Concatenated zigzag (CZ) codes are classified as one kind of parallel-concatenated codes with powerful performance and low complexity. This kind of codes has flexible implementation methods and a good application prospect. We propose a modified turbo-type decoder and adaptive extrinsic information scaling method based on the Max-Log-APP (MLA) algorithm, which can provide a performance improvement also under the relatively low decoding complexity. Simulation results show that the proposed method can effectively help the sub-optimal MLA algorithm to approach the optimal performance. Some contrasts with low-density parity-check (LDPC) codes are also presented in this paper.

This paper studies the performance of code-aided (CA) soft-information based carrier phase recovery, which iteratively exploits the extrinsic information from channel decoder to improve the accuracy of phase synchronization. To tackle the problem of strong coupling between phase recovery and decoding, a semi-analytical model is proposed to express the distribution of extrinsic information as a function of phase offset. Piecewise approximation of the hyperbolic tangent function is employed to linearize the expression of soft symbol decision. Building on this model, open-loop characteristic and closed-loop performance of CA iterative soft decision-directed (ISDD) carrier phase synchronizer are derived in closed-form. Monte Carlo simulation results corroborate that the proposed expressions are able to characterize the performance of CA ISDD carrier phase recovery for systems with different channel codes.

In this paper, through extrinsic information transfer (EXIT) band chart analysis, an adaptive iterative decoding approach (AIDA) is proposed to reduce the iterative decoding complexity and delay for finite-length differentially encoded Low-density parity-check (DE-LDPC) coded systems with multiple-symbol differential detection (MSDD). The proposed AIDA can adaptively adjust the observation window size (OWS) of the MSDD soft-input soft-output demodulator (SISOD) and the outer iteration number of the iterative decoder (consisting of the MSDD SISOD and the LDPC decoder) instead of setting fixed values for the two parameters of the considered systems. The performance of AIDA depends on its stopping criterion (SC) which is used to terminate the iterative decoding before reaching the maximum outer iteration number. Many SCs have been proposed; however, these approaches focus on turbo coded systems, and it has been proven that they do not well suit for LDPC coded systems. To solve this problem, a new SC called differential mutual information (DMI) criterion, which can track the convergence status of the iterative decoding, is proposed; it is based on tracking the difference of the output mutual information of the LDPC decoder between two consecutive outer iterations of the considered systems. AIDA using the DMI criterion can adaptively adjust the out iteration number and OWS according to the convergence situation of the iterative decoding. Simulation results show that compared with using the existing SCs, AIDA using the DMI criterion can further reduce the decoding complexity and delay, and its performance is not affected by a change in the LDPC code and transmission channel parameters.

This paper proposes a low-complexity concatenated (LCC) soft-in soft-out (SISO) detector for spreading OFDM systems. The LCC SISO detector uses the turbo principle to compute the extrinsic information of the optimal maximum a priori probability (MAP) SISO detector with extremely low complexity. To develop the LCC SISO detector, we first partition the spreading matrix into some concatenated sparse matrices separated by interleavers. Then, we use the turbo principle to concatenate some SISO detectors, which are separated by de-interleavers or interleavers. Each SISO detector computes the soft information for each sparse matrix. By exchanging the soft information between the SISO detectors, we find the extrinsic information of the MAP SISO detector with extremely low complexity. Simulation results show that using the LCC SISO detector produces a near-optimal performance for both uncoded and coded spreading OFDM systems. In addition, by using the LCC SISO detector, the spreading OFDM system significantly improves the BER of the conventional OFDM system.

Transmission of convolutionally encoded source-codec parameters over noisy channels can benefit from the turbo principle through iterative source-channel decoding. We first formulate a recursive implementation based on sectionalized code trellises for MAP symbol decoding of binary convolutional codes. Performance is further enhanced by the use of an interpolative softbit source decoder that takes into account the channel outputs within an interleaving block. Simulation results indicate that our proposed scheme allows to exchange between its constituent decoders the symbol-level extrinsic information and achieves high robustness against channel noises.

In this letter, we propose a two-bit representation method for turbo decoder extrinsic information based on bit error count minimization and parameter reset. We show that the performance of the proposed system approaches that of the full precision decoder within 0.17 dB and 0.48 dB at 1 % packet error rate for packet lengths of 500 and 10,000 information bits. The idea of parameter reset we introduce can be used not only in turbo decoder but also in many other iterative algorithms.

A method is presented that can substantially reduce the memory requirements of non-binary turbo decoders by efficient representation of the extrinsic information. In the case of the duo-binary turbo decoder employed by the IEEE 802.16e standard, the extrinsic information memory can be reduced by about 43%, which decreases the total decoder complexity by 18%. We also show that the proposed algorithm can be implemented by simple hardware architecture.

A novel low-complexity iterative receiver for coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is proposed in this letter. The iterative receiver uses the parallel interference cancellation (PIC)-maximum ratio combining (MRC) detector for MIMO-OFDM detection, which is a popular alternative to the minimum mean square error (MMSE) detector due to its lower computational complexity. However, we have found that the conventional PIC-MRC detector tends to underestimate the magnitude of its output log likelihood ratios (LLRs). Based on this discovery, we propose to multiply these LLRs by a constant factor, which is optimized according to the extrinsic information transfer (EXIT) chart of the soft-in soft-out (SISO) detector. Simulation results show that the proposed scheme significantly improves the performance of the PIC-MRC-based receiver with little additional cost in computational complexity, allowing it to closely approach the performance of receiver using the much more complex MMSE detector.