We propose a DSP scheme with soft-output maximum likelihood sequence equalizer (sMLSE) and low-overhead (8.51%) low density parity check (LDPC) code for C-band PAM-4 transmission. In order to apply LDPC code in conjunction with MLSE, the conventional hard-output MLSE is modified to have a soft-output value by using the Max-log BCJR algorithm. The feasibility of this approach is experimentally investigated in a 56 Gb/s C-band PAM-4 system. In order to investigate the advantages of the proposed scheme, we compare the performance of the sMLSE-LDPC code to that of MLSE-RS code. Relatively, additional OSNR gain of 0.6 dB ~2.1 dB is achieved. The variation of the relative OSNR gain depends on the burst errors, which originate from the power fading effect. By using an interleaver that spreads burst errors in time, one can see that the relative OSNR gain is improved as 1.6 dB ~2.1 dB. Using the proposed scheme with the interleaver, one can see that the 30 km transmission of 56 Gb/s PAM-4 in the C-band was experimentally demonstrated.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Due to the rapid development of real-time service, cloud network, and other data-consuming applications, data traffic is increasing dramatically. The pulse amplitude modulation-4 (PAM-4) signal format is considered as a strong candidate to accommodate this data traffic increase, because of its spectral efficiency, cost-effectiveness, energy efficiency, and simplicity [1–6]. Although PAM-4 signaling was considered for short-reach networks at the early time, PAM-4 signaling is now being considered for inter-data center networks [4,5] or mobile front-haul  in the C-band.
In C-band PAM-4 transmission, one of the most important issues is coping with inter-symbol interference (ISI) that is induced by chromatic dispersion of optical fiber. In efforts to combat the dispersion effect, a maximum likelihood sequence equalizer (MLSE) with hard-output has been studied [7–10]. Due to the use of a hard decision output, it is known to provide worse performance than using that obtained with a soft output in terms of decoding gain. To acquire additional decoding gain by using soft-decision forward error correction (SD-FEC), in this paper we propose a digital signal processing (DSP) scheme that has soft-output MLSE (sMLSE) in concatenation with low density parity check (LDPC) code. The performance is experimentally investigated in a 56 Gb/s PAM-4 system. sMLSE can be realized by the Bahl, Cocke, Jelinek and Raviv algorithm with max-log approximation (Max-log BCJR) or soft output Viterbi algorithm (SOVA) [11,12]. In this paper, we chose the Max-log BCJR algorithm because it provides better performance . In order to loosen the bandwidth requirement, a low-overhead (8.51%) LDPC code is adopted as a soft-decision FEC.
Experimental results show that the proposed scheme has a better performance of 0.6 ~2.1 dB when compared to using MLSE and RS code in terms of the required OSNR at 10−4 coded BER. It may be noted that the 10−4 BER was chosen referring on the threshold values of several widely used FEC codes, such as KP4-FEC and KR4-FEC . The relative OSNR gain shows variations depending on the burst errors induced from a power fading effect. An interleaver to spread burst errors is used to lessen the variations of the relative OSNR gain, which leads to improving to 1.6~2.1 dB gain. Using the proposed scheme and the interleaver, to the best of our knowledge, we showed the first time that a 56 Gb/s PAM-4 signal over 30 km transmission in the C-band is possible with DSP only.
2. sMLSE and low-overhead LDPC
2.1 Soft output MLSE
First, we briefly introduce the sMLSE to be concatenated with a LDPC decoder. As input values, the LDPC decoder requires the log likelihood ratio (LLR) of each bit. For PAM-4 systems, two LLR values (MSB and LSB) are derived from one received symbol. With Gray coding, the LLR values of MSB and LSB are expressed as
BCJR is one of the most commonly used algorithms to calculate the probability of a symbol from a given sequence. Its complexity can be greatly reduced by using max-log approximation with a negligible penalty . With max-log approximation, P(uk|r) is expressed as
Figure 1(a), Eq. (3) and Eq. (4) describe the derivation of αk(s). γ(s′,s,k) is the branch transition probability from s′ to s when the received signal at time k is yk. and are the expected value and standard deviation for the transition from s′ to s, respectively. Since we considered the PAM-4 symbol, four branches are merged into one state. With max-log approximation, the highest probability is selected for αk + 1(s), as shown in Eq. (4). It may be noted that αk(s) is exactly the same as the path metric in the Viterbi decoder of the conventional MLSE. βk(s) is calculated by a similar procedure as shown in Fig. 1(b), Eq. (3) and Eq. (5). The only difference is that βk(s) is calculated in the backward direction in time. After finding αk(s) and βk(s), the LLR values are calculated by Eq. (1) and Eq. (2).
Before proceeding, let us compare the computational complexities of sMLSE and the conventional MLSE. The conventional MLSE consists of two steps, path metric calculation and trace-back. Generally, the path metric calculation occupies the major portion in the complexity. The sMLSE is consisted of three steps, calculation of αk(s), βk(s) and P(u). The complexity of each of αk(s) and βk(s) is approximately equal to that of the path metric calculation. The complexity of the P(u) calculation is relatively light, since P(u) can be derived by simply adding αk(s) and βk(s). As a result, the sMLSE has approximately twofold higher complexity. Similarly, the latency of sMLSE is also approximately doubled. In Table 1, the complexities of sMLSE and the conventional MLSE are shown that is calculated with the experiment condition which will be described in the next section.
2.2 Performance of low overhead LDPC code
The calculated LLR values are inputted to the low overhead LDPC code. Here, the performance of the low-overhead LDPC decoder will be shown. LDPC code (2448,2256) having 8.51% overhead was chosen as a low-overhead LDPC code. Its encoding matrix was generated by additive groups of prime fields . In order to investigate the decoding performance of the low-overhead LDPC code, a simulated BER curve was derived as a function of Eb/No. The results are shown in Fig. 2(a). As shown in the Fig., if the target coded BER is 10−12, the required uncoded BER is ~10−3. To determine the performance improvement obtained by adopting SD FEC, the performance was compared with that of hard-decision FEC (HD-FEC) codes having similar overhead. RS code (558,514) having 8.56% overhead was selected for the comparison. Figure 2(b) shows the results. When the performance was compared at the 10−4 coded BER, the simulation result shows that ~1.8 dB additional decoding gain can be achieved by adopting SD FEC.
3.1 Experimental setup
To investigate the feasibility, the proposed scheme was applied to our previously proposed PAM-4 transmission system . Figure 3(a) shows the DSP structure. In the experiment, the DSP is emulated by software in a personal computer. The structure of the transmitter DSP is shown in the left part of Fig. 3(a). As a data sequence, pseudorandom binary sequence (PRBS) having 215-1 pattern length was used. It was then encoded by the low-overhead LDPC (2448, 2256) code. To enhance the decoding performance of the LDPC code, an interleaver was inserted. For reliable operation of the sMLSE, two block termination bits were inserted after every 62 bits (not shown in Fig. 3(a)). The bit stream was then mapped to PAM-4 signal format with Gray coding. Before data transmission, frame marker and training symbols were sent to mark the starting point of the transmission and to initialize equalizers. The frame structure is shown in the lower part of Fig. 3(a).
At the receiver DSP, the starting point of the transmission was found in the frame synchronization block. The frame synchronization block was inactivated after finding the frame start. For timing recovery, the Mueller-Müller algorithm was used. DFE was then used for pre-equalization in order to reduce the channel length at the MLSE input. In order to avoid error-burstiness that originates from the wrong decision at the slicer, we slightly modified the connection between DFE and MLSE, as shown in the right part of Fig. 3(a). As shown in the Fig., the output of the feed forward filter (i.e. before adding output of the feedback filter) was inputted to the sMLSE. The remaining ISI after the symbol-by-symbol equalizer can be compensated by the MLSE. When ISI is severe, the advantage by avoiding burst error outweighs the disadvantage by abandoning the output of the feedback filter. The conventional DFE output (summation of the outputs from feed forward filter and feedback filter) was fed back to the timing error recovery block, since the Mueller-Müller algorithm is a decision directed timing error estimation algorithm. In the sMLSE block, the mean value and the standard deviation of the inputted signal were calculated based on a histogram in order to calculate γ in Eq. (3). The sMLSE block length was 32 and the constraint length was 3. After sMLSE, the PAM-4 symbols were de-mapped to binary symbols and de-interleaved. The bits were then decoded at the LDPC decoder block. Uncoded BER and coded BER were monitored for a performance analysis.
Figure 3(b) shows the experimental setup for optical transmission. The frame from the transmitter DSP was stored in the memory of the pulse pattern generator (PPG). Using the saved pattern and a digital-to-analog convertor (DAC), a PAM-4 signal was generated. Since the sampling rate of the DAC was 28 GS/s, the data rate of our experiment was 56 Gb/s. A dual-drive Mach-Zehnder modulator (MZM), which has approximately zero chirp, was used as a modulator. We used the linear region of the MZM by restricting the amplitude of the modulation voltage. The wavelength of the C-band light source was 1548.3 nm. At the input of fiber, the optical power was + 3 dBm, which is sufficiently low to avoid fiber nonlinearity. The optical signal was transmitted through a single mode fiber. Erbium doped fiber amplifier (EDFA) was used to compensate the power loss after transmission. In order to adjust the OSNR at the receiver, an amplified spontaneous emission (ASE) source and a variable optical attenuator (VOA) were used. The transmitted optical signal was received by a PIN-PD and captured by a real-time oscilloscope (OSC). The captured signal was processed offline at the receiver DSP.
3.2 Results and Analysis
To verify concatenation of the sMLSE and the LDPC decoder, we measured the coded BER and uncoded BER in a back-to-back configuration. The interleaver and de-interleaver pair at the DSP was disabled to focus on the sMLSE-LDPC code performance. Figure 4(a) shows the coded BER and uncoded BER as a function of the OSNR. For comparison, the measured coded BER with MLSE-RS (558,514) code was plotted together. As shown in the Fig., ~2.1 dB of additional relative OSNR gain was achieved by using LDPC code instead of RS code. To investigate the decoding performance of the LDPC code, the coded BER as a function of the uncoded BER was plotted in Fig. 4(b). A simulation curve with AWGN was also plotted as a reference. As shown in Fig. 4(b), the experiment data closely matched the simulation data. These results verified the concatenation between sMLSE and LDPC code.
We then investigated the BER performance as a function of the transmission distance. Figure 5(a) shows the experimental results with sMLSE-LDPC code and MLSE-RS code. It was expected that the BER would decrease as the transmission length increases. However, the relative OSNR gain also decreased with transmission. This means that the performance degradation for sMLSE-LDPC code is more severe than that of MLSE-RS code. One more interesting behavior is that the reduction in the relative OSNR gain is not proportional to the transmission distance. The reduction for 20 km transmission was higher than that for 30 km transmission. It may be noted that reduction of the relative OSNR gain is undesirable, since it decreases the benefit of the proposed sMLSE-LDPC code scheme.
To identify the cause of this phenomenon, we compared the decoding performance of the LDPC code and the RS code with various transmission distances. Figure 5(b) and Fig. 5(c) show the relations between the coded BER and uncoded BER for the LDPC code and the RS code, respectively. As shown in Fig. 5(b), the decoding performance of the LDPC code was degraded with transmission. It was also observed that the degradation at 20 km transmission was more severe than that at 30 km transmission. In contrast, as shown in Fig. 5(c), no degradation was observed for the RS code case with transmission. Therefore, the reduction of the relative OSNR gain was due to the degradation of decoding performance of LDPC code.
The degradation of decoding performance of LDPC code is due to the burst errors at MLSE, which is generally known to generate burst errors. RS code is inherently designed to be robust to burst errors, but LDPC code is not. Degradation of LPDC code by the burst error thus will be more severe than that of RS code. In order to confirm the effect of the burst errors, we measured the error-burstiness with various transmission distances. The error-burstiness was measured by counting the maximum and mean number of bit-errors in erroneous MLSE blocks. The total number of errors was fixed at ~100. It may be noted that the maximum and mean number of errors can describe the error-burstiness.
The results are shown in Fig. 6. For comparison, the relative OSNR gain was plotted together. As shown in the Fig., it is clear that the relative OSNR gain was inversely proportional to the number of burst errors. This verifies that the reduction of the relative OSNR gain was due to the burst errors. In addition, the burst errors maximally occur at 20 km transmission. This is consistent with the result that the penalty with 20 km transmission is more severe than that with 30 km transmission.
The burst errors after transmission can be explained by the pattern dependency of the burst error and power fading after transmission. The burst error mostly occurs at the level-transitional pattern such as ‘low, high, low, high …’ [10,15,16]. This is because an error is easily propagated to the next symbol at the level-transitional pattern. Let us explain with an example. In IM/DD, commonly, a ‘high/low’ symbol increases/decreases the signal level of the next symbol. The MLSE is thus trained to increase/decrease the decision threshold level if the previous symbol is ‘high/low’. Let us consider the case where the transmitted symbol is ‘low’, but the MLSE wrongly decides that the symbol is ‘high’. Then the MLSE increases the decision threshold. This unintentionally increases the probability that the next symbol is decided as ‘low’. If the next transmitted symbol is ‘low’ (i.e. without level transition), it is not detrimental. However, if the next transmitted symbol is ‘high’ (i.e. with level transition), it increases the probability of a wrong decision. The error can then be propagated to the next symbol. Therefore, in terms of burst error, error at the level-transitional pattern is critical.
Since the period of the level-transitional pattern is twice that of the 1/ baud rate, the energy of the level-transitional pattern is concentrated at the half frequency of the baud rate. Thus, if the frequency component is lost, the error probability at the level-transitional pattern is increased and then burst error can be generated. In IM/DD, the power fading makes null points in the spectrum. The frequency of the uth null point is expressed as Eq. (6), the transmission distance that makes the spectrum null at the half frequency of the baud rate (B) can be derived asFig. 6. To clarify that the burst error originated from the frequency spectrum loss, we conducted an additional simulation. In the simulation, we filtered out the frequency components from the Tx output signal. The filtering was done by using a 2nd order notch filter having bandwidth of a 0.04 times baud rate. To generate errors, AWGN was added to the filtered signal. The signal was inputted to the receiver DSP. The same analysis as that shown in Fig. 6 was then performed, while varying the center frequency of the notch filter. The results are shown in Fig. 7. The burst errors maximally occurred when the frequency components at the half baud rate was filtered. This is consistent with our expectation.
As discussed until now, for the best performance of the proposed scheme, the effect of the burst errors should be mitigated. One of the possible methods to achieve this will be introduced in the next section.
3.3 Mitigation of burst error effect
The simplest method to mitigate the effect of burst error is using an interleaver that spreads burst errors into multiple LDPC decoding blocks. In this purpose, we designed a block interleaver/de-interleaver pair. The de-interleaver that distributes burst-errors was first designed, and then the paired interleaver was designed.
The structure of the de-interleaver is shown in Fig. 8. L × N length bits are distributed into N LDPC code blocks, where L is the bit length of one LDPC code block (in our experiment, 2448) and N is the number of LDPC code blocks. The numbers in Fig. 8 indicate the bits in time order. Since a PAM-4 system is considered here, bits labeled by odd numbers are MSB and bits labeled by even numbers are LSB. For the best performance, the de-interleaver was designed to place MSB and LSB equally in each LDPC code block, since the LLR value of MSB tends to be larger than that of LSB. The size of the designed de-interleaver matrix was 2N × L/2. The paired matrix for the interleaver can be determined by the inverse of the de-interleaver matrix. It is expected that the performance improvement will be saturated at a certain N. To find the N where saturation occurs, we measured the coded BER as function of the uncoded BER with an increase of N. Since the burst errors were maximized at 20 km transmission, the experiment was done at this transmission distance. Figure 9 shows the results. As expected, the decoding performance was improved with an increase of N. The improvement was saturated when N was increased to 8. With N = 8, the performance nearly matched the simulation results, and this means that the effect of burst errors was almost mitigated. Therefore, we chose a 16 × 1224 matrix for the block de-interleaver.
3.4 30 km transmission with interleaver
In order to investigate the improvement by adopting the interleaver, we measured BER curves with the interleaver. Figure 10(a) shows the measured BER curves for LDPC code and RS code as a function of OSNR at 20 km transmission. For a fair comparison, a similar size interleaver was used with the RS code. As shown in the Fig., the relative OSNR gain was increased from 0.6 dB to 1.6 dB due to the interleaver. We measured the relative OSNR gain as a function of the transmission distance. As shown in Fig. 10(b), the degradation was significantly reduced, and relative OSNR of 1.6 ~2.1 dB was achieved.
Finally, we showed the possibility of 30 km transmission with the proposed scheme. Since the required uncoded BER for 10−12 coded BER was ~10−3 (shown in Fig. 2(a)), we verified that uncoded BER 10−3 can be achieved with 30 km transmission. Figure 11(a) shows the measured BER curves with 30 km transmission. As shown in the Fig., uncoded BER of 10−3 was achieved at 30 km transmission. In addition, coded BER rapidly decreased as the OSNR increased. To confirm the decoding performance at 30 km transmission, the relation between coded BER and uncoded BER was compared with the simulation results. The results are shown in Fig. 11(b). It was observed that after 30 km transmission, the decoding performance nearly matched the simulation results. These results show the possibility of 30 km transmission with the proposed scheme.
In this paper, we proposed a DSP scheme with soft-output MLSE (sMLSE) and low-overhead (8.51%) LDPC code for C-band PAM-4 transmission. The sMLSE was realized using the Max-log BCJR algorithm. The performance was investigated in a 56 Gb/s PAM-4 system. When compared with MLSE-RS code, sMLSE-LDPC code has relative OSNR gain of 0.6 dB ~2.1 dB. The reduction of the relative OSNR gain is due to the burst errors at the MLSE. The burst errors maximally occurred when the spectrum null by power fading is placed at the half frequency of the baud rate. In our experiment, the burst errors were most severe at 20 km transmission. The effect of the burst error was mitigated by a block interleaver, which was designed to distribute burst errors into multiple LDPC code blocks. With the interleaver, the worst case relative OSNR gain was increased from 0.6 dB to 1.6 dB. As a result, relative OSNR gain of 1.6 dB ~2.1 dB was achieved. We also showed that 30 km transmission of a 56 Gb/s PAM-4 signal in the C-band is possible using our proposed scheme.
Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2017-0-00047, Development of 200Gb/s optical transceiver for metro-access network).
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