Near-capacity dirty-paper code design : a source-channel coding approach

This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity

DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

The work identifies the first general, explicit, and non-random MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions on Information Theor

Constellation Shaping for WDM systems using 256QAM/1024QAM with Probabilistic Optimization

In this paper, probabilistic shaping is numerically and experimentally investigated for increasing the transmission reach of wavelength division multiplexed (WDM) optical communication system employing quadrature amplitude modulation (QAM). An optimized probability mass function (PMF) of the QAM symbols is first found from a modified Blahut-Arimoto algorithm for the optical channel. A turbo coded bit interleaved coded modulation system is then applied, which relies on many-to-one labeling to achieve the desired PMF, thereby achieving shaping gain. Pilot symbols at rate at most 2% are used for synchronization and equalization, making it possible to receive input constellations as large as 1024QAM. The system is evaluated experimentally on a 10 GBaud, 5 channels WDM setup. The maximum system reach is increased w.r.t. standard 1024QAM by 20% at input data rate of 4.65 bits/symbol and up to 75% at 5.46 bits/symbol. It is shown that rate adaptation does not require changing of the modulation format. The performance of the proposed 1024QAM shaped system is validated on all 5 channels of the WDM signal for selected distances and rates. Finally, it was shown via EXIT charts and BER analysis that iterative demapping, while generally beneficial to the system, is not a requirement for achieving the shaping gain.Comment: 10 pages, 12 figures, Journal of Lightwave Technology, 201

Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.Comment: Accepted for Globecom 201

Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block 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