Abstract
Probabilistic amplitude shaping—implemented through a distribution matcher (DM)—is an effective approach to enhance the performance and the flexibility of bandwidth-efficient coded modulations. Different DM structures have been proposed in the literature. Typically, both their performance and their complexity increase with the block length. In this work, we present a hierarchical DM (Hi-DM) approach based on the combination of several DMs of different possible types, which provides the good performance of long DMs with the low complexity of several short DMs. The DMs are organized in layers. Each upper-layer DM encodes information on a sequence of lower-layer DMs, which are used as “virtual symbols”. First, we describe the Hi-DM structure, its properties, and the encoding and decoding procedures. Then, we present three particular Hi-DM configurations, providing some practical design guidelines, and investigating their performance in terms of rate loss and energy loss. Finally, we compare the system performance obtained with the proposed Hi-DM structures and with their single-layer counterparts: a SNR gain is obtained by a two-layer Hi-DM based on constant composition DMs (CCDM) compared to a single-layer CCDM with same complexity; a gain and a significant complexity reduction are obtained by a Hi-DM based on minimum-energy lookup tables compared to a single-layer DM based on enumerative sphere shaping with same memory requirements.
Highlights
Over the last few years, probabilistic shaping techniques have been widely investigated to improve the performance and the flexibility of optical fiber networks
We compare the system performance obtained with the proposed Hi-distribution matcher (DM) structures and with their single-layer counterparts: a 0.19 dB signal to noise ratio (SNR) gain is obtained by a two-layer hierarchical DM (Hi-DM) based on constant composition DMs (CCDM) compared to a single-layer
We have presented a general Hi-DM concept for the implementation of probabilistic amplitude shaping (PAS), in which several short DMs are combined in a hierarchical structure to form a longer DM
Summary
Over the last few years, probabilistic shaping techniques have been widely investigated to improve the performance and the flexibility of optical fiber networks. For a given block length N, the most efficient way to encode k information bits is to map their 2k possible realizations to the 2k minimum-energy sequences of N amplitudes. This approach is known as sphere shaping: representing the sequences of Namplitudes in an N-dimensional space, the minimum-energy sequences are all contained within a sphere of given radius. We show how to combine different DM types to obtain hierarchical structures based on code position modulation, CCDM, or LUTs. For each structure, we provide some simple examples, discuss the computational complexity and required memory, and compute the reduction of rate loss and energy loss obtained with respect to the equivalent-complexity single-layer structures.
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