[Paper Review] Experimental Demonstration of Capacity Increase and Rate-Adaptation by Probabilistically Shaped 64-QAM

Fred Buchali, Georg Böcherer+4 more|arXiv (Cornell University)|Sep 29, 2015

Error Correcting Code Techniques4 references4 citations

TL;DR

This paper demonstrates for the first time in optical transmission a rate-adaptive, capacity-increasing system using probabilistically shaped 64-QAM with fixed modulation format, baudrate, and FEC overhead. By employing a distribution matcher to shape symbol probabilities, the system achieves up to a 43% reach increase and 15% capacity gain over conventional 16-QAM at 200 Gbit/s, validating theoretical shaping gains in practice with low-complexity implementation.

ABSTRACT

We implemented a flexible transmission system operating at adjustable data rate and fixed bandwidth, baudrate, constellation and overhead using probabilistic shaping. We demonstrated in a transmission experiment up to 15% capacity and 43% reach increase versus 200 Gbit/s 16-QAM.

Motivation & Objective

• To address the limited flexibility of conventional optical transceivers that rely on coarse switching between fixed modulation and FEC modes.
• To close the gap to Shannon capacity in optical communication by implementing probabilistic constellation shaping (PS) with practical, low-complexity hardware.
• To enable continuous rate adaptation without changing FEC overhead, modulation format, or symbol rate by adjusting the input distribution via a distribution matcher.
• To experimentally validate theoretical gains in spectral efficiency and transmission reach predicted for shaped 64-QAM in real-world optical fiber systems.

Proposed method

• A distribution matcher (DM) generates non-uniformly distributed symbols from input data bits, shaping the constellation to match a Maxwell-Boltzmann distribution.
• The shaped symbols are encoded using a systematic spatially coupled LDPC (SC-LDPC) code with fixed rate 5/6 and 20% FEC overhead.
• The system uses 64-QAM with four distinct shaped distributions (P₁ to P₄), each with decreasing entropy (5.73 to 4.13 bits), enabling variable transmission rates.
• The transmission rate is calculated via R = H(P) − (1−c)·m, where H(P) is the entropy of the distribution, c=5/6 is the code rate, and m=6 is the number of bits per symbol.
• A data-aided DSP is used for PS-64-QAM modes P₂ to P₄, while blind adaptation is used for standard QAM and P₁; both are applied offline to measured sequences.
• Mutual information is measured to determine achievable rates, and error-free decoding defines the maximum transmission reach for each configuration.

Experimental results

Research questions

• RQ1 Can probabilistic shaping achieve significant reach and capacity gains in real optical fiber transmission without changing FEC overhead, modulation format, or symbol rate?
• RQ2 To what extent does shaping reduce the gap to Shannon capacity in practical optical systems with fixed system parameters?
• RQ3 How does the performance of rate-adaptive PS-64-QAM compare to conventional systems using uniform 64-QAM or 16-QAM with varying FEC overheads?
• RQ4 What is the achievable trade-off between net data rate and transmission reach using only distribution shaping?
• RQ5 Can low-complexity, practical implementations of distribution matching and soft-decision decoding achieve theoretical shaping gains in real-world optical links?

Key findings

• The system achieved a 43% reach increase at 200 Gbit/s compared to conventional 16-QAM with 28% FEC overhead, reaching 4800 km with PS-64-QAM using distribution P₄.
• At 300 Gbit/s, the reach increased by 25% compared to 16-QAM, achieving 1200 km with PS-64-QAM (P₁) and 20% FEC overhead.
• A 15% capacity increase was demonstrated over 16-QAM at 200 Gbit/s, with PS-64-QAM achieving 4800 km versus 3360 km for 16-QAM.
• The shaping gain was experimentally verified at 4.3 dB (equivalent to 1032 km reach gain) at 4 bits per symbol mutual information.
• The system maintained error-free decoding across all PS-64-QAM configurations with fixed FEC code and symbol rate, proving effective rate adaptation via shaping alone.
• The results confirm that shaping gains predicted by theory and simulation are achievable in practice with low-complexity, real-time DSP components.