In this paper, achievable information rates (AIR) for fiber optical communications are discussed. It is shown that AIRs such as the mutual information and generalized mutual information are good design metrics for coded optical systems. The theoretical predictions of AIRs are compared to the performance of modern codes including low-parity density check and polar codes. Two different computation methods for these AIRs are also discussed: Monte-Carlo integration and Gauss-Hermite quadrature. Closed-form ready-to-use approximations for such computations are provided for arbitrary constellations and the multidimensional AWGN channel. The computation of AIRs in optical experiments and simulations is also discussed.

A code is said to be an r-local locally repairable code (LRC) if each of its coordinates can be repaired by accessing at most r other coordinates. When some of the r coordinates are also erased, the r-local LRC cannot accomplish the local repair, which leads to the concept of (r, δ)-locality. A q-ary [n, k] linear code C is said to have (r, δ)-locality (δ ≥ 2) if for each coordinate i, there exists a punctured subcode of C with support containing i, whose length is at most r+δ-1, and whose minimum distance is at least δ. The (r, δ)-LRC can tolerate δ-1 erasures in every local code (i.e., punctured subcode), which degenerates to an r-local LRC when δ = 2. A q-ary (r, δ) LRC is called optimal if it meets the singleton-like bound for (r, δ)-LRCs. A class of optimal q-ary cyclic r-local LRCs with lengths n | q - 1 were constructed by Tamo, Barg, Goparaju, and Calderbank based on the q-ary Reed-Solomon codes. In this paper, we construct a class of optimal q-ary cyclic (r, δ)-LRCs (δ ≥ 2) with length n | q - 1, which generalizes the results of Tamo et al. Moreover, we construct a new class of optimal q-ary cyclic r-local LRCs with lengths n | q + 1 and a new class of optimal q-ary cyclic (r, δ)-LRCs (δ ≥ 2) with lengths n | q + 1. The constructed optimal LRCs with length n = q + 1 have the best-known length for a given finite field with size q when the minimum distance is larger than 4.

This paper addresses the nonlinear memory effects in the response of typical illumination Light Emitting Diodes (LEDs), in order to enhance the performance of Visible Light Communication (VLC) systems. These LEDs have a limited bandwidth of only several MHz. To reflect the physical mechanisms in the Quantum Well (QW), we describe the LED transient response by a nonlinear dynamic differential equation. Three different mechanisms of the nonlinearity are relevant in the Double Hetero-structure (DH) LEDs, which result in dynamic nonlinearities, that is, a mixture of nonlinearities and memory effects. Hitherto generic pre-distorter and non-linear equalizers have been studied for LEDs. Yet this work shows that recombination rates of photon generation can be translated into an equivalent discrete-time circuit, that can be inverted. This allows us to develop a new pre-distorter with simpler and more efficient structure than previously studied and overly generic approaches. The novel predistorter along with a parameter estimation can effectively overcome LED nonlinearity for high-speed VLC with amplitude-based single carrier modulations, including On-Off Keying (OOK) and Pulse Amplitude Modulation (PAM)-4 systems, and with the multi-carrier Orthogonal Frequency Division Multiplexing (OFDM). We report experimentally obtained eyediagrams, firstly to justify our choice for the LED model on which our nonlinear predistorter have been based, and secondly to verify the effectiveness in enhancing the VLC link performance to the extent predicted by our model.

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are ${jointly}$ optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.

A locally repairable code (LRC) is a linear code such that every code symbol can be recovered by accessing a small number of other code symbols. In this paper, we study bounds and constructions of LRCs from the viewpoint of paritycheck matrices. Firstly, a simple and unified framework based on parity-check matrix to analyze the bounds of LRCs is proposed, and several new explicit bounds on the minimum distance of LRCs in terms of the field size are presented. In particular, we give an alternate proof of the Singleton-like bound for LRCs first proved by Gopalan et al. Some structural properties on optimal LRCs that achieve the Singleton-like bound are given. Then, we focus on constructions of optimal LRCs over the binary field. It is proved that there are only five classes of possible parameters with which optimal binary LRCs exist. Moreover, by employing the proposed parity-check matrix approach, we completely enumerate all these five classes of optimal binary LRCs attaining the Singleton-like bound in the sense of equivalence of linear codes.