Achievable Rates for Shaped Bit-Metric Decoding

TL;DR

This paper derives a new achievable rate for bit-metric decoding that accounts for dependent bit-levels, demonstrating that probabilistic shaping with dependence improves performance on the AWGN channel.

Contribution

It introduces a new rate expression for BMD that allows for dependent bit-levels and evaluates its benefits over independent shaping methods.

Findings

Dependent bit-levels reduce the gap to channel capacity.

Shaped BMD outperforms bit-shaped and uniform BMD in numerical evaluations.

Dependence between bits is shown to be beneficial on the AWGN channel.

Abstract

A new achievable rate for bit-metric decoding (BMD) is derived using random coding arguments. The rate expression can be evaluated for any input distribution, and in particular the bit-levels of binary input labels can be stochastically dependent. Probabilistic shaping with dependent bit-levels (shaped BMD), shaping of independent bit-levels (bit-shaped BMD) and uniformly distributed independent bit-levels (uniform BMD) are evaluated on the additive white Gaussian noise (AWGN) channel with Gray labeled bipolar amplitude shift keying (ASK). For 32-ASK at a rate of 3.8 bits/channel use, the gap to 32-ASK capacity is 0.008 dB for shaped BMD, 0.46 dB for bit-shaped BMD, and 1.42 dB for uniform BMD. These numerical results illustrate that dependence between the bit-levels is beneficial on the AWGN channel. The relation to the LM rate and the generalized mutual information (GMI) is discussed.