Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe

Recent advances in coding theory for near error-free communications

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression

The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676

Parallel data compression

Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested

HybridConcatenated Coding Scheme for MIMO Systems

Abstract: Inthis paper, two hybrid concatenated super-orthogonal space-time trellis codes(SOSTTC) applying iterative decoding are proposed for flat fading channels. Theencoding operation is based on the concatenation of convolutional codes,interleaving and super-orthogonal space-time trellis codes. The firstconcatenated scheme consists of a serial concatenation of a parallelconcatenated convolutional code with a SOSTTC while the second consists ofparallel concatenation of two serially concatenated convolutional and SOSTTCcodes. The decoding of these two schemes is described, their pairwise errorprobabilities are derived and the frame error rate (FER) performances areevaluated by computer simulation in Rayleigh fading channels. The proposedtopologies are shown to perform better than existing concatenated schemes with aconstituent code of convolutional andspace-time codes in literature

An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor Product Code with Application to Data Storage