Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Abstract

Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengths and requires long blocklengths to achieve high shaping gain, which makes its implementation very challenging. In this paper, we propose to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same shaping rate, which makes it a suitable candidate to be implemented in real-time high-speed optical systems. In this paper, we first show that finite blocklength ESS and CCDM exhibit higher effective signal-to-noise ratio than their infinite blocklength counterparts. These results show that for the nonlinear fiber optical channel, large blocklengths should be avoided. We then show that for a 400 Gb/s dual-polarization 64-QAM WDM transmission system, ESS with short blocklengths outperforms both uniform signaling and CCDM. Gains in terms of both bit-metric decoding rate and bit-error rate are presented. ESS with a blocklength of 200 is shown to provide an extension reach of about 200 km in comparison with CCDM with the same blocklength. The obtained reach increase of ESS with a blocklength of 200 over uniform signaling is approximately 450 km (approximately 19%).

Performance Monitoring for Live Systems with Soft FEC and Multilevel Modulation

“…II-B. 3 If PS is employed, the BER after PS decoding, if that is placed after the FEC decoding, is more relevant [30]- [32].…”

Mitigating Fiber Nonlinearities by Short-length Probabilistic Shaping

“…Recent simulations [5] and experiments [6] found that the effective SNR after fiber transmission and digital signal processing (DSP) increases when the block length of the employed DM scheme is reduced. Such an effect had not been observed before, mainly due to random-draw based PAS emulation technique used previously.…”

First Experimental Demonstration of Probabilistic Enumerative Sphere Shaping in Optical Fiber Communications

“…ESS was introduced in 1993 [10] and has been recently considered for wireless communications [11]. Very recently, ESS has been introduced to the optical community in [12]. The main result of [12] is that short blocklength ESS outperforms CCDM at the same blocklength, long blocklength CCDM, and uniform.…”

“…Very recently, ESS has been introduced to the optical community in [12]. The main result of [12] is that short blocklength ESS outperforms CCDM at the same blocklength, long blocklength CCDM, and uniform. This gain is due to the combination of linear shaping gain and nonlinear tolerance.…”

“…This gain is due to the combination of linear shaping gain and nonlinear tolerance. The results in [12], however, are only based on numerical (split-step Fourier) simulations.…”