Low ML Decoding Complexity STBCs via Codes Over the Klein Group

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 this paper we introduce a new framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code is strictly less than M λ , where λ is the number of independent symbols in the STBC, and M is the constellation size. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 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 half as complex as the CML decoder.

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“…Fast-Decodable STBCs: An STBC is said to be fastdecodable [16] or conditionally g-group decodable [24] if there exists a subset Γ {1, . .…”

Section: B Fast Gdl Decodable Stbcsmentioning

confidence: 99%

Generalized Distributive Law for ML Decoding of Space–Time Block Codes

Natarajan

Rajan

2013

IEEE Trans. Inform. Theory

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“…Multigroup ML-decodable STBCs based on Clifford Unitary Weight Designs (CUWDs) were introduced in [14]. Low ML-decoding complexity STBCs that use Pauli matrices as the weight matrices were given in [15]. The g-group ML decodable codes from CUWDs [3] and from [15] can achieve a rate of g 2 ⌊ g+1 2 ⌋ cspcu, for arbitrary g and number of transmit antennas N = 2 m , m ≥ ⌈ g 2 − 1⌉.…”

Section: Thismentioning

confidence: 99%

“…Low ML-decoding complexity STBCs that use Pauli matrices as the weight matrices were given in [15]. The g-group ML decodable codes from CUWDs [3] and from [15] can achieve a rate of g 2 ⌊ g+1 2 ⌋ cspcu, for arbitrary g and number of transmit antennas N = 2 m , m ≥ ⌈ g 2 − 1⌉. Example 3: All the known families of asymptotically-good multigroup ML decodable codes: A 2-group ML-decodable, rate 5/4 code for 4 transmit antennas was reported in [16].…”

Section: Thismentioning

confidence: 99%

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

Natarajan

Rajan

2011

2011 IEEE International Conference on Communications (ICC)

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Abstract-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→∞. 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 > 1 and rates R > 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 > 5 have lower ML decoding complexity than all other families of asymptotically-optimal, fastdecodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper: (i) For g > 1, we construct g-group ML-decodable codes with rates greater than one cspcu. These codes are asymptotically-good too. For g > 2, these are the first instances of g-group ML-decodable codes with rates greater than 1 cspcu presented in the literature. (ii) We construct 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 < R ≤ 5/4. (iii) Given a design with fullrank 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 1 .

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“…It is shown in [22] that the new STBCs in Section IV-A for number of antennas N = 2 m , m > 1, and rate R > 1 can be ML decoded with complexity 3M 2 m−2 (4R−3)−0.5 .…”

Section: Comparison Of ML Decoding Complexitiesmentioning

confidence: 99%

“…The proofs for all the theorems, propositions and other claims in this paper have been omitted due to space considerations, but are available in [22]. Notation: For a complex matrix A, the transpose, the conjugate and the conjugate-transpose are denoted by A T ,Ā and A H respectively, A ⊗ B is the Kronecker product of matrices A and B, I n is the n × n identity matrix and 0 is the all zero matrix of appropriate dimension.…”

Section: Introductionmentioning

confidence: 99%

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Natarajan¹,

Rajan²

2011

2011 IEEE International Conference on Communications (ICC)

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Recently in [1], a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F 4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F 4 for number of transmit antennas N = 2 m , m > 1, and rates R > 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 F 4 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.

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Low ML Decoding Complexity STBCs via Codes Over the Klein Group

Cited by 5 publications

References 48 publications

Generalized Distributive Law for ML Decoding of Space–Time Block Codes

Generalized Distributive Law for ML Decoding of Space–Time Block Codes

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

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