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This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. [ABSTRACT FROM AUTHOR]

We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a window of size $w$ bits. These $\delta $ deletions do not necessarily occur in consecutive positions, but are restricted to the window of size $w$. The localized deletions model is a generalization of the bursty model, in which all the deleted bits are consecutive. In this paper, we construct new explicit codes for the localized model, based on the family of Guess & Check codes which was previously introduced by the authors. The codes that we construct can correct, with high probability, $\delta \leq w$ deletions that are localized in a single window of size $w$ , where $w$ grows with the block length. Moreover, these codes are systematic; have low redundancy; and have efficient deterministic encoding and decoding algorithms. We also generalize these codes to deletions that are localized within multiple windows in the codeword. [ABSTRACT FROM AUTHOR]

Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices, in Flash devices, in optical recording devices, and in some computer standards. This paper introduces a new family of fixed-length, binary constrained codes, named lexicographically-ordered constrained codes (LOCO codes), for bipolar non-return-to-zero signaling. LOCO codes are capacity-achieving, the lexicographic indexing enables simple, practical encoding and decoding, and this simplicity is demonstrated through analysis of circuit complexity. LOCO codes are easy to balance, and their inherent symmetry minimizes the rate loss with respect to unbalanced codes having the same constraints. Furthermore, LOCO codes that forbid certain patterns can be used to alleviate inter-symbol interference in MR systems and inter-cell interference in Flash systems. Numerical results demonstrate a gain of up to 10% in rate achieved by LOCO codes with respect to other practical constrained codes, including run-length-limited codes, designed for the same purpose. Simulation results suggest that it is possible to achieve a channel density gain of about 20% in MR systems by using a LOCO code to encode only the parity bits, limiting the rate loss, of a low-density parity-check code before writing. [ABSTRACT FROM AUTHOR]

Lattice codes are elegant and powerful structures that not only achieve the capacity of the additive white Gaussian noise (AWGN) channel but are also a key ingredient to many multiterminal schemes that exploit linearity properties. However, constructing lattice codes that can realize these benefits with low complexity is still a challenging problem. In this paper, efficient encoding and decoding algorithms are proposed for multilevel binary low-density parity-check (LDPC) lattices constructed via Construction $\text{D}'$ whose complexity is linear in the total number of coded bits. Moreover, a generalization of Construction $\text{D}'$ is proposed, which relaxes some of the nesting constraints on the parity-check matrices of the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage decoding is comparable to that of polar lattices and close to that of low-density lattice codes on the power-unconstrained AWGN channel. [ABSTRACT FROM AUTHOR]