Multilevel Coding Research Articles

Practical 8-PSK block-coded modulation with convolutional codes and soft decision block codes for packet networks

The design and performance of a class of practical rate 2/3, 8-PSK block-coded modulation (BCM) (also referred to as multilevel modulation codes) schemes are presented. These BCM schemes utilise both convolutional codes and block codes, and have block lengths that are matched with relatively short packet lengths to satisfy requirements in packet-wireless networks. Decoding issues such as optimum signal metrics and soft-decision decoding of block codes are addressed. Performance is evaluated and simulated. It is found that these BCM schemes exhibit a coding gain comparable to 16, 32 and 64 state Ungerboeck TCM codes, but require less complexity to decode.

Product coded modulation

This paper presents a new and powerful technique for constructing MPSK block modulation codes using product codes as the basic building blocks. Basic multilevel block modulation codes turn out to be a special case of this construction. Codes are constructed for both the AWGN and the Rayleigh fading channel and compared with the existing basic multilevel block modulation codes. Conditions on phase invariance of these codes are derived and two sub-optimal decoding schemes for these codes are proposed. Analytical performance bounds and simulation studies show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems. >

HDR satellite codec with concatenated multilevelcodes

The performance of a high data rate (HDR) codec based on a multidimensional modulation code derived from multilevel codes is evaluated for a satellite channel. The codec reliably supports HDR transmission for broadband ISDN over a 72 MHz satellite transponder and is designed to be used with an 8PSK modem. Results show that significant coding gain with higher spectral efficiency can be achieved compared to uncoded QPSK.

IMAGE COMPRESSION SCHEME WITH EMBEDDED MULTILEVEL BLOCK TRUNCATION CODING BASED ON HUMAN VISUAL EFFECT

ABSTRACT In this paper, we first propose a new embedded multilevel block truncation coding (BTC) technique. Unlike Differential pulse code modulation (DPCM), Vector quantization (VQ), and general multilevel BTC algorithms which determine the image quality at a time, the embedded multilevel BTC improves the image quality largely and progressively until obtaining an image with excellent quality. In order to reduce the bit rate efficiently, we propose a perception model and utilize it to develop a pruning algorithm. The pruning algorithm removes the useless information, which the human eyes are not sensitive, generated by the embedded multilevel BTC. The simulation results indicate that the bit rate with the proposed method is much less than that with the DPCM and general multilevel BTC under the same objective criterion, PSNR, or subjective criterion. This paper also shows that the computation complexity of the proposed method is much less than that with VQ under the same high quality reconstructed image.

Multilevel coded 16-QAM schemes for Rayleigh fadingchannels

Multilevel codes show better performance compared with trellis codes on Rayleigh fading channels at comparable decoder complexity and bandwidth. However, they suffer from performance degradation due to error propagation in the multistage decoder. The authors, with a view to minimising the error propagation, compare three multilevel coded 16-QAM schemes which are four-level codes, I/Q separated two-level codes and I/Q separated two-level codes with a new set partitioning.

On the spectrum of distances of a multilevel code, decoded by a multistage decoder

In this correspondence we are concerned with the error rates contributed by component codes in a multilevel code, decoded by a multistage decoder. These error rates are required for estimating the performance of the structure, but more importantly, they can serve as a design tool for achieving high coding gain. The latter objective can be reached by approaching a balance among these error rates. For evaluating the error rate contributed by a component code, it is essential to calculate the corresponding spectrum of Euclidean distances. A method for computing this spectrum is developed in this correspondence. The method is general and applicable to any signal constellation, and convolutional as well as block component codes. The error coefficient, available in the literature for some multilevel codes with an infinite size signal constellation, is shown to be significantly different from that of a practical finite constellation. Note that the complete spectrum is essential when codewords (of a component code) with Hamming distance beyond the minimum distance affect the error rate (see, e.g., Turbo codes).

Multiple symbol differentially detected multilevel codes for the Rayleigh-fading channel

Conventional differential detection is known to perform poorly on the fast-fading Rayleigh-fading channel due to the rapid variation of the channel state. The technique of multiple symbol differential detection (MSDD) improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process. To further reduce the error rate, we need to introduce some form of coding. Successful coding for the Rayleigh-fading channel requires interleaving to decorrelate the channel-a conflicting requirement to MSDD. We propose a solution consisting of interleaving blocks of L M-ary phase-shift keying (MPSK) symbols that are multiple symbol differentially detected. The blocks are treated as elements of an M/sup L/ symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined.

On block-coded modulation with interblock memory

Block-coded modulation with interblock memory (BCMIM) is a variation of block-coded modulation (BCM) which is designed for multilevel coding. By providing interblock memory between adjacent blocks, the coding rate of a BCMIM scheme can be increased without decreasing the minimum squared Euclidean distance (MSED) as compared to the original BCM. In an early version of BCMIM, interblock coding is provided only between the first two coding levels of adjacent blocks. In this paper, we design BCMIM with a more general form for which interblock coding can be introduced among many coding levels. In this way, we can further increase the coding rate of BCMIM without decreasing the MSED. We provide many examples to show the advantages of BCMIM with the general form. Most of the examples are designed based on multidimensional signal sets, since a multidimensional signal set can provide more coding levels than a two-dimensional (2-D) signal set.

Block Multidimensional MPSK Modulation Codes with Unequal Error Protection

The construction of block multidimensional M-PSK modulation codes with unequal error protection (UEP) is considered. An UEP profile for the Rayleigh fading channel is obtained by partitioning fourdimensional constellations that are Cartesian products of non-uniform 8-PSK modulations or are subsets of a product of uniform modulations. New codes are constructed by using the multilevel coding technique with very simple binary component codes. These codes are matched to the vector-sum excited linear predictive (VSELP) codec described in the IS-54 mobile system. .One of the constructed codes has four levels of protection and achieves a coding gain of 16.0 dB (at a SEGSNR of 2.0 dB) in comparison with a system that employs uncoded 4-PSK modulation.

Nearly optimum multilevel block truncation coding based on a mean absolute error criterion

A new generalized multilevel block truncation coding (BTC) algorithm based on a mean absolute error criterion is proposed. The proposed multilevel BTC algorithm requires only additions/subtractions to segment a block into desired regions. The simulation results indicate that the mean absolute error and peak signal-to-noise ratio (PSNR) of the algorithm is very close to those of the optimum BTC. The performance of the algorithm is superior to other multilevel BTC algorithms that have been proposed, both in image quality and in computational complexity.

Two-level codes for frequency/phase modulation

Trellis codes for frequency/phase modulation have larger asymptotic coding gain than trellis codes for phase modulation. Multilevel codes which enable multistage decoding have the advantage of larger asymptotic coding gain and lower decoder complexity than trellis codes. Combining these results, new two-level codes for frequency/phase modulation are presented.

Power and bandwidth efficient digital communication using turbo codes in multilevel codes

AbstractThe recently proposed Turbo codes are applied to bandwidth efficient modulation schemes via multilevel coding. For this purpose, Turbo codes are extended for a wide range of fine tunable rates by puncturing. A straightforward derivation of iterative Turbo decoding and the concept of extrinsic information is presented. New design rules for multilevel codes with arbitrary component codes and codeword lengths are derived from information theory. Simulation results show that application of Turbo codes to properly designed multilevel coding schemes leads to digital transmission schemes with high power and bandwidth efficiency.

The performance of multilevel coding employing hard decision and hybrid decoders on fading and Gaussian channels

Considers the use of hard decision decoders and hybrid decoders employing both hard and soft decisions in a multilevel coding scheme. The multilevel code is applied to MPSK signaling on the Rayleigh fading channel. Using hard decisions, the authors give the error performance of this approach. Additionally, codes that perform well on both fading and non-fading channels are explored. >

Performance evaluation of coded modulation schemes based on binary lattices

We describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding. These techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based. Multilevel coded-modulation schemes can also be described through a trellis; by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum-likelihood decoding using the Viterbi algorithm and for computing the error probability. An upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels, and is applicable to both maximum-likelihood and staged decoding. >

Multilevel construction of block and trellis group codes

The theory of group codes has been shown to be a useful starting point for the construction of good geometrically uniform codes. In this paper we study the problem of building multilevel group codes, i.e., codes obtained combining separate coding at different levels in such a way that the resulting code is a group code. A construction leading to multilevel group codes for semi-direct and direct products is illustrated. The codes that can be obtained in this way are identified. New geometrically uniform Euclidean-space codes obtained from multilevel codes over abelian and nonabelian groups are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Integrated receiver structure of staged decoder and CCI canceller for CDMA with multilevel coded modulation

AbstractThis work presents a direct sequence spread‐spectrum multiaccess (DS/CDMA) receiver that employs integrated structure of staged decoder and CCI (co‐channel interference) canceller, when multilevel coded modulation is used and the system undergoes fading channel. We exploit the attractive multistage decoding method of multilevel coding. Each stage decoding is jointly done with the data estimation process and thus replicas of CCI can be formed with high precision, which ultimately results in performance improvement without any additional decoding delay or circuit complexity. We have chosen appropriate multilevel 8‐PSK coded modulation schemes for the integrated receiver of staged decoder and CCI canceller in fading channels. Computer simulation results show the significant coding gain that can be achieved by the proposed scheme in comparison with the conventional scheme. The effect of estimation error as well as unequal power is also investigated.

Multilevel block codes for Rayleigh-fading channels

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm. >

Improved geometric Goppa codes. I. Basic theory

In this paper, we present a construction of improved geometric Goppa codes which, for the case of r<2g, are often more efficient than the current geometric Goppa codes derived from some varieties, which include algebraic curves, hyperplanes, surfaces, and other varieties. For the special case of a plane in a three-dimensional projective space, the improved geometric Goppa codes are reduced to linear multilevel codes. For these improved geometric Goppa codes, a designed minimum distance can be easily determined and a decoding procedure which corrects up to half the designed minimum distance is also given.

Complexity/performance tradeoffs in multistage decoders

AbstractThis paper describes suboptimal decoding methods for multilevel block‐encoded modulation schemes. These decoding methods can achieve large coding gains with relatively low decoding complexity, and operate, in part, by decoding a supercode of the code to be decoded. By decomposing the multilevel codes in various ways, a wide range of performance/complexity tradeoff points can be obtained. Introducing syndrome checking can further reduce the average decoding complexity with no degradation in performance. Both analysis and extensive simulation results confirm that a given coding gain can be achieved with significantly smaller decoding complexity than Viterbi decoding.

Capacities of equivalent channels inmultilevel coding schemes

The channel capacity of an M-ary digital transmission scheme M > 2 can in principle be achieved by multilevel codes together with multistage decoding, if the rates of the component codes are equal to the capacities of the equivalent channels for each coding level.