Iterative Decoding Scheme Research Articles

Linear Precoders for Bit-Interleaved Coded Modulation on AWGN Channels: Analysis and Design Criteria

This paper investigates linear precoding for bit-interleaved coded modulation (BICM) on additive white Gaussian noise (AWGN) channels. Concatenating a linear precoder as an inner encoder with an outer (convolutional) encoder produces a powerful code with a limited decoding complexity. Linear precoders are examined and optimized for two scenarios: using (i) a noniterative decoding strategy and (ii) an iterative decoding strategy under a perfect feedback assumption. The precoder design is based on an information-theoretical approach, on the one hand, and a pair-wise error probability (PEP) analysis, on the other hand. Both approaches render convenient precoder design rules. For a binary phase-shift keying (BPSK) signal set, the optimal precoders that result from these rules are also derived. Numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach.

Soft-Output Decoding of Rotationally Invariant Codes Over Channels With Phase Noise

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider rotationally invariant (RI) trellis-coded modulations transmitted over channels affected by phase noise. To describe the main ideas of this paper, we first concentrate, as a case study, on the simplest RI scheme, namely the differentially encoded <emphasis emphasistype="italic">M</emphasis>-ary phase-shift keying signal. For this problem, we use the framework based on factor graphs and the sum–product algorithm to derive the exact maximum <emphasis emphasistype="italic">a posteriori</emphasis> symbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forward–backward estimator of the phase probability density function, followed by a symbol-by-symbol completion to produce the <emphasis emphasistype="italic">a posteriori </emphasis> probabilities of the information symbols. To practically implement the forward–backward phase estimator, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance, and in one case, only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase. The properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic RI code. The proposed soft-output algorithms can also be used in iterative decoding schemes for concatenated codes employing RI inner components. Among them, in the numerical results, we consider repeat-accumulate codes and other serially concatenated schemes recently proposed in the technical literature. </para>

Iterative Decoding Using Attenuated Extrinsic Information from Sum-Product Decoder for PMR Channel With Patterned Medium

An LDPC coding and iterative decoding system is studied in perpendicular magnetic recording (PMR) with a bit-patterned medium. We propose an iterative decoding scheme using attenuated extrinsic information from a sum-product decoder, and the bit error rate (BER) performance of the LDPC coding and iterative decoding system is evaluated by R/W computer simulations. It has been clarified that at an areal density of 1 Tbpsi the proposed system provides a jitter margin of the island edges of approximately 0.6% larger than the conventional system using (3, 18)-regular LDPC code

Iterative channel estimation and decoding in turbo coded space‐time systems

AbstractA noncoherent multiple antenna coded communication system over both block fading and time‐selective flat fading Rayleigh channel is considered. Several iterative decoding strategies consisting of pilot symbol assisted demodulation and turbo decoding are proposed. It is shown that, at a system rate of 0.9 bits per channel use, the SNR required to achieve a BER of 10−4 is only about 2dB from the imperfect CSI capacity lower bound. The channel estimation error variance is demonstrated to be close to the theoretical limit set by the Modified Cramér‐Rao bound. The simulation results coincide with the trends dictated by recent information‐theoretic analysis and demonstrate the effect that inaccuracy of the channel estimation has on the performance of the iterative decoding scheme. Copyright © 2007 John Wiley &amp; Sons, Ltd.

New iterative super-trellis decoding with source a priori information for VLCs with turbo codes

A novel Joint Source and Channel Decoding (JSCD) scheme for Variable Length Codes (VLCs) concatenated with turbo codes utilizing a new super-trellis decoding algorithm is presented in this letter. The basic idea of our decoding algorithm is that source a priori information with the form of bit transition probabilities corresponding to the VLC tree can be derived directly from sub-state transitions in new composite-state represented super-trellis. A Maximum Likelihood (ML) decoding algorithm for VLC sequence estimations based on the proposed super-trellis is also described. Simulation results show that the new iterative decoding scheme can obtain obvious encoding gain especially for Reversible Variable Length Codes (RVLCs), when compared with the classical separated turbo decoding and the previous joint decoding not considering source statistical characteristics.

An MSE-Based Transfer Chart for Analyzing Iterative Decoding Schemes Using a Gaussian Approximation

An alternative to extrinsic information transfer (EXIT) charts called mean-square error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean-square error (MMSE) for the additive white Gaussian noise (AWGN) channel, a relationship between the rate of any code and the area under a plot of MMSE versus signal-to-noise ratio (SNR) is obtained, when the a priori log-likelihood ratio (LLR) is from a binary input Gaussian channel. Using this result, a justification is provided for designing concatenated codes by matching the EXIT curves of the inner and outer decoder, when the LLRs are assumed to be Gaussian which is also the typical assumption used for code design using EXIT charts. Even though the Gaussian assumption is almost never true, the results presented in this paper represent a step toward the analysis of iterative decoding schemes using a single parameter. Finally, for the special case of AWGN channel it is shown that any capacity-achieving code has an EXIT curve that is a step function

How to Use A Priori Information of Data Symbols for SNR Estimation

We address the problem of how to use a priori information of data symbols to improve signal-to-noise ratio (SNR) estimation. Digital transmission with binary phase-shift keying (BPSK) over additive white Gaussian noise (AWGN) channels serves as a background. At the receive side, both pilot and data symbols are used to estimate the SNR. In addition, we assume that a priori information of the data symbols is available. Our proposed estimator is then derived as an approximate solution of the maximum-likelihood (ML) approach. A significant improvement in the low-SNR regime over the corresponding estimator without a priori information is shown. Hence, an estimator that uses a priori information of data symbols is suitable to be embedded in iterative decoding schemes like, e.g., turbo decoding or turbo equalization. In addition, the Cramer-Rao lower bound (CRLB) for SNR estimators using a priori information of data symbols is derived

Bounds on the Decoding Error Probability of Binary Block Codes over Noncoherent Block AWGN and Fading Channels

We derive upper bounds on the decoding error probability of binary block codes over noncoherent block additive white Gaussian noise (AWGN) and fading channels, with applications to turbo codes. By a block AWGN (or fading) channel, we mean that the carrier phase (or fading) is assumed to be constant over each block but independently varying from one block to another. The union bounds are derived for both noncoherent block AWGN and fading channels. For the block fading channel with a small number of fading blocks, we further derive an improved bound by employing Gallager's first bounding technique. The analytical bounds are compared to the simulation results for a coded block-based differential phase shift keying (B-DPSK) system under a practical noncoherent iterative decoding scheme proposed by Chen et al. We show that the proposed Gallager bound is very tight for the block fading channel with a small number of fading blocks, and the practical noncoherent receiver performs well for a wide range of block fading channels

Iterative Source-Channel Decoding With Markov Random Field Source Models

We propose a joint source-channel decoding approach for multidimensional correlated source signals. A Markov random field (MRF) source model is used which exemplarily considers the residual spatial correlations in an image signal after source encoding. Furthermore, the MRF parameters are selected via an analysis based on extrinsic information transfer charts. Due to the link between MRFs and the Gibbs distribution, the resulting soft-input soft-output (SISO) source decoder can be implemented with very low complexity. We prove that the inclusion of a high-rate block code after the quantization stage allows the MRF-based decoder to yield the maximum average extrinsic information. When channel codes are used for additional error protection the MRF-based SISO source decoder can be used as the outer constituent decoder in an iterative source-channel decoding scheme. Considering an example of a simple image transmission system we show that iterative decoding can be successfully employed for recovering the image data, especially when the channel is heavily corrupted

Low complexity iterative decoding for bit-interleaved coded modulation

Bit-interleaved coded modulation with iterative decoding (ID) is an effective scheme for both AWGN and fading channels because it simultaneously realizes large Euclidean distance and high diversity. In the literature, ID schemes with hard-decision feedback (HDF), as well as soft-decision feedback (SDF), have been investigated. While HDF/ID exhibits a performance inferior to SDF/ID, it is much simpler to implement. To enhance the performance of HDF/ID with moderate additional complexity, we propose a uniform soft-decision feedback ID (USF/ID) scheme. The proposed scheme is applicable in both single antenna and multiple antenna communication systems. The simulation results verify that it achieves impressive performance gain over HDF/ID and has a practically more attractive implementation than SDF/ID, especially for complexity-constrained wireless applications

Performance of non-uniform 16QAM modulation over linear and nonlinear channels

A technique of using a non-uniform 16QAM modulation combined with bit interleaved coded modulation and a new iterative decoding (BICM-ID) scheme is investigated. Simulation results of a parallel concatenated convolutional code shows a gain of 0.95 dB at a BER of 10−5 compared to conventional uniform 16QAM modulation in a linear channel. For a nonlinear satellite channel, this scheme offers a gain of 1.2 dB at the same BER compared to a uniform constellation.

Nonlinear dynamics of iterative decoding systems: analysis and applications

Iterative decoding algorithms may be viewed as high-dimensional nonlinear dynamical systems, depending on a large number of parameters. In this work, we introduce a simplified description of several iterative decoding algorithms in terms of the a posteriori average entropy, and study them as a function of a single parameter that closely approximates the signal-to-noise ratio (SNR). Using this approach, we show that virtually all the iterative decoding schemes in use today exhibit similar qualitative dynamics. In particular, a whole range of phenomena known to occur in nonlinear systems, such as existence of multiple fixed points, oscillatory behavior, bifurcations, chaos, and transient chaos are found in iterative decoding algorithms. As an application, we develop an adaptive technique to control transient chaos in the turbo-decoding algorithm, leading to a substantial improvement in performance. We also propose a new stopping criterion for turbo codes that achieves the same performance with considerably fewer iterations.

LDPC-coded MIMO systems with unknown block fading channels: soft MIMO detector design, channel estimation, and code optimization

This paper considers the design of a practical low-density parity check (LDPC)-coded multiple-input multiple-output (MIMO) system composed of M transmit and N receive antennas operating in a flat-fading environment where channel state information (CSI) is assumed to be unavailable both to the transmitter and the receiver. A soft iterative receiver structure is developed, which consists of three main blocks: a soft MIMO detector and two LDPC component soft decoders. We first propose at the component level several soft-input soft-output MIMO detectors whose performances are much better than the conventional minimal mean square error (MMSE)-based detectors. In particular, one optimal soft MIMO detector and two simplified suboptimal detectors are developed that do not require an explicit channel estimate and offer an effective tradeoff between complexity and performance. In addition, a modified expectation maximization (EM)-based MIMO detector is developed that completely removes positive feedback between input and output extrinsic information and provides much better performance compared with the direct EM-based detector that has strong correlations especially in fast-fading channels. At the structural level, the LDPC-coded MIMO receiver is constructed in an unconventional manner where the soft MIMO detector and LDPC variable node decoder form one super soft-decoding unit, and the LDPC check node decoder forms the other component of the iterative decoding scheme. By exploiting the proposed receiver structure, tractable extrinsic information transfer functions of the component soft decoders are obtained, which further lead to a simple and efficient LDPC code degree profile optimization algorithm with proven global optimality and guaranteed convergence from any initialization. Finally, numerical and simulation results are provided to confirm the advantages of the proposed design approach for the coded MIMO system.

Iterative detection and decoding with an improved V-BLAST for MIMO-OFDM systems

Multiple-input-multiple-output (MIMO) systems provide a very promising means to increase the spectral efficiency for wireless systems. By using orthogonal frequency-division multiplexing (OFDM), wideband transmission can be achieved over frequency-selective fading radio channels. First, in this paper, we introduce an improved vertical Bell Labs layered space-time (V-BLAST) receiver which takes the decision errors into account. Second, we propose an iterative detection and decoding (IDD) scheme for coded layered space-time architectures in MIMO-OFDM systems. For the iterative process, a low-complexity demapper is developed by making use of both nonlinear interference cancellation and linear minimum mean-square error filtering. Also, a simple cancellation method based on hard decision is presented to reduce the overall complexity. Simulation results demonstrate that the proposed IDD scheme combined with the improved V-BLAST performs almost as well as the optimal turbo-MIMO approach, while providing tremendous savings in computational complexity.

Bit‐interleaved coded irregular modulation

AbstractWe consider a simple method to improve the adaptiveness and flexibility of bit‐interleaved coded modulation (BICM) with different iterative decoding schemes for bandwidth efficient transmission. The basic idea is to apply different signal constellations and mappings within one code word. The combination of different signal constellations allows a fine adaptation of the data rate to the channel characteristics with the modulation, even if only the average channel state is known at the transmitter. For a receiver performing iterative demapping and decoding (so called BICM‐ID system), the mixture of different mappings enables an optimisation of the iterative decoding process according to the system requirements. We call this approach bit‐interleaved coded irregular modulation (BICIM) and analyse it using EXIT charts, capacity, error bounds and error rate simulations. Copyright © 2006 AEIT.

Correction of extrinsic information for iterative decoding in a serially concatenated multiuser DS-CDMA system

The system under study is a coded asynchronous DS-CDMA system with orthogonal modulation in time-varying Rayleigh fading multipath channels. Information bits are convolutionally encoded, block interleaved, and mapped to M-ary orthogonal Walsh codes, where the last step is essentially a process of block coding. This paper aims at tackling the problem of joint iterative decoding of this serially concatenated inner block code and outer convolutional code and estimating frequency-selective fading channels in multiuser environments. The (logarithm) maximum a posteriori probability, (Log)-MAP criterion is used to derive the iterative decoding schemes. In our system, the soft output from inner block decoder is used as a priori information for the outer decoder. The soft output from outer convolutional decoder is used for two purposes. First, it may be fed back to the inner decoder as extrinsic information for the systematic bits of the Walsh codeword. Secondly, it is utilized for channel estimation and multiuser detection (MUD). We also show that the inner decoding can be accomplished without extrinsic information, and in some cases, e.g., when the system is heavily loaded, yields better performance than the decoding with unprocessed extrinsic information. This implies the need for correcting the extrinsic information obtained from outer decoder. Different schemes are examined and compared numerically, and it is shown that iterative decoding with properly corrected extrinsic information or with non-extrinsic/extrinsic adaptation enables the system to operate reliably in the presence of severe multiuser interference, especially when the inner decoding is assisted by decision directed channel estimation and interference cancellation techniques.

Low-density Parity-check codes with run length limited (RLL) constraints

This paper addresses a new scheme by Vasic and Pedagani to combine low-density parity-check (LDPC) codes with run length limited (RLL) constraints. In this method, the RLL constraints are embedded into the LDPC codewords by deliberately flipping the bits of LDPC codewords that violate the RLL constraints. It is important to keep the number of flipped bits small in order to not overburden the LDPC decoder. In this paper, we introduce a method to control the number of flipped bits by using pseudorandom sequences. We present a new low-complexity iterative decoding and detection scheme to correct both the flipped bits and channel errors in a partial response channel. Analyses and simulation results show that the proposed method has good performance and reasonable complexity for (0,k) RLL constraints.

Low-Complexity Iterative Joint Source- Channel Decoding for Variable-Length Encoded Markov Sources

In this paper, we present a novel packetized bit-level decoding algorithm for variable-length encoded Markov sources, which calculates reliability information for the decoded bits in the form of a posteriori probabilities (APPs). An interesting feature of the proposed approach is that symbol-based source statistics in the form of the transition probabilities of the Markov source are exploited as a priori information on a bit-level trellis. This method is especially well-suited for long input blocks, since in contrast to other symbol-based APP decoding approaches, the number of trellis states does not depend on the packet length. When additionally the variable-length encoded source data is protected by channel codes, an iterative source-channel decoding scheme can be obtained in the same way as for serially concatenated codes. Furthermore, based on an analysis of the iterative decoder via extrinsic information transfer charts, it can be shown that by using reversible variable-length codes with a free distance of two, in combination with rate-1 channel codes and residual source redundancy, a reliable transmission is possible even for highly corrupted channels. This justifies a new source-channel encoding technique where explicit redundancy for error protection is only added in the source encoder.

Turbo-like iterative least-squares decoding of analogue codes

A turbo-like iterative decoding scheme for analogue product codes is described. It is proved that the iterative decoding method is an iterative projection in Euclidean space and converges to the least-squares solution. Using this geometric point of view, any block analogue codes can be decoded by a similar iterative method. The described procedure may serve as a step towards a more intuitive understanding of turbo decoding.

Comparison of bit error rate and convergence of four different iterative receivers for wireless OFDM-CDM

In this paper we investigate four different detection methods for Orthogonal Frequency Division Multiplexing Code Division Multiplexing (OFDM-CDM). The first method applies the Maximum A Posteriori (MAP) algorithm. The second and the third method use detection algorithms which are based on the Minimum Mean Squared Error (MMSE) criterion. The second method uses the Soft Symbol Based (SSB)-MMSE algorithm whereas the third receiver applies the Soft Chip Based (SCB)-MMSE algorithm. The fourth detection method uses a hybrid detection scheme which applies the SCB-MMSE and the Soft Interference Cancellation (SIC) detection method. We concatenate each detection method with the outer channel decoder which allows for iterative decoding at the receiver side. This system can be considered as a serially concatenated iterative decoding scheme whereby the inner decoder is replaced by the respective detection method. For the comparison of the four different detection methods the Bit Error Rate as a function of the signal to noise ratio is used as a performance measure. In addition the convergence of the iterative decoding loop is studied with the Extrinsic Information Transfer (EXIT) chart.