Concatenated Coded Modulation for Optical ...

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B. E. Basch is with Verizon, Verizon Network and Technology, Verizon Lab- oratories, Waltham, MA 02451 USA (e-mail: [email protected]



Concatenated Coded Modulation for Optical Communications Systems Maurizio Magarini, Member, IEEE, René-Jean Essiambre, Senior Member, IEEE, Bert E. Basch, Senior Member, IEEE, Alexei Ashikhmin, Senior Member, IEEE, Gerhard Kramer, Fellow, IEEE, and Adriaan J. de Lind van Wijngaarden, Senior Member, IEEE Abstract—The use of trellis-coded modulation (TCM) in combination with an outer block code is considered for next-generation 100-Gb/s optical transmission systems. Two block codes are employed as an outer code: a 16 times interleaved byte-oriented (255,239) Reed Solomon (RS) code and a code consisting of two interleaved extended three-error correcting Bose Chaudhuri Hocquenghem (BCH) (1020,988) codes. Simulations show that soft-decision decoding of a selected TCM inner code in combination with hard-decision decoding of the outer RS code achieves a net coding . When the congain (NCG) of 8.42 dB at a bit-error rate of catenated code based on the two interleaved BCH codes is used as the outer code, the NCG is 9.7 dB. The impact of quantization on the performance of the concatenated TCM scheme with the two interleaved BCH outer codes is evaluated, and it is shown that 4-bit quantization is sufficient to approach the “infinite precision” performance to within 0.15 dB. Index Terms—Concatenated coding, forward-error correction (FEC), optical communications, quantization, trellis-coded modulation (TCM).



HE 100-Gb/s long-haul optical transport systems that are currently under development make use of polarization-division multiplexing (PDM) and coherent demodulation of quadrature phase-shift-keying (QPSK) modulation to operate over an existing network infrastructure [1]. Codes evaluated for PDM-QPSK 100-Gb/s optical systems are generally designed for binary-input/binary-output channels [2]. Such systems typically employ a hard-decision decoder. It is well known that soft-decision decoding has the potential to improve the performance over hard-decision decoding when the forward-error correction (FEC) overhead is sufficiently high. For binary transmission FEC coding requires raising the symbol Manuscript received March 28, 2010; revised May 19, 2010; accepted May 24, 2010. Date of publication June 10, 2010; date of current version July 23, 2010. M. Magarini is with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133 Milano, Italy (e-mail: [email protected]). R.-J. Essiambre is with Bell Laboratories, Alcatel-Lucent, Holmdel, NJ 07733 USA (e-mail: [email protected]). B. E. Basch is with Verizon, Verizon Network and Technology, Verizon Laboratories, Waltham, MA 02451 USA (e-mail: [email protected]). A. Ashikhmin and A. J. de Lind van Wijngaarden are with Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ 07974 USA (e-mail: [email protected]; [email protected]). G. Kramer was with Bell Laboratories, Alcatel-Lucent, and is now with the Department of Electrical Engineering–Systems, University of Southern California, Los Angeles, CA 90089-2565 USA (e-mail: [email protected]). Color versions of one or more of the figures in this letter are available online at Digital Object Identifier 10.1109/LPT.2010.2052030

rate and thus increasing the transmitted signal bandwidth. However, significant coding gain can be achieved without bandwidth expansion by using coded modulation [3], [4]. The use of trellis-coded modulation (TCM) as a technique to combine coding and modulation has been considered in different forms in [5]–[8]. To achieve better performance, bit interleaved coded modulation schemes based on binary low-density parity-check (LDPC) component codes have been proposed in [9]. However, due to the high implementation complexity of the soft iterative decoding process of LDPC codes at speeds of 100 Gb/s, only component codes of moderate length are considered in [9]. This introduces a non-negligible loss in terms of net coding gain (NCG) at the bit-error rate (BER) of interest for optical transmission systems. In this letter, we consider the use of TCM as the inner code in a concatenated coding scheme. A soft-decision inner decoder and a hard-decision outer decoder are employed, thus allowing for a reasonable implementation complexity. Two block codes specified in ITU-T recommendation G.975.1 [10] are used as an outer code. The effect of quantization of the in-phase and quadrature components of the received signal samples after optical–electronic (o/e) conversion is investigated as well. II. SYSTEM MODEL Code concatenation is one of the most effective ways to construct long, powerful error correcting codes from short component codes [3]. The general structure of a concatenated encoding scheme consists of an outer encoder and an inner encoder, which are usually separated by an interleaver. Space communication systems often use a TCM inner code and a Reed Solomon (RS) outer code [11]. This concatenated coding scheme has a low decoding complexity and achieves a large coding gain and high spectral efficiency. We consider a PDM transmission system where the 8PSK symbol sequences at the output of two TCM encoders are separately applied to a digital-to-analog converter (DAC). A polarization beam combiner (PBC) then modulates the resulting signals into the and states of polarization. This is illustrated in Fig. 1. At the receiver side, the two polarization states are separated by a polarization beam splitter (PBS) and the received signals after ideal coherent demodulation are sampled to produce the inputs for the two TCM decoders. The continuous samples are quantized into one of the finite number of discrete output symbols through an analog-to-digital converter (ADC). Each TCM decoder performs soft-decision decoding on the basis of the signal samples at its input. The output of the TCM decoder produces hard-decision bits that are fed to the block outer decoder.

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Fig. 1. Structure of the considered concatenated TCM scheme with PDM. The perform interleaving and deinterleaving, respectively. blocks and

III. CONCATENATED TCM SCHEMES TCM is an effective method to improve the reliability of communication systems over band-limited channels. It is based on binary conthe combination of an ordinary rate points volutional code with a signal constellation of [3], [4]. In this work, we consider two different implementations of TCM inner codes designed for an 8PSK signal constellation. The first one is the 4-state 8PSK Ungerboeck TCM (8PSK UTCM) code proposed in [4]. The 8PSK UTCM code has been found by code search and is usually considered as a reference. The second TCM encoder is the 64-state 8PSK pragmatic TCM (8PSK PTCM) code proposed in [12]. In contrast to the UTCM code, where the best trellis encoder changes according to the constellation and the code complexity, the PTCM code uses a single basic convolutional code, that is, the standard 64-state rate-1/2 convolutional code, in combination with QPSK, 8PSK, and 16PSK modulation formats. The potential advantage of this approach is that it allows different spectral efficiencies by only changing the modulation without modifying the encoder structure. Soft-decision decoding of the TCM coding scheme is performed by using the Viterbi algorithm [3], [4] that computes the most likely transmitted sequence at its output, which is the one at minimum Euclidean distance from the received sequence. It is worth noting that for both the two considered TCM codes, the combination of the 8PSK modulation format with a convogives the same spectral efficiency lutional code of rate as uncoded QPSK modulation. The first outer block code considered is the standard (255,239) RS code with interleaving depth 16 as specified in the ITU-T G.975.1 recommendation [10]. We remark that RS codes are able to handle bursts of errors that are present in the binary sequence at the output the TCM decoder. The RS codewords are read into a block interleaver, row-by-row, where each row consists of an RS codeword. The number of rows is called the interleaver depth. Data of the interleaver are read out byte-wise column-by-column. The second outer block code we focus on is specified in subclause I.9 of [10]. It consists of two interleaved three-error correcting extended (1020,988) Bose Chaudhuri Hocquenghem (BCH) codes that are iteratively decoded by using algebraic hard-decision decoding. As shown in [10], due to the high length of its codewords (255 1020 bits) and its internal interleaving structure, the code has excellent random error correction capabilities and outperforms an optimized binary LDPC code with hard decisions specified in subclause I.6 of [10] while allowing us to keep decoding complexity at a similar level. IV. CONCATENATED TCM PERFORMANCE EVALUATION In order to evaluate the performance of the two concatenated TCM implementations, we consider a target post-FEC BER of . The additive white Gaussian noise (AWGN) channel

Fig. 2. Output BER versus SNR for the two considered 8PSK TCM schemes concatenated with the (255,239) RS code.

model is assumed in the following. Monte Carlo simulations have been conducted to measure the BER of the coded binary sequence at the output of the TCM decoder. The BER characteristic for the concatenated TCM scheme is then obtained by considering the known relation between the BER at the input of the outer decoder, i.e., the binary sequence at the output of the TCM decoder, and the BER at the output of the outer decoder [10]. It is worth noting that due to the structure of the two chosen outer codes, no interleaving is required between the inner and the outer code. Fig. 2 shows the output BER performance versus the signal-to-noise ratio (SNR) per information bit, SNR , for the (255,239) RS code in the case of concatenation with the two considered inner 8PSK TCM codes and in the case of QPSK transmission. The spectral efficiency for each polarization bits symbol. An NCG of is 5.84 dB is obtained for the (255,239) RS code for an output . From this figure, we observe that the conBER catenation with the 8PSK UTCM and the 8PSK PTCM allow us to achieve an NCG of 8.06 and 8.70 dB, respectively. The improvement in NCG compared to QPSK transmission with the RS code is 2.22 and 2.86 dB, respectively. As a reference, dB, defined by the unconstrained the value of SNR dB, AWGN Shannon limit, and the value of SNR defined by the constrained AWGN Shannon limit of the 8PSK constellation with equiprobable symbols, to achieve a spectral bits symbol are reported as well efficiency of [13]. The relation between optical SNR (OSNR) and SNR is given by [14] (1) where is the information bit rate and is the reference bandwidth (12.5 GHz). In Fig. 3, the performance obtained from the concatenation of the two extended (1020,988) BCH interleaved codes is shown with the same 8PSK TCM inner codes considered in Fig. 2. The NCG of the two extended (1020,988) BCH interleaved codes in case of QPSK transmission is 8.57 dB. The concatenation of this code with the two different 8PSK TCM codes allows us to achieve an NCG of 9.41 and 9.7 dB for 8PSK UTCM and 8PSK

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minimizing the SNR required to achieve the target BER perfor the given number of quantization bits. formance of We have found that 5-bit quantization bits gives virtually the same performance as infinite precision. The performance loss due to 3-bit quantization and 4-bit quantization relative to infinite precision is 0.55 and 0.15 dB, respectively. The performance of 8PSK PTCM with 2-bit quantization is worse than the performance of coded QPSK transmission with 1-bit quantization (hard decisions).

Fig. 3. Output BER versus SNR for the two considered 8PSK TCM schemes concatenated with the two extended (1020,988) interleaved BCH codes.

V. CONCLUSION We have shown that concatenated TCM schemes based on the concatenation of 8PSK TCM inner codes and block outer codes used in optical communication systems allows us to improve appreciably the NCG achieved by the same codes in case of QPSK transmission. This is achieved by performing soft decision decoding of the inner TCM code while preserving the same spectral efficiency as the QPSK case. Simulations show that the use of a 64-state 8PSK pragmatic TCM inner code achieves an NCG and transmission over of up to 9.7 dB for a target BER of an AWGN channel. It is also shown that a 4-bit quantizer from an ADC allows us to approach the infinite precision converter SNR to within 0.15 dB. REFERENCES

Fig. 4. Sensitivity of the output BER to the number of quantization levels for the 8PSK PTCM scheme concatenated with the two extended (1020,988) interleaved BCH codes.

PTCM, respectively. In this case, the NCG gain relative to coded QPSK transmission is 0.84 and 1.13 dB, respectively. It is worth emphasizing that for the best of the two cases, the required SNR is only 2 dB higher than that defined by the constrained AWGN capacity of the 8PSK constellation with equiprobable symbols. This is much better than the NCG of the LDPC-coded 8PSK scheme considered in [9] where, at a rate of 2.25 bits/symbol, the distance from the constrained Shannon bound is about 4 dB . at a BER Fig. 4 shows the performance of the scheme based on the concatenation of the 8PSK PTCM and the two extended (1020,988) BCH interleaved codes when the amplitudes of the two quadrature components of the signal at the input of the TCM decoders are individually uniformly quantized. The optimum quantization thresholds have to be adjusted by selecting the clipping level relative to the nominal signal level. In the same way as [15], in our simulations, the clipping level has been chosen by

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