U. Wachsmann, R. F. H. Fischer, and J. B. Huber. Multilevel codes: Theoretical concepts and practical design rules. IEEE Trans. Information Theory, 45(7):1361--1391, July 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of Multidimensional MLC for OTD Suppose that the goal is to design a coded modulation scheme with rate 3 b s Hz and total diversity gain of 4. We use a 4D 256 point lattice constellation with 2D constituents coming from a 16QAM constellation, along with a two level MLC [16] 17] 14] 18] [19], which provides minimum Hamming distance of 2. Two convolutional encoders of rates 2 3 and 4 5 are used as the first and second level encoders. The 4D set partitioning chain 0 0 0 is used to partition the 256 point constellation into 8 subsets of size 32, as explained in [20] ....

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, "Multilevel codes: Theoretical concepts and practical design rules," IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1361--1391, July 1999.

....binary coding. This is based on using a set of parallel binary block codes to specify different bit values in a given binary labeling of the constellation points. The basic structure proposed in [3] has been further studied and generalized in a number of subsequent research works. Reference [4] which is the state of the art article in this category includes a detailed review of the relevant literature. Shaping concerns the selection of the boundary of a multidimensional signal constellation to reduce its average energy. It is well known that by using shaping techniques in conjunction ....

....Reference [32] discuses the application of shaping technique to Turbo codes using a nonuniform constellation. However, the shaping gain achievable using the method proposed in [32] is limited to about 0.2 db. The problem of shaping in conjunction with Turbo codes is also briefly mentioned in [4]. A common approach to Turbo coded modulation is based on a direct mapping of the output bits of a binary Turbo code to the points of a base constellation via an interleaver. In this configuration, the channel can be considered as m binary input, continuous output channels (the output of each ....

U. Wachsmann, R. F. H. Fischer and J. B. Huber, "Multilevel codes: theoretical concepts and practical design rules," IEEE Transactions on Information Theory, vol.45, no. 5, July 1999, pp. 1361-1391

....length, standard TCM codes are not very powerful, which prevents the turbo equalizer from attaining high coding gains. A particular solution to this problem is the use of block coded modulation (BCM) 96] 104 instead of TCM at the transmitter. An important subclass is multilevel coded modulation [127] whichisknown to provide performance improvements over trellis codes and be suitable for iterative decoding [128, 129] As mentioned in Chapter 2, TCM uses only two levels: one for the uncoded bits and a second for the convolutional encoder in order to generate the coded bits. On the other hand, ....

U. Wachsmann, R.F.H. Fischer, and J.B. Huber, \Multilevel codes: theoretical concepts and practical design rules," IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1361-91, July 1999.

....binary coding. This is based on using a set of parallel binary block codes to specify different bit values in a given binary labeling of the constellation points. The basic structure proposed in [3] has been further studied and generalized in a number of subsequent research works. Reference [4] which is the state of the art article in this category includes a detailed review of the relevant literature. It is also a well established fact that such a multi level coding scheme can approach the maximum theoretically achievable rate associated with a set of constellation points if: i) ....

.... the maximum theoretically achievable rate associated with a set of constellation points if: i) the rate of the underlying binary codes are adjusted properly, and (ii) these codes are decoded sequentially where each decoder takes advantage of the decoded bit value produced by its earlier stages [4]. It should be also mentioned that some of the generalizations reported in the literature (e.g. 5] 6] 7] almost remove the thin line of distinction between the above two families of schemes (namely those emerging from [2] and [3] respectively) and explain all known methods of combined coding ....

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U. Wachsmann, R. F. H. Fischer and J. B. Huber, "Multilevel codes: theoretical concepts and practical design rules," IEEE Transactions on Information Theory, vol.45, no. 5, July 1999, pp. 1361-1391

....the labeling strategy. In MLC, assuming equal coding rates R i , UEP is achieved through the labeling strategy. The use of equal coding rates allows for simplicity at the decoder and more importantly in no error propagation in the multi stage decoding module when block partitioning is used [6]. Our implementation uses equal coding rates and block partitioning. To explain this labeling strategy, let assume first that only one bit is taken from each layer to select a constellation point (symbol) in the complex plane R . Hence the constellation size is 2 . The bit taken from the ....

....level i, than it is with subsets at partition level i 1. Therefore, the data from video layer i would be more protected than the data from video layer i 1 and hence UEP is achieved. Each partition level in an MLC scheme can be thought of as an equivalent channel with information capacity C i [6]. For the block partitioning the following could be said regarding the information capacity at each level: C i C i 1 ; i = 1; L 1: 3) For a given user and SNR, the user can decode all L levels of the received signal if C i R i for 8i. However, if one of the rates R i exceeds the ....

U. Wachsmann, R.F.H. Fischer, and J.B. Huber, Multilevel Codes: Theoretical Concepts and Practical Design Rules, IEEE Trans. on Info. Theory, July 1999.

.... 4 15 8 3 5 14 9 2 1 0 10 11 13 12 6 7 4 15 8 3 5 14 9 2 1 0 10 11 13 12 6 7 4 15 8 3 5 14 9 d Figure 5: Illustration of multilevel coset interpretation of coding framework design the code and the constellation parameter akin to the framework of Multilevel Codes [14, 22] starting with optimizing the parameter d # , which gives the scale of the mapping from the code space into the Euclidean space; The larger the chosen value of d # , the larger the inter coset distance in the Euclidean space and better the noise resilience. But at the same time, the larger ....

U. Wachsmann, R. F. M. Fischer, and J. B. Huber. Multilevel codes: Theoretical concepts and practical design rules. IEEE Transactions on Information Theory, IT-45:1361--1391, July 1999.

....the full price zone from the discount zone. Of course, one can use multiple syndrome markers to reflect different shades of discount. These markers need to be optimized based on problem constraints. We draw parallels from this framework to that of multilevel coding in error correcting codes [22]. Note however that the analogy between DISCUS and the use of UEP codes for data transmission is completely opposite: in the latter, it is the MSBs that need higher strength codes Deployment in a Sensor Network We illustrate through a simple example the power of DISCUS in the context of a ....

U. Wachsmann, R.F.H. Fischer, and J.B. Huber, "Multilevel codes: Theoretical concepts and practical design rules," IEEE Trans. Inform. Theory, vol. 45, pp. 1361-1391, July 1999.

....idea then is to split the incoming data into L streams or levels as shown in Fig 4 and encode the data in each stream with a di#erent code C of rate R at level i. The rates for each of the levels then have to be chosen carefully. Di#erent methods for calculating these rates are available in [16]. We review some of the methods like balanced distances rule, coding exponent rule and the capacity design rule in the next subsection. The rule we used to choose the rates at each of the level is called the capacity Design rule [16] The decoding of Multilevel codes is then done using a type of ....

....Di#erent methods for calculating these rates are available in [16] We review some of the methods like balanced distances rule, coding exponent rule and the capacity design rule in the next subsection. The rule we used to choose the rates at each of the level is called the capacity Design rule [16]. The decoding of Multilevel codes is then done using a type of decoding known as multistage decoding(MSD) In conventional multi stage decoding L di#erent decoders are used as shown in Fig.4. Level 1 is decoded first whose decisions are then fed to decoder 2 which then decodes the level 2 data ....

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Udo Wachsmann, Robert.F.H.Fischer and J.B.Huber, "Multilevel Codes:Theoretical Concepts and practical design rules," IEEE Trans. Info. theory, vol 45,pp1361-1391,July 1999.

....choices are illustrated and the implementation on FPGA is presented. The authors conclude by analyzing the performance of the system and by showing experimental results. Keywords Multilevel Coded Modulation, Reed Solomon Codes, Ordered Statistics Decoding. I. INTRODUCTION It has been shown [1, 2] that multilevel codes (MLC) combined with staged decoding can reach high coding gain and reduce decoding complexity with respect to Maximum Likelihood (ML) decoding. Nevertheless, staged decoding of the outer codes may increase both storage requirements and system delay. These parameters cannot ....

U.Wachsmann, R.F.H.Fischer and J.B.Huber, `Multilevel codes: theoretical concepts and practical designing rules', IEEE Trans. Inform. Theory, vol. IT-45, pp.13611391, July 1999.

....and optimized in [5, 7] The combination of multilevel signaling with error correction coding generally requires the joint optimization of coding and modulation. This is e.g. true for the design of space time trellis codes [23] However, for single antenna transmission schemes it has been proven [24] that the optimization problem can be separated by applying properly designed multilevel coding (MLC) with multistage decoding (MSD) 25, 24] along with (standard) binary component codes. Furthermore, if the labeling of signal points is chosen such that decoding at higher levels is almost ....

....of coding and modulation. This is e.g. true for the design of space time trellis codes [23] However, for single antenna transmission schemes it has been proven [24] that the optimization problem can be separated by applying properly designed multilevel coding (MLC) with multistage decoding (MSD) [25, 24] along with (standard) binary component codes. Furthermore, if the labeling of signal points is chosen such that decoding at higher levels is almost independent from decisions already made at lower levels, parallel decoding of levels can be applied without loss in performance (cf. 24] Now, ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel Codes: Theoretical Concepts and Practical Design Rules. IEEE Trans. Inf. Theory, 44(3):927-946, May 1999.

....Three unconventional set partitionings are applied to asymmetric 8 PSK constellations and their error performance is discussed. Upper bounds on the bit error probability, when linear block component codes are used over the AWGN channel, are derived by extending union bound arguments introduced in [2, 8, 10] to asymmetric PSK constellations. In deriving the pairwise error probabilities contributing to the corresponding union bounds for multistage decoding of multilevel coded modulation schemes, two general cases are explicitly distinguished and applied in this paper. In the first case, each pair of ....

....2w dimensional decision region. These 2w dimensional decision regions simply correspond to the underlying two dimensional constellation, replicated in w orthogonal dimensions, so that Pythagoras theorem holds. This method applies to conventional Ungerboeck type partitioning [9] as shown in [2, 10]. However, for many unconventional partitionings (possibly together with asymmetric constellations) different pairs of code sequences considered in the union bound share the same decision regions, so that Pythagoras theorem no longer holds. In this case, the line joining the code sequences of ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer and J.B. Huber,"Multilevel codes: theoretical concepts and practical design rules," IEEE Trans. Inform. Theory, vol.45, no.5, pp.1361-1391, July 1999.

....decoding techniques is indicated. Assuming fast fading with respect to one code word, the capacity of the ergodic channel for a given ST constellation is considered as appropriate performance measure. As optimum coded modulation strategy multilevel coding (MLC) with multistage decoding (MSD) [3, 4] is devised. To reduce the implementational complexity of MLC, we propose to merge coding levels yielding hybrid coded modulation (HCM) schemes, cf. 5] If only one level remains, simple bit interleaved coded modulation (BICM) 6, 7] is obtained as a special case. At the receiver, multiple symbol ....

....over the set S. 3 Coded Modulation for DSTM and MSDD It is apparent from the equivalent model in Fig. 1, that coded modulation schemes matched to DSTM with MSDD should perform coding on matrix symbols V [k N ] To this end, we discuss the application of well known multilevel coding (MLC) [3, 4] and bit interleaved coded modulation (BICM) 6, 7] and so called hybrid coded modulation (HCM) 5] which combines the power eciency of MLC with the simplicity of BICM. Moreover, a low complexity version of MSDD, which is referred to as simpli ed MSDD [11] is applied. We would like to ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel Codes: Theoretical Concepts and Practical Design Rules. IEEE Trans. Inf. Theory, 44(3):927-946, May 1999.

....(ML) decoding possible. Assuming fast fading with respect to one code word, the capacity of the ergodic channel for a given ST constellation is considered as appropriate performance measure. As optimum coded modulation strategy multilevel coding (MLC) with multistage decoding (MSD) 4] [5] is devised. To reduce the implementational complexity of MLC, we propose to merge coding levels yielding hybrid coded modulation (HCM) schemes, cf. 6] If only one level remains, simple bit interleaved coded modulation (BICM) 7] is obtained as a special case. At the receiver, multiple symbol ....

....channel between R[kN ] can be regarded as memoryless. III. CODED MODULATION AND CAPACITY Apparently, coded modulation schemes matched to DSTM with MSDD should perform coding on matrix symbols V [k N ] To this end, we discuss the application of well known multilevel coding (MLC) 4] [5], bit interleaved coded modulation (BICM) 7] and so called hybrid coded modulation (HCM) 6] which are illustrated in Fig. 1 Moreover, a low complexity version of MSDD, which is referred to as simplified MSDD [9] is applied. We consider binary component codes and separate labeling of the N 1 ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel Codes: Theoretical Concepts and Practical Design Rules. IEEE Trans. Inf. Theory, 44(3):927--946, May 1999.

....on fast fading channels with channel state information available at the receiver only. Regarding multiple antenna signaling as multi dimensional modulation we propose to separate the optimization of coding and modulation. Such an approach has shown to be optimum for single antenna systems [8]. In perfect analogy, the mutual information chain rule immediately leads to the application of multilevel coding (MLC) with multistage decoding (MSD) 9, 8] in the case of multiple antenna systems, too. As modulation strategy we consider both independent signaling over each transmit antenna and ....

....we propose to separate the optimization of coding and modulation. Such an approach has shown to be optimum for single antenna systems [8] In perfect analogy, the mutual information chain rule immediately leads to the application of multilevel coding (MLC) with multistage decoding (MSD) [9, 8] in the case of multiple antenna systems, too. As modulation strategy we consider both independent signaling over each transmit antenna and space time block codes (STBC) 10, 11] employing phase shift keying (PSK) and quadratureamplitude modulation (QAM) respectively. Here, we exclusively ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel Codes: Theoretical Concepts and Practical Design Rules. IEEE Trans. Inf. Theory, 44(3):927--946, May 1999.

....This vec 1Corresponding Author tot channel is completely characterized by the single complex N dimensional probability density function (pdf) pyN(YNlaN l) of YN for given av 1. Details are given in [2] In this letter, the application of multilevel coding (MLC) with multistage decoding (MSD) [3, 4] to noncoherent transmission with MSDD is treated. In particular, a simple metric generation for MSD and MSDD with N 2 is presented, which requires a simi lar computational complexity as conventional differential detection (N = 2) But since longer blocks (N 2) are processed, power efficiency ....

....Multilevel Coding and Low Complexity Decoding As natural choice when performing MSDD, coding is done with respect to the vectors aN 1. For the resulting coded modulation scheme with (N 1) log2(M ) binary address symbols b i per modulation symbol aN 1, we apply well known multilevel coding (MLC) [3, 4]. In MLC, the binary digits b i stem from individual encoding. For MSDD and MLC with MSD, at level i metrics are based on the two pdfs pyN(Yvl bi, be, bi 1] of Yv given the decisions be, b i 1 of lower levels and a trial symbol b i 0, 1 . Optimally, these pdfs are obtained by averaging ....

[Article contains additional citation context not shown here]

U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel Codes: Theoretical Concepts and Practical Design Rules. IEEE Trans. on Inf. Theory, 44(3):927-946, May 1999.

....additional outer binary codes C i with rate R i = I(U i ; # Y j(U 1 U i 1 ) and thus lowering the total rate below C. This scheme is depicted in Fig. 5. The chain rule leads immediately to the multilevel structure of generalized concatenated codes [25] designed w.r.t. a capacity criterion [22]. Furthermore we see, that multistage decoding is optimum in principle, as it has the potential to achieve capacity. Fig. 5. Generalized concatenated code with multistage decoding. As mentined above I( # U ; # Y ) is independent of the particular encoding used, but I(U i ; # Y j(U 1 U i ....

U. Wachsmann, R. Fischer, J. Huber, "Multilevel Codes: Theoretical Concepts and Practical Design Rules". IEEE Transactions on Information Theory, pp. 1361-1391, July 1999.

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U. Wachsmann, R. F. H. Fischer, and J. B. Huber. Multilevel codes: Theoretical concepts and practical design rules. IEEE Trans. Information Theory, 45(7):1361--1391, July 1999.

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U. Wachsmann, R.F.H. Fischer, J.B. Huber, "Multilevel codes: theoretical concepts and practical design rules " IEEE Trans. Inform. Theory, vol. 45, pp. 1361-1391, July 1999.

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U. Wachsmann, R.F.H. Fischer and J.B. Huber, "Multilevel codes: theoretical concepts and practical design rules " IEEE Transactions Inform. Theory, vol. 45, pp. 1361-1391, July 1999.

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U. Wachsmann, F. H. Fischer, and J. B. Huber, "Multilevel codes: Theoretical concepts and practical design rules," IEEE Trans. Inform. Theory, vol. 45, pp. 1361--1391, July 1999.

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U. Wachsmann, F. H. Fischer, and J. B. Huber. Multilevel codes: theoretical concepts and practical design rules. IEEE Trans. on Info. Theory, 45(5):1361--1391, July 1999.

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U. Wachsmann, R.F.H. Fischer, J.B. Huber, "Multilevel codes: theoretical concepts and practical design rules " IEEE Trans. Inform. Theory, vol. 45, pp. 1361-1391, July 1999.

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U. Wachsmann, R.F.H. Fischer, and J.B. Huber. Multilevel codes: theoretical concepts and practical design rules. IEEE Transactions on Information

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U. Wachsmann, R. Fischer, J. Huber, "Multilevel codes: theoretical concepts and practical design rules", IEEE Trans. on Info. Theory, vol. 45, no. 5, July 1999, pp. 1361-91.

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U. Wachsmann, R. F. H. Fischer, and J. B. Huber, "Multilevel Codes: Theoretical Concepts and Practical Design Rules," IEEE Transactions on Information Theory 45, pp. 1361-1391, July 1999.

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