An Adaptive Conditional Zero-Forcing Decoder with Full-diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the 3 antenna Perfect code was introduced by Sirianunpiboon, Howard and 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, 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 and 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 decoding complexity and error performance for 2,3 and 4 transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.Comment: 11 pages, 4 figures. Corrected a minor typographical erro

Polar Codes: Reliable Communication with Complexity Polynomial in the Gap to Shannon Capacity (Invited Talk)

Shannon\u27s monumental 1948 work laid the foundations for the rich fields of information and coding theory. The quest for efficient coding schemes to approach Shannon capacity has occupied researchers ever since, with spectacular progress enabling the widespread use of error-correcting codes in practice. Yet the theoretical problem of approaching capacity arbitrarily closely with polynomial complexity remained open except in the special case of erasure channels. In 2008, Arikan proposed an insightful new method for constructing capacity-achieving codes based on channel polarization. In this talk, I will begin with a self-contained survey of Arikan\u27s celebrated construction of polar codes, and then discuss our recent proof (with Patrick Xia) that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within epsilon > 0 of the Shannon capacity with block length (delay), construction complexity, and decoding complexity all bounded by a polynomial in the gap to capacity, i.e., by poly(1/epsilon). Polar coding gives the first explicit construction with rigorous proofs of all these properties; previous constructions were not known to achieve capacity with less than exp(1/epsilon) decoding complexity. We establish the capacity-achieving property of polar codes via a direct analysis of the underlying martingale of conditional entropies, without relying on the martingale convergence theorem. This step gives rough polarization (noise levels epsilon for the good channels), which can then be adequately amplified by tracking the decay of the channel Bhattacharyya parameters. Our effective bounds imply that polar codes can have block length bounded by poly(1/epsilon). We also show that the generator matrix of such polar codes can be constructed in polynomial time by algorithmically computing an adequate approximation of the polarization process

High-Rate Space Coding for Reconfigurable 2x2 Millimeter-Wave MIMO Systems

Millimeter-wave links are of a line-of-sight nature. Hence, multiple-input multiple-output (MIMO) systems operating in the millimeter-wave band may not achieve full spatial diversity or multiplexing. In this paper, we utilize reconfigurable antennas and the high antenna directivity in the millimeter-wave band to propose a rate-two space coding design for 2x2 MIMO systems. The proposed scheme can be decoded with a low complexity maximum-likelihood detector at the receiver and yet it can enhance the bit-error-rate performance of millimeter-wave systems compared to traditional spatial multiplexing schemes, such as the Vertical Bell Laboratories Layered Space-Time Architecture (VBLAST). Using numerical simulations, we demonstrate the efficiency of the proposed code and show its superiority compared to existing rate-two space-time block codes

Universal lossless source coding with the Burrows Wheeler transform

The Burrows Wheeler transform (1994) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: (1) statistical characterizations of the BWT output on both finite strings and sequences of length n → ∞, (2) a variety of very simple new techniques for BWT-based lossless source coding, and (3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory source