the results of a field trials campaign in a park, a wide street, a narrow street and office environments are presented in this paper. The trials are carried out using a real time 4x4 MIMO-OFDM testbed working in the 2.4 GHz ISM band and a 20 MHz bandwidth. The testbed supports both spatial multiplexing and transmit and receive diversity. We compare the system performance using different number of spatial streams in different environments. We also determine the maximum number of spatial streams that can be supported in the indoor and outdoor environments respectively. We found that the maximum achievable throughput for the system in the indoor environment is almost double the maximum achievable throughput in the outdoor environment at the same receive power. This is mainly due to the richness of scattering elements in an indoor setting. Our outdoor trials showed that supporting more than two spatial streams will not introduce any throughput gain.

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an interleaver is a common measure for turbo coding applications. Maximum-spread interleavers are interleavers whose spread factors achieve the upper bound. An infinite sequence of quadratic PPs over integer rings that generate maximum-spread interleavers is presented. New properties of PP interleavers are investigated from an algebraic-geometric perspective resulting in a new non- linearity metric for interleavers. A new interleaver metric that is a function of both the nonlinearity metric and the spread factor is proposed. It is numerically demonstrated that the spread factor has a diminishing importance with the block length. A table of good interleavers for a variety of interleaver lengths according to the new metric is listed. Extensive computer simulation results with impressive frame error rates confirm the efficacy of the new metric. Further, when tail-biting constituent codes are used, the resulting turbo codes are quasi-cyclic.

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Also, the recently proposed quadratic permutation polynomial (QPP) based interleavers by Sun and Takeshita (IEEE Trans. Inform. Theory, Jan. 2005) provide excellent performance for short-to-medium block lengths. In this work the minimum distance of turbo codes with QPP-based interleavers is considered in detail. Large tables of optimum (in terms of turbo code minimum distance and multiplicity) QPPs for turbo codes with 8-state and 16-state constituent codes are presented. The minimum distances are compared to existing results in the literature on dithered relative prime (DRP) interleavers. The optimality of the new tables makes them an excellent source of information to advance the understanding of permutation polynomial (PP) based interleavers

A construction is proposed for low density parity check codes using quadratic permutation polynomials over finite integer rings. Graph isomorphisms and automorphisms are identified and used in an efficient search for good codes. Graphs with girth as large as 12 were found. Upper bounds on the minimum Hamming distance are found algorithmically. The bounds indicate that the minimum distance grows with block length. One of the new codes has a similar error performance as the best known PEG LDPC code. Finally, the new codes are quasi-cyclic

The spread factor of an interleaver is a common measure for turbo coding applications. Maximum-spread interleavers are interleavers whose spread factors achieve the upper bound. An infinite sequence of quadratic permutation polynomials over integer rings that generate maximum-spread interleavers is presented. New properties of permutation polynomial interleavers are investigated from an algebraic-geometric perspective resulting in a new non-linearity metric for interleavers. A new interleaver metric that is a function of both the non-linearity metric and the spread factor is proposed. A table of good interleavers for a variety of interleaver lengths according to the new metric is listed. Extensive computer simulation results with impressive frame error rates confirm the efficacy of the new metric. Further, when tail-biting constituent codes are used, the resulting turbo codes are quasi-cyclic

Rapid frequency and frame synchronization scheme is proposed to minimize channel switching time and improve the synchronization performance during channel switching in IEEE 802.11p standard. As a measure of performance, theoretical formula for false alarm and detection probability is derived. It is shown that optimal threshold value is less than 0.5 dB and overall performance gain is given by the amount of the power gain of control channel, which is normally 10 dB

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. In this correspondence, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. All but one of the quadratic interleavers proposed earlier by Sun and Takeshita are found to admit a quadratic inverse, although none were explicitly designed to do so. An explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contention-free interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that permutation polynomials generate maximum contention-free interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the Third Generation Partnership Project (3GPP) standard

In this paper, two iterative message passing algorithms based on belief propagation proposed for the decoding of any binary linear block code are compared. The innovation of these algorithms lies in the fact that the structure of the graph of the parity check matrix is adaptively modified to render it suitable to belief propagation decoding. The modification is done such that the least reliable bits received from the channel are leaves of the graph. These algorithms perform favorably when compared with existing hard and iterative soft decision decoding algorithms in terms of error rate while maintaining a complexity polynomial in block length. It was found that while these two algorithms are conceptually similar, their performance in terms of word error rate (as a function of signal-to-noise ratio), decoding time (average number of iterations) and the updated bit reliabilities are very different

This letter extends a low-density parity-check code construction using maximum-length linear congruential sequences by Prabhakar and Narayanan. The corresponding bipartite graphs of their construction were guaranteed to have a girth larger than four by a sufficient condition. However, their sufficient condition was limited to regular codes and data-node degree equal to three. The extension in this letter allows arbitrary data-node degrees and is applicable to irregular codes. Further, simpler sufficient conditions are derived and larger girths are addressed.

A class of deterministic interleavers for turbo codes (TCs) based on permutation polynomials over /spl Zopf//sub N/ is introduced. The main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code. Moreover, since the interleaver can be generated by a few simple computations, storage of the interleaver tables can be avoided. By using the permutation polynomial-based interleavers, the design of the interleavers reduces to the selection of the coefficients of the polynomials. It is observed that the performance of the TCs using these permutation polynomial-based interleavers is usually dominated by a subset of input weight 2m error events. The minimum distance and its multiplicity (or the first few spectrum lines) of this subset are used as design criterion to select good permutation polynomials. A simple method to enumerate these error events for small m is presented. Searches for good interleavers are performed. The decoding performance of these interleavers is close to S-random interleavers for long frame sizes. For short frame sizes, the new interleavers outperform S-random interleavers.

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.

Space-time coding has been studied extensively as a powerful error correction coding for systems with multiple transmit antennas. An important design goal is to maximize the level of space diversity that a code can achieve. Toward this goal, the only systematic algebraic coding theory so far is binary rank theory by Hammons and El Gamal (see ibid. vol. 46, p.524-42, 2000) for binary phase-shift keying (BPSK) modulated codes defined over binary field and quaternary phase-shift keying (QPSK) modulated codes defined over modulo four finite ring. To design codes with higher bandwidth efficiency, we develop an algebraic rank theory to ensure full space diversity for 2/sup 2k/ quadrature and amplitude modulated (QAM) codes for any positive integer k. The theory provides the most general sufficient condition of full space diversity so far. It includes the BPSK binary rank theory as a special case. Since the condition is over the same domain that a code is defined, the full space diversity code design is greatly simplified. The usefulness of the theory is illustrated in examples, such as analyses of existing codes, constructions of new space-time codes with better performance, including the full diversity space-time turbo codes.

This paper studies the space time code design for single carrier transmission over frequency selective fading channels. The design criteria are derived first and then we apply the algebraic /spl Sigma//sub 0/-rank theory to show how to design codes to take advantage of space and frequency diversity simultaneously. Finally, example codes are shown to achieve desired level of diversity by simulation results.

This paper proposes a class of full space diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. A rank theory proposed by the authors earlier is employed to check the full space diversity of the codes. The simulations show that the space-time turbo codes can take full advantage of space diversity and time diversity if they are available in the channels. We also study the robustness of performance of both turbo codes and trellis codes in space-time correlated fading channels.

Turbo codes with long frame lengths are usually constructed using a randomly chosen interleaver. Statistically, this guarantees excellent bit-error rate (BER) performance but also generates a certain number of low weight codewords, resulting in the appearance of an error floor in the BER curve. Several methods, including using an outer code, have been proposed to improve the error floor region of the BER curve. We study the effect of an outer BCH code on the frame-error rate (FER) of turbo codes. We show that additional coding gain is possible not only in the error floor region but also in the waterfall region. Also, the outer code improves the iterative APP decoder by providing a stopping criterion and alleviating convergence problems. With this method, we obtain codes whose performance is within 0.6 dB of the sphere packing bound at an FER of 10/sup -6/.

This paper proposes a class of full space diversity QPSK space-time codes based on parallel concatenated convolutional (turbo) codes. A rank criterion of full space diversity is used in the design. Compared with space-time trellis codes, the simulations show it has robust performance at both a quasi-static fading channel and a time varying fading channel.

Recursive constituent codes are required for parallel concatenated turbo-codes. Some conditions for recursiveness of non-linear constituent codes are given.

It is well known that an interleaver with random properties, quite often generated by pseudo-random algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance and lack of a compact representation that leads to a simple implementation. We present several new classes of deterministic interleavers of length N, with construction complexity O(N), that permute a sequence of bits with nearly the same statistical distribution as a random interleaver and perform as well as or better than the average of a set of random interleavers. The new classes of deterministic interleavers have a very simple representation based on quadratic congruences and hence have a structure that allows the possibility of analysis as well as a straightforward implementation. Using the new interleavers, a turbo code of length 16384 that is only 0.7 dB away from capacy at a bit-error rate (BER) of 10/sup -5/ is constructed. We also generalize the theory of previously known deterministic interleavers that are based on block interleavers, and we apply this theory to the construction of a nonrandom turbo code of length 16384 with a very regular structure whose performance is only 1.1 dB away from capacity at a BER of 10/sup -5/.