Lattices from Codes for Harnessing Interference: An Overview and Generalizations

In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D, and Construction $\pi_A$ (previously called product construction) recently proposed by the authors. We then discuss two generalizations where the first one is a general construction of lattices named Construction $\pi_D$ subsuming the above three constructions as special cases and the second one is to go beyond principal ideal domains and build lattices over algebraic integers

Second-Order Weight Distributions

A fundamental property of codes, the second-order weight distribution, is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles. A series of results, parallel to those for weight distributions, is established for second-order weight distributions. In particular, an analogue of MacWilliams identities is proved. The second-order weight distributions of regular LDPC code ensembles are then computed. As easy consequences, the second moments of weight distributions of regular LDPC code ensembles are obtained. Furthermore, the application of second-order weight distributions in random coding approach is discussed. The second-order weight distributions of the ensembles generated by a so-called 2-good random generator or parity-check matrix are computed, where a 2-good random matrix is a kind of generalization of the uniformly distributed random matrix over a finite filed and is very useful for solving problems that involve pairwise or triple-wise properties of sequences. It is shown that the 2-good property is reflected in the second-order weight distribution, which thus plays a fundamental role in some well-known problems in coding theory and combinatorics. An example of linear intersecting codes is finally provided to illustrate this fact.Comment: 10 pages, accepted for publication in IEEE Transactions on Information Theory, May 201

Near-Capacity Turbo Coded Soft-decision Aided DAPSK/Star-QAM for Amplify-and-Forward based Cooperative Communications

Multilevel Differential Amplitude and Phase-Shift Keying (DAPSK) schemes do not require any channel estimation, which results in low complexity. In this treatise we derive the soft-output probability formulas required for a soft-decision based demodulation of high-order DAPSK, in order to facilitate iterative detection by exchanging extrinsic information with an outer Turbo Code (TC). Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. Compared to the identical-throughput TC assisted 64-ary Differential Phase-Shift Keying (64-DPSK) scheme, the 4-ring based TC assisted 64-ary DAPSK arrangement has a power-efficiency improvement of 2.3 dB at a bit error rate (BER) of 10-5 . Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. More specifically, when using a TC block length of 400 modulated symbols, the 64 DAPSK (4, 16) scheme is 7.56 dB away from its capacity curve, while it had a reduced gap as low as 2.25 dB, when using a longer TC block length of 40 000 modulated symbols. Finally, as a novel application example, the soft-decision M-DAPSK scheme was incorporated into an Amplify-and-Forward (AF) based cooperative communication system, which attains another 4.5 dB SNR improvement for a TC block length of 40 000 modulated symbols

Algebraic Approach to Physical-Layer Network Coding

The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, an algebraic approach is taken to show its potential in practical, non-asymptotic, settings. A general framework is developed for studying nested-lattice-based PNC schemes---called lattice network coding (LNC) schemes for short---by making a direct connection between C&F and module theory. In particular, a generic LNC scheme is presented that makes no assumptions on the underlying nested lattice code. C&F is re-interpreted in this framework, and several generalized constructions of LNC schemes are given. The generic LNC scheme naturally leads to a linear network coding channel over modules, based on which non-coherent network coding can be achieved. Next, performance/complexity tradeoffs of LNC schemes are studied, with a particular focus on hypercube-shaped LNC schemes. The error probability of this class of LNC schemes is largely determined by the minimum inter-coset distances of the underlying nested lattice code. Several illustrative hypercube-shaped LNC schemes are designed based on Construction A and D, showing that nominal coding gains of 3 to 7.5 dB can be obtained with reasonable decoding complexity. Finally, the possibility of decoding multiple linear combinations is considered and related to the shortest independent vectors problem. A notion of dominant solutions is developed together with a suitable lattice-reduction-based algorithm.Comment: Submitted to IEEE Transactions on Information Theory, July 21, 2011. Revised version submitted Sept. 17, 2012. Final version submitted July 3, 201

Challenges and Some New Directions in Channel Coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: spatially coupled Low-Density Parity-Check (LDPC) codes, nonbinary LDPC codes, and polar coding.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/JCN.2015.00006

Coding Theory

Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances

Design guidelines for spatial modulation

A new class of low-complexity, yet energyefficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO) has emerged. These systems are capable of exploiting the spatial dimensions (i.e. the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication whilst relying on a single-Radio Frequency (RF) chain. Moreover, SM may also be viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/ cooperative protocol design issues, and on their meritorious variants

On chip interconnects for multiprocessor turbo decoding architectures

International audienc

Optimization of a Coded-Modulation System with Shaped Constellation

Conventional communication systems transmit signals that are selected from a signal constellation with uniform probability. However, information-theoretic results suggest that performance may be improved by shaping the constellation such that lower-energy signals are selected more frequently than higher-energy signals. This dissertation presents an energy efficient approach for shaping the constellations used by coded-modulation systems. The focus is on designing shaping techniques for systems that use a combination of amplitude phase shift keying (APSK) and low-density parity check (LDPC) coding. Such a combination is typical of modern satellite communications, such as the system used by the DVB-S2 standard.;The system implementation requires that a subset of the bits at the output of the LDPC encoder are passed through a nonlinear shaping encoder whose output bits are more likely to be a zero than a one. The constellation is partitioned into a plurality of sub-constellations, each with a different average signal energy, and the shaping bits are used to select the sub-constellation. An iterative receiver exchanges soft information among the demodulator, LDPC decoder, and shaping decoder. Parameters associated with the modulation and shaping code are optimized with respect to information rate, while the design of the LDPC code is optimized for the shaped modulation with the assistance of extrinsic-information transfer (EXIT) charts. The rule for labeling the constellation with bits is optimized using a novel hybrid cost function and a binary switching algorithm.;Simulation results show that the combination of constellation shaping, LDPC code optimization, and optimized bit labeling can achieve a gain in excess of 1 dB in an additive white Gaussian noise (AWGN) channel at a rate of 3 bits/symbol compared with a system that adheres directly to the DVB-S2 standard