Udo Wachsmann

Multilevel codes: theoretical concepts and practical design rules

This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD). The known result that MLC and MSD suffice to approach capacity if the rates at each level are appropriately chosen is reviewed. Using multiuser information theory, it is shown that there is a large space of rate combinations such that MLC and full maximum-likelihood decoding (MLD) can approach capacity. It is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and, therefore, require the huge complexity of MLD. The capacity rule, the balanced distances rules, and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design. Simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies. Moreover, topics relevant in practical applications such as signal set labeling, dimensionality of the constituent constellation, and hard-decision decoding are emphasized. Bit interleaved coded modulation, proposed by Caire et al. (see ibid., vol.44, p.927-46, 1998), is reviewed in the context of MLC. Finally, the combination of signal shaping and coding is discussed. Significant shaping gains are achievable in practice only if these design rules are taken into account.

Structure and performance of the HIPERLAN/2 physical layer

At present, standards for broadband wireless multimedia communications in the 5 GHz band are being developed in Europe as well as in the USA and Japan. HIPERLAN/2 is an upcoming standard which is being specified by the ETSI Project BRAN and is intended to be finished in April 2000. The physical layers of the three systems will be well-harmonized whereas the upper layer protocols are different. In this paper, the concepts and parameters of the physical layer of HIPERLAN/2 are described. According to the harmonization with the American and the Japanese system similarities and differences are pointed out. Furthermore, exemplary performance results are included and discussed.

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

The 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.

Exploiting the data-rate potential of MIMO channels: multi-stratum space-time coding

There is a high potential with respect to Shannon capacity in having a multiple-input multiple-output (MIMO) channel. In this paper a new MIMO coding approach, called multi-stratum space-time coding (MSSTC) is presented The principle of MSSTC is to partition the data stream and to transmit the substreams on separate strata. The transmission on every stratum is based on space-time block coding (STBC) yielding full diversity. Orthogonal superposition of the strata results in independent transmit symbols and enables therefore a high data rate. Decoding may be done successively stratum by stratum yielding reasonable receiver complexity. The structural properties inherent in MSSTC make it a robust scheme for varying channel conditions. A Shannon capacity comparison to other MIMO schemes like V- and D-BLAST is presented showing the robustness of MSSTC in different environments.

Multilevel coding: aspects from information theory

Important issues for coded modulation in practice are derived from information theoretic parameters. Optimality of multilevel coding as well as various rules to assign rates to the individual component codes are discussed. Moreover, suitable dimensionality of the signal constellation used for coding is considered. All phenomena predicted from information theory are confirmed by simulation results. Finally, optimum combination of coding and signal shaping is derived. Noticeable shaping gains are only achievable if presented rules are taken into account.

Modulation for HIPERLAN type 2

Currently, standards for wireless multimedia communication with high bit rate in the 5 GHz band are being developed in the US, Europe, and Japan. The available user data rate for these systems is supposed to be significantly greater than 10 Mbps. The high data rate and the channel characteristics are the main challenges for the design of the physical layer and in particular the selection of modulation technique for such a system. In this paper two modulation techniques, single-carrier and multicarrier modulation (implemented by OFDM), are considered as candidates. Both techniques are introduced, individually optimized to some extent and finally compared with regard to link performance and other aspects like coverage and power consumption. It is shown that for the assumed conditions the addressed coherent OFDM scheme provides about 2-3 dB performance gain compared to single-carrier modulation as well as non-coherent OFDM.

Mutual Information of MIMO Transmission over Correlated Channels with Finite Symbol Alphabets and Link Adaptation

In this paper, results on the mutual information of MIMO transmission over spatially correlated channels in slow fading environments are presented. Different receiver techniques such as optimal maximum likelihood detection, parallel layer detection, successive interference cancelation detection and linear detection are compared. The transmit signals are derived from finite signal alphabets such as M-QAM. Different degrees of adapting the transmit signals to the channel state are taken into account. Results show that the gap between successive interference cancelation and maximum likelihood detection almost vanishes in a 2x2 MIMO transmission setup if link adaptation can be applied, regardless of spatial correlation.

Mutual information maximizing linear precoding for parallel layer MIMO detection

In this paper mutual information maximizing linear precoding for MIMO transmission using finite signal alphabets and a parallel layer MIMO detection scheme is derived. The derivation exploits that the mutual information of the parallel detection scheme can be expressed in terms of the mutual information associated with optimal maximum likelihood detection. Results show that the large performance gap between parallel layer detection and maximum likelihood detection in ill conditioned channels can be substantially alleviated by optimal precoding.

Codierte Modulation mittels Multilevel-Codes: Entwicklung und aktueller Stand der Forschung

Während der ersten 25 Jahre nach der Begründung der Informationstheorie durch C.E. Shannon vor jetzt genau 50 Jahren konzentrierte sich die Entwicklung der Kanalcodierung nahezu ausschlieÿlich auf die binäre digitale Übertragung, also z.B. binäre Amplituden bzw. Phasenmodulation (BPSK), quaternäre Phasenmodulation mit unabhängiger binärer Übertragung in beiden Quadraturkomponenten (QPSK mit Gray Zuordnung bzw. 4 QAM). Man stellte jedoch bald fest, daÿ eine direkte Anwendung von binären Codes zur Vorwärtsfehlerkorrektur (Forward Error Correction: FEC) gemäÿ Bild 1 auf höherstu ge Übertragungsverfahren, die eine höhere Bandbreitene zienz (Informations uÿ bit s je Hz Signalbandbreite) bieten, wenig e zient ist. Dieser E ekt wird anhand eines Vergleichs von Übertragungsverfahren im Leistungs Bandbreiten Diagramm (LBD) für den Kanal mit Störung durch weiÿes Gauÿsches Rauschen (AWGN Kanalmodell) deutlich, das in Bild 2 dargestellt ist. Hierbei wird die Leistungse zienz durch den Störabstand, gemessen in äquivalenter Energie Eb je Informationsbit bezogen auf die einseitige Rauschleistungsdichte N0, repräsentiert, der notwendig ist, um eine hinreichende Zuverlässigkeit der digitalen Übertragung zu erreichen (hier Bitfehlerrate BER 10 ). Die gestrichelten Kurven gelten für binäre, primitive BCH Codes (siehe z.B. [12]) mit Blocklänge 31 bzw. 255. Mit zunehmender Korrekturfähigkeit wird zwar der erforderliche Störabstand geringer, zugleich fällt jedoch die Bandbreitene zienz infolge der Übertragung von mehr Kontrollsymbolen (sinkende Coderate). Bei gleicher Bandbreitene zienz sind nur rel. geringe Gewinne (ca. 2 dB) mit langen Codes im Vergleich zu uncodierter Übertragung zu erzielen, während sich kurze Codes im Bereich gröÿerer Bandbreitene zienz ( 2) als völlig nutzlos erweisen. Aus diesem Grund hat im Jahr 1974 J.L. Massey vorgeschlagen [13], Kanalcodierung und Modulation als Einheit zu betrachten und gemeinsam zu optimieren, und damit die sog. codierte Modulation begründet. In den Jahren 1976/77 haben Ungerböck [16, 15] und Imai [10] unabhängig voneinander leistungsfähige Verfahren zur codierte Modulation vorgestellt. In beiden Ansätzen wird anstelle der Hammingdistanz die minimale Euklidische Distanz der Signalpunkte im Signalraum maximiert. Bandbreitene ziente digitale Übertragungsverfahren beruhen für 3 Hz verzugsweise auf digitaler Pulsamplituden Modulation (PAM) mit einer Basissignalkonstellationen A IR in D Dimensionen (D = 1: ASK; D = 2: PSK, QAM) und M := 2` Signalpunkten. Zentral ist das Konzept der Zuordnung von binären Adressvektoren xm = (x0m; x 1 m; : : : ; x ` 1 m ), xm 2 f0; 1g zu den 2 ` Signalpunkten am, m = 1; 2; : : : ;M , der Signalkonstellation A. Vorzugsweise wird diese durch fortgesetzte Partitionierung der Signalmenge festgelegt. Die am häu gsten verwendete Zuordnungsmethode maximiert die minimale Euklidische Distanz innerhalb der Teil-

Distance profile of multilevel coded transmission and rate design

The analytic estimation of the error probability at the individual levels of a multilevel coding (MLC) scheme based on the distance profile in Euclidean space is given. An obvious application is to design the individual rates of an MLC scheme according to the criterion of approximately equal bit error probabilities at all levels. This so-called error probability rule is demonstrated for 16-state convolutional codes.