule for the transmitted code
sequence
• No CSI: channel is not memoryless, • Also, assuming ideal interleaver: For any K ϲ Ƶ with |K|<∞,
• new average transition pdf: p(Y|X)= EƟ[pƟ(Y|X)]
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Coded Modulation
Fig : Configuration of an 8PSK modulator using coded modulation
Fig : Configuration of an Ungerboeck coded modulator
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Coded Modulation
Fig : Performance of coded modulation using convolutional code
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Bit Interleaved Coded Modulation
Binary Code Ĉ ENC μπ
χ Channel
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Bit Interleaved Coded Modulation
Bit Interleaved Coded Modulation(Notation)
• ĉ π (ĉ) Break into sub-sequences, m-bits each μ
• Interleaver, π : k (k‘, i)
• li(x): ith bit of label X ϵ {0, 1}
• χib = { X ϵ χ: li(X) = b}
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Bit Interleaved Coded Modulation
• Assuming Ideal Interleaving,
• ML detection: For each signal time k’, DEM produces 2m such metrics:
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Bit Interleaved Coded Modulation(Simplified Bit Metrics)
• BICM Branch Metric:
• 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
Seminar on Signal Processing in Wireless Communications 2011
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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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Capacity
Unlike CM, the capacity of BICM depends on how bits are mapped to symbols
• As with CM, BICM Capacity can be computed using a Monte Carlo integration
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Capacity
• CM
• BICM
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Capacity
• Also, b X CM Y
• Since, conditioned on X, Y and b are statistically independent,
CCM ≥ CBICM
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Bit Interleaved Coded Modulation
Fig: CM and BICM capacity for 16QAM in AWGN
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Cut-off Rate
• Cut-off Rate: • Was important for comparing channels where finite
complexity coding schemes were used• Cut off Rate Ȓ o of the discrete-input continuous-output
channel generated by a CM scheme
, perfect CSI
, no CSI
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Cut-off Rate
• The cutoff rate of a BICM scheme can be obtained from theBhattacharyya 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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Information-theoritic view of BICM: Cut-off Rate
• Perfect CSI
• No CSI
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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
• Hence, cut-off rate Ȓ o for BICM: (resorting to Monte Carlo numerical integration for calculation)
Ȓ o= m(1-log2(B+1))
Seminar on Signal Processing in Wireless Communications 2011
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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
•g is a scalar complex fading gain• ɸ is the carrier phase, independent of X and g and uniformly distributed over [-π, π]
Seminar on Signal Processing in Wireless Communications 2011
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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
Seminar on Signal Processing in Wireless Communications 2011
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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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Information-theoretic view of BICM: Numerical results
• BICM is shown to be a more robust choice than CM
• No CSI: Choose χ to be N-ary orthogonal (N = 2m).Eg. Hadamard sequences.
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Error Probability Analysis
• Symmetrization:
• Time-varying labeling map: In the parallel channel model, to make the channel symmetric
• μ’ = compliment of μ
• For each coded bit bi, let Ui be a binary random variable determining whether μ’ or μ is used
• Assume U is known to the receiver
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Error Probability Analysis
• Assuming CSI
• 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
• Pairwise Error Event: {c ĉ }
• Pairwise Error Probability (PEP): P(c ĉ)
• P(c ĉ)= f (d, µ, χ)
Seminar on Signal Processing in Wireless Communications 2011
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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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Upper Bound on f (d, µ, χ)• Given earlier by Bhattacharyya Union Bound
• f (d, µ, χ) ≤ Bd
• BICM Union Bound derived free of Bhattacharyya and Chernoff upper bounds
• loose but provided basis for tight upper bounds
• Tight upper bound to the PEP of BICM for Rician fading channels with perfect CSI
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
BICM with Iterative Decoding (BICM-ID)
BinaryEncoder
BitwiseInterleaver
Binaryto M-arymapping
M-ary-modulator
Soft-InBinary
Decoder
BitwiseDeinterleaver
LLRBit Metric
Calculation
Receiverfrontend
AWGN
Complex flat-fading
ku kc kc' ms )(ts
)(ta
)(tn
)(trrk'kku
BitwiseInterleaverSoft-Output Estimates
of Coded Bits
kv'
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
BICM-ID• Converts a 2m ary signaling scheme into m independent parallel binary schemes
•First iteration - Gray labeling optimal here• Gray labeling has a lower number of nearest neighbors compared to SP -
based labeling.• The higher the number of nearest neighbor the higher the chances for a
bit to be decoded into wrong region
• Second iteration• The soft information allows to confine the decision region into a pair of
constellation points• We want to maximize the minimum Euclidean distance between any two
points in the possible phasor pairs for all the bits
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
BICM-ID
• Feeding back from decoder to demod can improve the performance of noncoherent M-FSK
•For M=16 and r=⅓ coding, the improvement is 0.7 dB in Rayleigh flat fading
•The additional complexity is negligible• No extra iterations needed• Only need to update demod metrics during each iteration
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
BICM in Orthogonal Frequency Division Mutiplexing (OFDM)
• Employed in the WLAN standard IEEE 802.11a • 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
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
BICM-OFDM
Fig: System Model of an adaptive BICM-OFDM
FEC π Mod IFFT GI
DEC π-1 Mod-1 FFT GI-1
bc x d
y
h
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
802.11a Transmitter
channelencoder
andpuncturer
QAMmapper iFFT
add cyclicextension(guard)
addtrainingsymbols
interpol.and filter,
limiter
bit interleaver
add pilotsymbols
D/A up-converter
amplifier
binary source
• Channel encoder (error correcting coding) and QAM symbol mapper are connected through a bit interleaver
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
802.11a Receiver
decimateandfilter
synchr.frequencycorrection FFT QAM
demapper
bit deinterleaver
de-punct.and
channeldecoder
down-converter
amplifier A/D
frequ.offset
estimator
channelestimator
andtracker
binary sink
pilotremoval
-1
Seminar on Signal Processing in Wireless Communications 2011
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Bit Interleaved Coded Modulation
Summary
• BICM
• system model
• analyzed in information-theoritical framework
• error probability analysis
• BICM-ID
• BICM-OFDM
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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
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Bit Interleaved Coded Modulation
Thank You!!!