Iterative Equalisation and Forward Error Correction

Transcription

1 EHRSTUHL FÜR Prof. Dr.-Ing. R. Urbansky ACHRICHTENTECHNIK Iterative Equalisation an Forwar Error Correction R. Urbansky University of Kaiserslautern, Germany, Communications Engineering ECOC 9, Workshop DSP & FEC: Towars the Shannon Limit, September, 9, Vienna

2 Outline FEC, Viterbi Equalisation an Capacity Turbo Equalisation (TE) Low-Density Parity-Check (LDPC) Coes an TE Equalisation an FEC in OFDM Systems R. Urbansky

3 Fibre-Optical Transmission System Moulator OA FEC a Pulse former x(t) - Moulation format - Optical power - Chirp - Extinction ratio Transmission fibre - Polarisation moe ispersion (PMD) - Chromatic ispersion (CD) - Kerr non-linearity Gb/s Gb/s BER < -6 Receiver - Gain - Noise figure OA ^ FEC ^ a Equaliser & Detector Electrical filter - OSNR Optical filter Electronic signal processing r (t) B el - Direct etection. B opt - Receive power Chromatic ispersion (CD) group velocity ispersion (GVD) Polarisation moe ispersion (PMD) ifferential group elay (DGD) Amplifie spontaneous emission (ASE) noise an other noise Self phase moulation (SPM) an cross phase moulation (XPM) noise R. Urbansky 3

4 Forwar Error Correction (FEC) Coing Error Control Coes systematic / non systematic linear / non-linear Concatenate Coes non-cyclic Block-Coes cyclic Convolutional Coes non-recursive recursive BCH x BCH RS x RS RS x CC serial con.cc parallel con. CC = Turbo Coes LDPC-Coes BCH-Coes RS-Coes puncture CC Net coing gain (NCG) for coe rate BER= -6 First generation FEC: RS(55,39): NCG = 6.3 B RS(7,55): NCG = 8. B Concatenate coes: RS(55,45) x RS(46, 4): NCG = 9.B BCH(4, 93) x BCH(386,384): NCG = 9.3B BER FEC performance, R=.93, AWGN channel uncoe Stanar RS GF( 8 ) RS GF( ) RS-RS LDPC (bit.flip) BCH-BCH LDPC ( bits,soft) LDPC coes: LDPC(364,3595), har, bit-flip: NCG = 8.B LDPC (364,3595), soft, Sum Pro.Alg.: NCG = 9.7B E s /N / B R. Urbansky 4

5 System Concept I Stanar equalisation an ecoing: separate FEC ecoing an equalisation for channel ispersion suboptimum receiver RS FEC Dispersive n Suboptimum Receiver ^ RS Viterbi Equaliser R. Urbansky 5

6 System Concept II Stanar equalisation an ecoing: separate FEC ecoing an equalisation for channel ispersion suboptimum receiver Optimum equalisation an ecoing: over-all maximum-likelihoo ecoing of combine FEC an ispersion coe too complex for implementation at Gb/s Gb/s an BER < -6 Combine FEC & Dispersion Coe T T T h(t, CC Dispersion n ^ Optimum Receiver Over-all Maximum-Likelihoo of Combine FEC & Dispersion Coe R. Urbansky 6

7 System Concept III Stanar equalisation an ecoing: separate FEC ecoing an equalisation for channel ispersion suboptimum receiver Optimum equalisation an ecoing: over-all maximum-likelihoo ecoing of combine FEC an ispersion coe too complex for implementation at Gb/s Gb/s an BER < -6 Approach: iterative equalisation an ecoing = Turbo Equalisation (TE) - puncture convolutional coe (CC) - low-ensity parity-check (LDPC) coe emaning for BER << -4 CC / LDPC Turbo ISI n Turbo Equaliser ^ MAP - SSE Equaliser MAP - SSE R. Urbansky 7

8 System Concept IV Stanar equalisation an ecoing: separate FEC ecoing an equalisation for channel ispersion suboptimum receiver Optimum equalisation an ecoing: over-all maximum-likelihoo ecoing of combine FEC an ispersion coe too complex for implementation at Gb/s Gb/s an BER < -6 Approach: iterative equalisation an ecoing = Turbo Equalisation (TE) - puncture convolutional coe (CC) - low-ensity parity-check (LDPC) coe TE with outer Ree-Solomon (RS) coe RS Outer Enc. Outer Dec. CC / LDPC Turbo ISI Turbo Equaliser n outer coe rate R RS.93 inner coe rate R TE.97 total coe rate R = R TE R RS.9 ^ RS MAP - SSE Equaliser MAP - SSE R. Urbansky 8

9 Performance Bouns of a Simplifie DGD Moel Linear approximation of DGD cannel, /T : impulse response (T space) accoring to [*] (worst-case channel moel) h cos 4, cos 4, cos 4 T T T with chi-square noise [*] Jäger, Speiel, Bülow et al., JLT, vol. 4, pp.6-35, Mar. 6 Mutual information I(X;Y) to calculate performance bouns inepenent of equaliser implementation Entropy H(X) Equivocation H(X Y) X Irrelevance H(Y X) Coing Theorem: for quasi error free ecoing, an FEC coe is require with overall coe rate R I(X;Y) Mutual information I(X;Y) Y H(Y) OSNR penalty / = h(t, ) t / T T R. Urbansky 9 T h(t, ) I(X;Y)=.9, performance boun.5 / T.5 Chi-square noise OSNR penalty normalise to =, I(X;Y) =.9 unachievable penalty region ue to channel capacity limits for NRZ signaling an irect etecte DGD channels / T.5.5

10 Viterbi Equalisation Using Outer FEC Coe Maximum Likelihoo Sequence Estimation (MLSE) = Viterbi equaliser (VE) Probabilistic channel moel use for metric calculation f r( t) a,..., f r( t ) a L estimation by aaptive histogram methos w b Viterbi Equaliser 3 B, B, B, B, B, B, Signal Processing Unit B, B, B, B 3, B 3, B 3, Upate q + + Sequence Sequence Estimation Estimation log(pr( w b)) Probability Estimation â L w RS Discrete Time Noisy DGD ADC q bits Branch Metrics Look-Up Table â = arg max Pr( b=a w) b A RS Outer RS(55,39) coe for BER=-6 VE (4 states), q=4 bit ADC, T-space log-likelihoo lookup-table, histogram-base aaptation Gap to mutual information boun: 6 B OSNR penalty / = OSNR penalty normalise to =, I(X;Y) =.9 MLSE, RS(55,39) I(X;Y)=.9, performance boun unachievable penalty region ue to channel capacity limits for NRZ signaling an irect etecte DGD channels / T B R. Urbansky

11 Turbo Equalisation with Puncture Convolutional Coe (CC) RS Outer Enc. k ck Transmitter Interleaver ak Dispersive Turbo Equaliser MAP-SSE Equaliser Deinterleaver MAP-SSE - ( a ) E ( a k ) ( c k k ) ( a ) Soft-input / soft-output maximum a-posteriori symbol-by-symbol estimator (MAP-SSE) Feeback of extrinsic information (estimate symbol reliabilities excluing a-priori information) Remove correlations: interleaver, einterleaver - = pseuo-ranom permutation of bit positions yk n k rk Interleaver D k ˆk RS Outer Dec. ^ BER - -4 Convergence of iterations Turbo. Iter. Turbo. Iter. Turbo 4. Iter Turbo 8. Iter. Turbo. Iter. MLSE OSNR penalty normalise to =, I(X;Y) =.9 MLSE, RS(55,39) CC TE,RS(55,47) ( ; )=.9, performance boun.3 B OSNR / B unachievable penalty region ue to channel capacity limits for NRZ signaling an irect etecte DGD channels /.5.5 R. Urbansky

12 TE with Low-Density Parity-Check (LDPC) Coes u T ch Block coing c = ug r Parity-check matrix H variable noes check noes Tanner graph Block coe efine by sparse parity-check matrix or by Tanner graph Near Shannon limit performance for large coes (n >> ) Soft-ecision soft-input ecoing algorithms: Belief Propagation, Sum-Prouct,... Arbitrary coe rate, coe esign tools, efficient encoers,... LDPC coes combine with equalisation TE BER performance, R =.5, n = 6, AWGN channel Shannon limit Irregular LDPC coe Turbo coe Regular LDPC coe E b /N / B Richarson, Shokrollahi, Urbanke, IEEE Trans. Inform. Theory, Feb. R. Urbansky

13 Gap to Capacity Limit OSNR penalty / = OSNR penalty normalise to =, I(X;Y) =.9 MLSE,4 bits, RS(55,39) MLSE, unq., RS(55,39) CC TE,4 bits, RS(55,39) CC TE, unq.,rs(55,47) LDPC TE, unq., RS(55,39) IX;Y)=.9, performance boun unachievable penalty region ue to channel capacity limits for NRZ signaling an irect etecte DGD channels.5.5 / T 3.4 B.9 B.4 B Typical OSNR gap to channel capacity MLSE + RS(55,47): B CC-TE + RS(55,47):.8.8 B LDPC-coe TE + RS(55,47):.9.5 B LDPC-coe TE + RS(7,636):.7.3 B R. Urbansky 3

14 Approach: Coherent Detection an OFDM Optical Orthogonal Frequency Division Multiplexing (OFDM) u C M - QAM S/P IFFT P/S CP DAC s I (t), s Q (t) I/Q-Mo. x4 9 hybri û C - LLR Demapping S/PFFT EQP/S CP ADC r I (t), r Q (t) Parallel transmission by a large number of OFDM sub-carriers (64...4) Coherent system; frequency an channel estimation by pilot symbols Multi-level moulation (M - QAM) Polarisation multiplex (PolMUX) R. Urbansky 4

15 MIMO Optical OFDM an Equalisation Polarisation multiplex = x multiple input / multiple output (MIMO) system Bit interleave coe moulation (BICM) on OFDM sub-carriers BICM Outer u C Mapping x y S/P IDFT P/S CP DAC s I (t), s Q (t) BICM Iterative Demapping POL MUX I/Q- Mo. Pol MUX Pol MUX Pol MUX x4 9 hybri BER< -6 BER< -3 Outer û C - LLR Demapping r S/P MIMO EQ EQ DFT P/S CP ADC PMD: MIMO receiver = x matrix per sub-carrier CD: DCF, OFDM pre-istortion or OFDM equaliser QAM: Iterative emapping an ecoing of BICM Performance limitation by SPM/XPM an ASE noise, loss ue to guar interval R. Urbansky 5

16 Conclusions capacity constraints: OSNR penalty TE outperforms Viterbi equalisation an ecoing About B gap to mutual information limit Approach to ecrease mutual information limit: - coherent technique - multi-level moulation - polarisation multiplex - optical OFDM References: - W. Sauer-Greff an R. Urbansky, "Iterative Equalization an FEC Decoing in Optical Communication Systems: Concepts an Performance," Optical Fiber Conference (OFC), paper OThO, 8. - H. Haunstein, T. Schorr, A. Zottmann, W. Sauer-Greff an R. Urbansky, "Performance Comparison of MLSE an Iterative Equalization in FEC Systems for PMD s With Respect to Implementation Complexity," J. Lightwave Technol., vol. 4, pp , 6. R. Urbansky 6