119 research outputs found
Algebraic number theory and code design for Rayleigh fading channels
Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available.
The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible
to a large audience
A Differential Turbo Detection Aided Sphere Packing Modulated Space-Time Coding Scheme
A signal construction method that combines orthogonal design with sphere packing has recently shown useful performance improvements over the conventional orthogonal design. In this contribution, we extend this concept and propose a novel Sphere Packing (SP) modulated differential Space-Time Block Coded (DSTBC) scheme, referred to here as (DSTBC-SP), which shows performance advantages over conventional DSTBC schemes. We also demonstrate that the performance of DSTBC-SP systems can be further improved by concatenating sphere packing aided modulation with channel coding and performing SP-symbol-to bit demapping as well as channel decoding iteratively. We also investigate the convergence behaviour of this concatenated scheme with the aid of Extrinsic Information Transfer (EXIT) Charts. The proposed turbo-detected DSTBC-SP scheme exhibits a ’turbo-cliff’ at Eb/N0 = 6dB and provides Eb/N0 gains of 23.7dB and 1.7dB at a BER of 10?5 over an equivalent-throughput uncoded DSTBC-SP scheme and a turbo-detected QPSK modulated DSTBC scheme, respectively
On the BICM Capacity
Optimal binary labelings, input distributions, and input alphabets are
analyzed for the so-called bit-interleaved coded modulation (BICM) capacity,
paying special attention to the low signal-to-noise ratio (SNR) regime. For
8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded
binary code results in a higher capacity than the binary reflected gray code
(BRGC) and the natural binary code (NBC). The 1 dB gap between the additive
white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be
almost completely removed if the input symbol distribution is properly
selected. First-order asymptotics of the BICM capacity for arbitrary input
alphabets and distributions, dimensions, mean, variance, and binary labeling
are developed. These asymptotics are used to define first-order optimal (FOO)
constellations for BICM, i.e. constellations that make BICM achieve the Shannon
limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable
transmission at asymptotically low rates in BICM can be as high as infinity,
that for uniform input distributions and 8-PAM there are only 72 classes of
binary labelings with a different first-order asymptotic behavior, and that
this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general
answer to the question of FOO constellations for BICM is also given: using the
Hadamard transform, it is found that for uniform input distributions, a
constellation for BICM is FOO if and only if it is a linear projection of a
hypercube. A constellation based on PAM or quadrature amplitude modulation
input alphabets is FOO if and only if they are labeled by the NBC; if the
constellation is based on PSK input alphabets instead, it can never be FOO if
the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor
A co-designed equalization, modulation, and coding scheme
The commercial impact and technical success of Trellis Coded Modulation seems to illustrate that, if Shannon's capacity is going to be neared, the modulation and coding of an analogue signal ought to be viewed as an integrated process. More recent work has focused on going beyond the gains obtained for Average White Gaussian Noise and has tried to combine the coding/modulation with adaptive equalization. The motive is to gain similar advances on less perfect or idealized channels
Low Complexity Decoding for Higher Order Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels
Trellis-coded modulation (TCM) is a power and bandwidth efficient digital
transmission scheme which offers very low structural delay of the data stream.
Classical TCM uses a signal constellation of twice the cardinality compared to
an uncoded transmission with one bit of redundancy per PAM symbol, i.e.,
application of codes with rates when denotes the
cardinality of the signal constellation.
Recently published work allows rate adjustment for TCM by means of puncturing
the convolutional code (CC) on which a TCM scheme is based on.
In this paper it is shown how punctured TCM-signals transmitted over
intersymbol interference (ISI) channels can favorably be decoded. Significant
complexity reductions at only minor performance loss can be achieved by means
of reduced state sequence estimation.Comment: 4 pages, 5 figures, 3 algorithms, accepted and published at 6th
International Symposium on Communications, Control, and Signal Processing
(ISCCSP 2014
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
On Optimal TCM Encoders
An asymptotically optimal trellis-coded modulation (TCM) encoder requires the
joint design of the encoder and the binary labeling of the constellation. Since
analytical approaches are unknown, the only available solution is to perform an
exhaustive search over the encoder and the labeling. For large constellation
sizes and/or many encoder states, however, an exhaustive search is unfeasible.
Traditional TCM designs overcome this problem by using a labeling that follows
the set-partitioning principle and by performing an exhaustive search over the
encoders. In this paper we study binary labelings for TCM and show how they can
be grouped into classes, which considerably reduces the search space in a joint
design. For 8-ary constellations, the number of different binary labelings that
must be tested is reduced from 8!=40320 to 240. For the particular case of an
8-ary pulse amplitude modulation constellation, this number is further reduced
to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate
one labeling in each class is also introduced. Asymptotically optimal TCM
encoders are tabulated which are up to 0.3 dB better than the previously best
known encoders
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