Towards Fully Optimized BICM Transceivers

Bit-interleaved coded modulation (BICM) transceivers often use equally spaced constellations and a random interleaver. In this paper, we propose a new BICM design, which considers hierarchical (nonequally spaced) constellations, a bit-level multiplexer, and multiple interleavers. It is shown that this new scheme increases the degrees of freedom that can be exploited in order to improve its performance. Analytical bounds on the bit error rate (BER) of the system in terms of the constellation parameters and the multiplexing rules are developed for the additive white Gaussian Noise (AWGN) and Nakagami-$m$ fading channels. These bounds are then used to design the BICM transceiver. Numerical results show that, compared to conventional BICM designs, and for a target BER of $10^{-6}$, gains up to 3 dB in the AWGN channel are obtained. For fading channels, the gains depend on the fading parameter, and reach 2 dB for a target BER of $10^{-7}$ and $m=5$.Comment: Submitted to the IEEE Transactions on Communication

On the Asymptotic Performance of Bit-Wise Decoders for Coded Modulation

Two decoder structures for coded modulation over the Gaussian and flat fading channels are studied: the maximum likelihood symbol-wise decoder, and the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled by a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that for the Gaussian channel the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Constellation Optimization in the Presence of Strong Phase Noise

In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

Rate-adaptive optical transceivers can play an important role in exploiting the available resources in dynamic optical networks, in which different links yield different signal qualities. We study rate-adaptive joint coding and modulation, often called coded modulation (CM), addressing non-dispersion-managed (non-DM) links, exploiting recent advances in channel modeling of these links. We introduce a four-dimensional CM scheme, which shows a better tradeoff between digital signal processing complexity and transparent reach than existing methods. We construct a rate-adaptive CM scheme combining a single low-density parity-check code with a family of three signal constellations and using probabilistic signal shaping. We evaluate the performance of the proposed CM scheme for single-channel transmission through long-haul non-DM fiber-optic systems with electronic chromatic-dispersion compensation. The numerical results demonstrate improvement of spectral efficiency over a wide range of transparent reaches, an improvement over 1 dB compared to existing methods