Wireless Communications

Alhussein Abouzeid Rensselaer Polytechnic Institute Raviraj Adve University of Toronto Dharma Agrawal University of Cincinnati Walid Ahmed Tyco M/A-COM Sonia Aissa University of Quebec, INRSEMT Huseyin Arslan University of South Florida Nallanathan Arumugam National University of Singapore Saewoong Bahk Seoul National University Claus Bauer Dolby Laboratories Brahim Bensaou Hong Kong University of Science and Technology Rick Blum Lehigh University Michael Buehrer Virginia Tech Antonio Capone Politecnico di Milano Javier Gómez Castellanos National University of Mexico Claude Castelluccia INRIA Henry Chan The Hong Kong Polytechnic University Ajit Chaturvedi Indian Institute of Technology Kanpur Jyh-Cheng Chen National Tsing Hua University Yong Huat Chew Institute for Infocomm Research Tricia Chigan Michigan Tech Dong-Ho Cho Korea Advanced Institute of Science and Tech. Jinho Choi University of New South Wales Carlos Cordeiro Philips Research USA Laurie Cuthbert Queen Mary University of London Arek Dadej University of South Australia Sajal Das University of Texas at Arlington Franco Davoli DIST University of Genoa Xiaodai Dong, University of Alberta Hassan El-sallabi Helsinki University of Technology Ozgur Ercetin Sabanci University Elza Erkip Polytechnic University Romano Fantacci University of Florence Frank Fitzek Aalborg University Mario Freire University of Beira Interior Vincent Gaudet University of Alberta Jairo Gutierrez University of Auckland Michael Hadjitheodosiou University of Maryland Zhu Han University of Maryland College Park Christian Hartmann Technische Universitat Munchen Hossam Hassanein Queen's University Soong Boon Hee Nanyang Technological University Paul Ho Simon Fraser University Antonio Iera University "Mediterranea" of Reggio Calabria Markku Juntti University of Oulu Stefan Kaiser DoCoMo Euro-Labs Nei Kato Tohoku University Dongkyun Kim Kyungpook National University Ryuji Kohno Yokohama National University Bhaskar Krishnamachari University of Southern California Giridhar Krishnamurthy Indian Institute of Technology Madras Lutz Lampe University of British Columbia Bjorn Landfeldt The University of Sydney Peter Langendoerfer IHP Microelectronics Technologies Eddie Law Ryerson University in Toronto

Wireless communications

This paper presents a new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving. Decoding calls on iterative processing in which each component decoder takes advantage of the work of the other at the previous step, with the aid of the original concept of extrinsic information. For sufficiently large interleaving sizes, the correcting performance of turbo-codes, investigated by simulation, appears to be close to the theoretical limit predicted by Shannon.

/pdf/near-optimum-error-correcting-coding-and-decoding-turbo-1rr3xsfa1x.pdf

Near optimum error correcting coding and decoding: turbo-codes

Iterative decoding of two-dimensional systematic convolutional codes has been termed "turbo" (de)coding. Using log-likelihood algebra, we show that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 2/3. Any combination of block and convolutional component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of 10/sup -4/ the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations.

http://www.wireless.ece.ufl.edu/eel6550/lit/HagenauerIterativeDecoding.pdf

Iterative decoding of binary block and convolutional codes

Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes.

/pdf/convergence-behavior-of-iteratively-decoded-parallel-4rfahetw9j.pdf

Convergence behavior of iteratively decoded parallel concatenated codes

For estimating the states or outputs of a Markov process, the symbol-by-symbol MAP algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of nonlinear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low SNR (a common example is the max-log-MAP because of its use of the max function). A further simplification yields the soft-output Viterbi algorithm (SOVA). We present a log-MAP algorithm that avoids the approximations in the max-log-MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (log-)MAP, max-log-MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example forming the basis for simulations, we consider Turbo decoding, where recursive systematic convolutional component codes are decoded with the three algorithms, and we also demonstrate the practical suitability of the log-MAP by including quantization effects. The SOVA is, at 10/sup -4/, approximately 0.7 dB inferior to the (log-)MAP, the max-log-MAP lying roughly in between. We also present some complexity comparisons and conclude that the three algorithms increase in complexity in the order of their optimality.

A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain

The potential of pilot-symbol-aided channel estimation in two dimensions are explored. In order to procure this goal, the discrete shift-variant 2-D Wiener filter is derived and analyzed given an arbitrary sampling grid, an arbitrary (but possibly optimized) selection of observations, and the possibility of model mismatch. Filtering in two dimensions is revealed to outperform filtering in just one dimension with respect to overhead and mean-square error performance. However, two cascaded orthogonal 1-D filters are simpler to implement and shown to be virtually as good as true 2-D filters.

Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering

For estimating the states or outputs of a Markov process, the symbol-by-symbol maximum a posteriori (MAP) algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of non-linear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low SNR (a common example is the Max-Log-MAP because of its use of the max function). A further simplification yields the soft-output Viterbi algorithm (SOVA). In this paper, we present a Log-MAP algorithm that avoids the approximations in the Max-Log-MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (Log-)MAP, Max-Log-MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example, we consider Turbo decoding, and we also demonstrate the practical suitability of the Log-MAP by including quantization effects. The SOVA is, at 10−4, approximately 0.7 dB inferior to the (Log-)MAP, the Max-Log-MAP lying roughly in between. The channel capacities of the three algorithms -when employed in a Turbo decoder- are evaluated numerically.

Optimal and Sub-optimal Maximum A-Posteriori Algorithms Suitable for Turbo-Decoding.

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used.

/pdf/bandwidth-efficient-turbo-trellis-coded-modulation-using-ck6infru9m.pdf

Bandwidth-efficient turbo trellis-coded modulation using punctured component codes

A coding scheme (turbo codes) was proposed, that achieves almost reliable data communication at signal-to-noise ratios very close to the Shannon-limit. We show that the associated iterative decoder can be formulated in a simpler fashion by passing information from one decoder to the next using log-likelihood ratios as opposed to channel values that need to be normalized. Also no heuristically determined correction parameters are necessary for stable decoding. In addition, we can reduce the average number of iterations needed for the same BER performance by determining when further iterations achieve no more benefit. Furthermore, it seems that the trellis-termination problem appears non-trivial and we give a pragmatic suboptimal solution. We investigate different block sizes and also a hybrid scheme that performs extremely well with less computations. A drawback of the codes has been discovered: the BER curves show a flattening at higher signal-to-noise ratios, this is due to the small minimum distance of the whole code. By analyzing the interleaver used in the encoder we can calculate approximations to the BER at high SNRs. Finally, by careful interleaver manipulation the minimum distance of the code can be increased and the error-coefficient for the remaining small distance events can be further reduced. Furthermore, we have investigated the influence of the interleaver length on the SNR needed to achieve a certain BER. Simulations confirm both the analytical approximation to the BER as well as the method for interleaver design which yields a marked improvement at higher SNR.

Patrick Robertson

Papers

A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain

Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering

Optimal and Sub-optimal Maximum A-Posteriori Algorithms Suitable for Turbo-Decoding.

Bandwidth-efficient turbo trellis-coded modulation using punctured component codes

Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes