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

Spatially Coupled Turbo Codes: Principles and Finite Length Performance

In this paper, we give an overview of spatially coupled turbo codes (SC-TCs), the spatial coupling of parallel and serially concatenated convolutional codes, recently introduced by the authors. For presentation purposes, we focus on spatially coupled serially concatenated codes (SC-SCCs). We review the main principles of SC-TCs and discuss their exact density evolution (DE) analysis on the binary erasure channel. We also consider the construction of a family of rate-compatible SC-SCCs with simple 4-state component encoders. For all considered code rates, threshold saturation of the belief propagation (BP) to the maximum a posteriori threshold of the uncoupled ensemble is demonstrated, and it is shown that the BP threshold approaches the Shannon limit as the coupling memory increases. Finally we give some simulation results for finite lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems (ISWCS), Aug. 201

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

Spatially Coupled Turbo Codes

In this paper, we introduce the concept of spatially coupled turbo codes (SC-TCs), as the turbo codes counterpart of spatially coupled low-density parity-check codes. We describe spatial coupling for both Berrou et al. and Benedetto et al. parallel and serially concatenated codes. For the binary erasure channel, we derive the exact density evolution (DE) equations of SC-TCs by using the method proposed by Kurkoski et al. to compute the decoding erasure probability of convolutional encoders. Using DE, we then analyze the asymptotic behavior of SC-TCs. We observe that the belief propagation (BP) threshold of SC-TCs improves with respect to that of the uncoupled ensemble and approaches its maximum a posteriori threshold. This phenomenon is especially significant for serially concatenated codes, whose uncoupled ensemble suffers from a poor BP threshold.Comment: in Proc. 8th International Symposium on Turbo Codes & Iterative Information Processing 2014, Bremen, Germany, August 2014. To appear. (The PCC ensemble is changed with respect to the one in the previous version of the paper. However, it gives identical thresholds

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

Binary Multilevel Convolutional Codes with Unequal Error Protection Capabilities

Binary multilevel convolutional codes (CCs) with unequal error protection (UEP) capabilities are studied. These codes belong to the class of generalized concatenated (GC) codes. Binary CCs are used as outer codes. Binary linear block codes of short length, and selected subcodes in their two-way subcode partition chain, are used as inner codes. Multistage decodings are presented that use Viterbi decoders operating on trellises with similar structure to that of the constituent binary CCs. Simulation results of example binary two-level CC\u27s are also reported