On the Computation of EXIT Characteristics for Symbol-Based Iterative Decoding

In this paper we propose an efficient method for computing index-based extrinsic information transfer (EXIT) charts, which are useful for estimating the convergence properties of non-binary iterative decoding. A standard method is to apply <i>a priori</i> reliability information to the <i>a posteriori</i> probability (APP) constituent decoder and compute the resulting average extrinsic information at the decoder output via multidimensional histogram measurements. However, this technique is only reasonable for very small index lengths as the complexity of this approach grows exponentially with the index length. We show that by averaging over a function of the extrinsic APPs for a long block the extrinsic information can be estimated with very low complexity. In contrast to using histogram measurements this method allows to generate EXIT charts even for larger index alphabets. Examples for a non-binary serial concatenated code and for turbo trellis-coded modulation, resp., demonstrate the capabilities of the proposed approach

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

Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding—Part I: Symmetric Constellations

In this paper, theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection (UEP) and multistage decoding are presented. It is shown that nonstandard signal set partitionings and multistage decoding provide excellent UEP capabilities beyond those achievable with conventional coded modulation. The coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits. The large effective error coefficients, normally associated with standard mapping by set partitioning, are reduced by considering nonstandard partitionings of the underlying signal set. The bits-to-signal mappings induced by these partitionings allow the use of soft-decision decoding of binary block codes. Moreover, parallel operation of some of the staged decoders is possible, to achieve high data rate transmission, so that there is no error propagation between these decoders. Hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels. The error performance of specific examples of multilevel codes over 8-PSK and 64-QAM signal sets are simulated and compared with theoretical upper bounds on the error performance

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

Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454

Punctured Trellis-Coded Modulation

In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of $\frac{K}{K+1}$ when $2^{K+1}$ denotes the cardinality of the signal constellation. In order to support different rates, multi-dimensional (i.e., $\mathcal{D}$-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM-schemes with $\frac{1}{\mathcal{D}}$ bit redundancy per real dimension. In contrast, in this paper we propose to perform rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM-scheme is based on. It is shown, that due to the nontrivial mapping of the output symbols of the CC to signal points in the case of puncturing, a modification of the corresponding Viterbi-decoder algorithm and an optimization of the CC and the puncturing scheme are necessary.Comment: 5 pages, 10 figures, submitted to IEEE International Symposium on Information Theory 2013 (ISIT