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IIT Hyderabad

A Finite Feedback Scheme (FFS) for a quasi-static MIMO block fading channel with finite N-ary delay-free noise-free feedback consists of N Space-Time Block Codes (STBCs) at the transmitter, one corresponding to each possible value of feedback, and a function at the receiver that generates N-ary feedback. A number of FFSs are available in the literature that provably attain full-diversity. However, there is no known full-diversity criterion that universally applies to all FFSs. In this paper a universal necessary condition for any FFS to achieve full-diversity is given, and based on this criterion the notion of Feedback-Transmission duration optimal (FT-optimal) FFSs is introduced, which are schemes that use minimum amount of feedback N for the given transmission duration T, and minimum T for the given N to achieve full-diversity. When there is no feedback (N=1) an FT-optimal scheme consists of a single STBC, and the proposed condition reduces to the well known necessary and sufficient condition for an STBC to achieve full-diversity. Also, a sufficient criterion for full-diversity is given for FFSs in which the component STBC yielding the largest minimum Euclidean distance is chosen, using which full-rate (N t complex symbols per channel use) full-diversity FT-optimal schemes are constructed for all Nt&gt;1. These are the first full-rate full-diversity FFSs reported in the literature for T&lt;Nt. Simulation results show that the new schemes have the best error performance among all known FFSs. © 2002-2012 IEEE.

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IEEE Transactions on Wireless Communications

Full-rate full-diversity finite feedback space-time schemes with minimum feedback and transmission duration

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In [1], we introduced a framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm, and showed that for two specific families of STBCs, the Toepltiz codes and the Overlapped Alamouti Codes (OACs), the GDL based ML decoders have strictly less complexity than the CML decoders. In this paper, we introduce a 'traceback' step to the GDL decoding algorithm of STBCs, which enables roughly 4 times reduction in the complexity of the GDL decoders proposed in [1]. Utilizing this complexity reduction from 'traceback', we then show that for any STBC (not just the Toeplitz and Overlapped Alamouti Codes), the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras that is not multigroup or conditionally multigroup decodable, the GDL decoder provides approximately 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only about half as complex as the CML decoder. © 2012 IEEE.

IEEE International Symposium on Information Theory - Proceedings

Generalized distributive law for ML decoding of STBCs: Further results

A low complexity decoding technique with an essentially-ML performance for the Golden code and the 3 antenna Perfect code was introduced by Sirianunpiboon, Howard &amp; Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs) - the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity under Rayleigh fading, and we give sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the 3 and 4 antenna Perfect codes, the 3 antenna Threaded Algebraic Space-Time code and the 4 antenna rate 2 code of Srinath &amp; Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm outperform all known codes in terms of both decoding complexity and error performance for Nt ≤ 4 transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. The proposed decoders for all the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. © 2012 IEICE Institute of Electronics Informati.

2012 International Symposium on Information Theory and Its Applications, ISITA 2012

An adaptive conditional zero-forcing decoder with full-diversity, least complexity and essentially-ML performance for STBCs

A Space-Time Block Code (STBC) is said to be multigroup ML decodable if the information symbols encoded by it can be partitioned into two or more groups, such that each group of symbols can be ML decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix R encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high rate (rate greater than 1) multigroup ML decodable codes have rank-deficient R matrix, even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the average sphere decoding complexity of the STBCs whose R matrix is rank-deficient is polynomial in the constellation size, and hence is high. We derive the sphere decoding complexity of most of the known high rate multigroup ML decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas. © 2012 IEEE.

On the sphere decoding complexity of high rate multigroup ML decodable STBCs

Recently, a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field double-struck F4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over double-struck F4 for number of transmit antennas N=2m, m &gt; 1, and rates R &gt; 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N,R) pairs. The new full-rate codes of this paper (R=N) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over double-struck F4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations. © 2011 IEEE.

IEEE International Conference on Communications

Fast-group-decodable STBCs via codes over GF(4): Further results

In this second part of a two part series of papers, we construct a new class of Space-Time Block Codes (STBCs) for point-to-point MIMO channel and Distributed STBCs (DSTBCs) for the amplify-and-forward relay channel that give full-diversity with Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC) decoders. The proposed class of STBCs include most of the known full-diversity low complexity PIC/PIC-SIC decodable STBCs as special cases. We also show that a number of known full-diversity PIC/PIC-SIC decodable STBCs that were constructed for the point-to-point MIMO channel can be used as full-diversity PIC/PIC-SIC decodable DSTBCs in relay networks. For the same decoding complexity, the proposed STBCs and DSTBCs achieve higher rates than the known low decoding complexity codes. Simulation results show that the new codes have a better bit error rate performance than the low ML decoding complexity codes available in the literature. © 2006 IEEE.

Collocated and distributed STBCs with partial interference cancellation decoding, part II: Code construction

The Generalized Distributive Law (GDL) is a message passing algorithm which can efficiently solve a certain class of computational problems, and includes as special cases the Viterbi's algorithm, the BCJR algorithm, the Fast-Fourier Transform, Turbo and LDPC decoding algorithms. In this paper GDL based maximum-likelihood (ML) decoding of Space-Time Block Codes (STBCs) is introduced and a sufficient condition for an STBC to admit low GDL decoding complexity is given. Fast-decoding and multigroup decoding are the two algorithms used in the literature to ML decode STBCs with low complexity. An algorithm which exploits the advantages of both these two is called Conditional ML (CML) decoding. It is shown in this paper that the GDL decoding complexity of any STBC is upper bounded by its CML decoding complexity, and that there exist codes for which the GDL complexity is strictly less than the CML complexity. Explicit examples of two such families of STBCs is given in this paper. Thus the CML is in general suboptimal in reducing the ML decoding complexity of a code, and one should design codes with low GDL complexity rather than low CML complexity. © 2011 IEEE.

2011 IEEE Information Theory Workshop, ITW 2011

Generalized distributive law for ML decoding of STBCs

In this paper, we give a new framework for constructing low ML decoding complexity space-time block codes (STBCs) using codes over the Klein group K. Almost all known low ML decoding complexity STBCs can be obtained via this approach. New full-diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over K, for number of transmit antennas N=2m, m ≥ 1, and rates R &gt; 1 complex symbols per channel use. When R = N , the new STBCs are information-lossless as well. The new class of STBCs have the least known ML decoding complexity among all the codes available in the literature for a large set of (N,R) pairs. © 2006 IEEE.

IEEE Transactions on Information Theory

Low ML decoding complexity STBCs via codes over the Klein group

Recently, Guo and Xia introduced low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, for point-to-point MIMO channels. In this paper, we show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks. We give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders and construct a new class of DSTBCs with low complexity full-diversity PIC-SIC decoding using complex orthogonal designs. The new class of codes includes a number of known full-diversity PIC/PIC-SIC decodable Space-Time Block Codes (STBCs) constructed for point-to-point channels as special cases. The proposed DSTBCs achieve higher rates (in complex symbols per channel use) than the multigroup ML decodable DSTBCs available in the literature. Simulation results show that the proposed codes have better bit error rate performance than the best known low complexity, full-diversity DSTBCs. © 2011 IEEE.

Distributed STBCs with full-diversity partial interference cancellation decoding

For a family/sequence of Space-Time Block Codes (STBCs) C1, C2..., with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use (cspcu), i = 1,2,..., the asymptotic normalized rate is defined as limi→∞R i/Ni. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least maximum-likelihood (ML) decoding complexity among all known codes for any number of transmit antennas N &gt; and rates R &gt; 1 cspcu. For a large set of (R, N) pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes (R=N) are asymptotically-optimal and fast-decodable, and for N &gt; 5 have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper: (i) Construction of a new class of asymptotically-good, full-diversity multigroup ML decodable codes, that not only includes STBCs for a larger set of antennas, but also either matches in rate or contains as a proper subset all other high-rate or asymptotically-good, delay-optimal, multigroup ML decodable codes available in the literature. (ii) Construction of a new class of fast-group-decodable codes (codes that combine the low ML decoding complexity properties of multigroup ML decodable codes and fast-decodable codes) for all even number of transmit antennas and rates 1 &lt; R ≤ 5/4. (iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations. © 2011 IEEE.

Asymptotically-optimal, fast-decodable, full-diversity STBCs

Low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, were given by Guo and Xia along with sufficient conditions for a Space-Time Block Code (STBC) to achieve full diversity with PIC/PIC-SIC decoding for point-to-point MIMO channels. In Part-I of this two part series of papers, we give new conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. We then show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks and give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders. In Part-II, we construct new low complexity full-diversity PIC/PIC-SIC decodable STBCs and DSTBCs that achieve higher rates than the known full-diversity low complexity ML decodable STBCs and DSTBCs. © 2006 IEEE.

Collocated and distributed STBCs with partial interference cancellation decoding, part I: Full-diversity criterion

Recently, Guo and Xia gave sufficient conditions for an STBC to achieve full diversity when a PIC (Partial Interference Cancellation) or a PIC-SIC (PIC with Successive Interference Cancellation) decoder is used at the receiver. In this paper, we give alternative conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. Using these conditions, we construct a new class of full diversity PIC-SIC decodable codes, which contain the Toeplitz codes and a family of codes recently proposed by Zhang, Xu et. al. as proper subclasses. With the help of the new criteria, we also show that a class of PIC-SIC decodable codes recently proposed by Zhang, Shi et. al. can be decoded with much lower complexity than what is reported, without compromising on full diversity. © 2010 IEEE.

2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

A new full-diversity criterion and low-complexity STBCs with Partial Interference Cancellation decoding

In this paper we construct low ML decoding complexity STBCs by using the Pauli matrices as linear dispersion matrices. In this case the Hurwitz-Radon orthogonality condition is shown to be easily checked by transferring the problem to F4 domain. The problem of constructing low ML decoding complexity STBCs is shown to be equivalent to finding certain codes over F 4. It is shown that almost all known low ML decoding complexity STBCs can be obtained by this approach. New classes of codes are given that have the least known ML decoding complexity in some ranges of rate. © 2010 IEEE.

Fast-group-decodable STBCs via codes over GF(4)

For a family/sequence of Space-Time Block Codes (STBCs) C1, C2, . . . , with increasing number of transmit antennas N i, with rates Ri complex symbols per channel use, i = 1, 2, . . . , the asymptotic normalized rate is defined as lim i→∞ Ri/Ni. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a nonzero fraction of the number of transmit antennas. An STBC C is said to be g-group ML-decodable if its information symbols can be partitioned into g groups, such that each group of symbols can be ML decoded independently of others. In this paper, for g ≥ 2, we construct g-group ML-decodable codes with rates greater than one complex symbol per channel use. These codes are asymptotically good too. For g &gt; 2, these are the first instances of g-group ML-decodable codes, with rates greater than 1, presented in the literature. We also construct multigroup ML-decodable codes with the best known asymptotic normalized rates. Specifically, we propose delay-optimal 2-group ML-decodable codes for number of antennas N &gt; 1 with rate N/4 + 1/N for even N and rate N/4 + 5/4N - 1/2 for odd N. We construct delay optimal, g-group ML-decodable codes, g &gt; 2, for number of antennas N that are a multiple of g2⌊g-1/2⌋ with rate N/g2g-1 + g 2-g/2N . We also construct non-delay-optimal g-group ML-decodable codes, g ≥ 2, for number of antennas N that are a multiple of 2⌊g-1/2⌋, with delay gN and rate N/2g-1 + g-1/2N. ©2010 IEEE.