Parallel-Amplitude Architecture and Subset Ranking for Fast Distribution Matching

Abstract

A distribution matcher (DM) maps a binary input sequence into a block of nonuniformly distributed symbols. To facilitate the implementation of shaped signaling, fast DM solutions with high throughput and low serialism are required. We propose a novel DM architecture with parallel amplitudes (PA-DM) for which m−1 component DMs, each with a different binary output alphabet, are operated in parallel in order to generate a shaped sequence with m amplitudes. With negligible rate loss compared to a single nonbinary DM, PA-DM has a parallelization factor that grows linearly with m, and the component DMs have reduced output lengths. For such binary-output DMs, a novel constant-composition DM (CCDM) algorithm based on subset ranking (SR) is proposed. We present SR-CCDM algorithms that are serial in the minimum number of occurrences of either binary symbol for mapping and fully parallel in demapping. For distributions that are optimized for the additive white Gaussian noise (AWGN) channel, we numerically show that PA-DM combined with SR-CCDM can reduce the number of sequential processing steps by more than an order of magnitude, while having a rate loss that is comparable to conventional nonbinary CCDM with arithmetic coding.

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

“…Furthermore, the mapping algorithm can operate on one nonbinary or several binary subsets of the output sequence. Bit-level [ 51 , 57 ] and parallel-amplitude [ 58 ] designs are modifications to the conventional CCDM architecture that carry out such a transformation from one nonbinary to several binary DMs. Among all algorithms, a LUT is probably the simplest way to solve the CCDM indexing problem, yet the LUT size table is prohibitively large as it reaches gigabit size already for short blocklengths [ 76 ].…”

“…This approach has been numerically shown to have reduced rate loss compared to a single nonbinary DM, yet comes at the expense of having the DM output limited to compositions that are generated from a product distribution. In [ 58 ], a different parallelization technique has been proposed, which operates on amplitudes rather than on bit levels. For each of the out of amplitudes, a binary-alphabet DM is operated in parallel, with the first DM determining the position of the first amplitude, the second DM where to position the second amplitude within those positions that have not been occupied by the preceding, i.e., the first, amplitude.…”

“…In the context of BICM, product distributions were studied extensively in [ 41 ]). In [ 58 ], a parallel-amplitude (PA) architecture is proposed for DM to enable even higher degrees of parallelization. Also in [ 58 ], subset ranking (SR) is introduced as an alternative to the conventional AC method for binary-output CCDM.…”

“…In [ 58 ], a parallel-amplitude (PA) architecture is proposed for DM to enable even higher degrees of parallelization. Also in [ 58 ], subset ranking (SR) is introduced as an alternative to the conventional AC method for binary-output CCDM. As for direct shaping methods, enumerative sphere shaping (ESS) and shell mapping (SM) are notable SpSh algorithms which are initially proposed in [ 22 , 59 ] respectively.…”

“…By realizing a binary-to-nonbinary transformation with AC [ 52 , 53 ], CCDM can directly be used to produce amplitude sequences. On the other hand, separate binary-to-binary transformations can be employed for different bit-levels using AC [ 53 ] or SR [ 58 ]. Then these bit-levels can be combined such that the corresponding channel input distribution is close to the capacity-achieving distribution [ 51 , 57 ].…”