Optimization of scaling soft information in iterative decoding via density evolution methods

Density evolution has recently been used to analyze iterative decoding and explain many characteristics of iterative decoding including convergence of performance and preferred structures for the constituent codes. The scaling of extrinsic information (messages) has been heuristically used to enhance the performance in the iterative decoding literature, particularly based on the min-sum message passing algorithm. In this paper, it is demonstrated that density evolution can be used to obtain the optimal scaling factor and also estimate the maximum achievable scaling gain. For low density parity check (LDPC (codes and serially) concatenated convolutional codes (SCCC) with two-state constituent codes, the analytic density evolution technique is used, while the signal-to-noise ratio (SNR) evolution technique and the EXIT chart technique is used for SCCC with more than 2 state constituent codes. Simulation results show that the scaling gain predicted by density evolution or SNR evolution matches well with the scaling gain observed by simulation.     

Turbo decoder

We propose an adaptive channel SNR estimation algorithm required for the iterative MAP decoding of turbo decoders. The proposed algorithm uses the extrinsic values generated within the iterative MAP decoder to update the channel SNR estimate toward its optimum value per each decoder iteration or per each turbo code frame     

Efficient Computation of EXIT Functions for Nonbinary Iterative Decoding

The calculation of nonbinary extrinsic information transfer charts for the iterative decoding of concatenated index-based codes is addressed. We show that the extrinsic information at the output of a constituent a posteriori probability decoder can be calculated with very low complexity, where expensive histogram measurements are not required any more. An example for turbo trellis-coded modulation demonstrates the capabilities of the proposed approach     

Convergence behavior of iteratively decoded parallel concatenatedcodes

Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes     

Joint source-channel turbo coding for binary Markov sources

We investigate the construction of joint source-channel (JSC) turbo codes for the reliable communication of binary Markov sources over additive white Gaussian noise and Rayleigh fading channels. To exploit the source Markovian redundancy, the first constituent turbo decoder is designed according to a modified version of Berrou's original decoding algorithm that employs the Gaussian assumption for the extrinsic information. Due to interleaving, the second constituent decoder is unable to adopt the same decoding method; so its extrinsic information is appropriately adjusted via a weighted correction term. The turbo encoder is also optimized according to the Markovian source statistics and by allowing different or asymmetric constituent encoders. Simulation results demonstrate substantial gains over the original (unoptimized) Turbo codes, hence significantly reducing the performance gap to the Shannon limit. Finally, we show that our JSC coding system considerably outperforms tandem coding schemes for bit error rates smaller than 10/sup -4/, while enjoying a lower system complexity.     

Analysis and Design of Power-Efficient Coding Schemes With Parallel Concatenated Convolutional Codes

Analysis and Design of Power-Efficient Coding Schemes With Parallel Concatenated Convolutional Codes In the low signal-to-noise ratio regime, the performance of concatenated coding schemes is limited by the convergence properties of the iterative decoder. Idealizing the model of iterative decoding by an independence assumption, which represents the case in which the codeword length is infinitely large, leads to analyzable structures from which this performance limit can be predicted. Mutual information-transfer characteristics of the constituent coding schemes comprising convolutional encoders and soft-in/soft-out decoders have been shown to be sufficient to characterize the components within this model. Analyzing serial and parallel concatenations is possible just by these characteristics. In this paper, we extend the method of extrinsic information transfer charts that is limited to the case of a concatenation of two component codes, to the case of multiple turbo codes. Multiple turbo codes are parallel concatenations of three or more constituent codes, which, in general, may not be identical and may not have identical code rates. For the construction of low-rate codes, this concept seems to be very favorable, as power efficiencies close to the Shannon limit can be achieved with reasonable complexity.     

SNR estimation in Nakagami-m fading with diversity combining and its application to turbo decoding

We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.     

Iterative decoding for partial response (PR), equalized,magneto-optical (MO) data storage channels

Turbo codes and low-density parity check (LDPC) codes with iterative decoding have received significant research attention because of their remarkable near-capacity performance for additive white Gaussian noise (AWGN) channels. Previously, turbo code and LDPC code variants are being investigated as potential candidates for high-density magnetic recording channels suffering from low signal-to-noise ratios (SNR). We address the application of turbo codes and LDPC codes to magneto-optical (MO) recording channels. Our results focus on a variety of practical MO storage channel aspects, including storage density, partial response targets, the type of precoder used, and mark edge jitter. Instead of focusing just on bit error rates (BER), we also study the block error statistics. Our results for MO storage channels indicate that turbo codes of rate 16/17 can achieve coding gains of 3-5 dB over partial response maximum likelihood (PRML) methods for a 10^-4 target BER. Simulations also show that the performance of LDPC codes for MO channels is comparable to that of turbo codes, while requiring less computational complexity. Both LDPC codes and turbo codes with iterative decoding are seen to be robust to mark edge jitter     

Soft multiuser demodulation and iterative decoding for FH/SSMA with a block turbo code

The number of users that can be supported by frequency-hopped, spread-spectrum multiple-access systems can be increased greatly by using multiuser demodulation and iterative decoding. In the receiver employed hard-decision multiuser demodulation followed by iterative decoding, users exchange decoded information with each other. Additional information from multiuser demodulation in the first decoding iteration is limited by the hard-decision output of the multiuser demodulator. The error-correction used was an errors-and-erasures Reed-Solomon (RS) decoder. We revisit hard-decision demodulation and conventional RS decoding. Hard-decision multiuser demodulation is modified to provide a soft output, which is then given to a nonbinary block turbo code with shortened RS codes as the constituent codes. An iterative multiuser decoding algorithm is developed to do soft multiuser interference cancellation. This soft receiver with soft demodulation and decoding is shown to be more resistant to multiuser interference and channel noise, especially at lower values of signal-to-noise ratio. The results show a great improvement in the ability of the system to support more users (more than three times in some cases), as compared with systems that erase all hits or employ hard-decision multiuser demodulation followed by RS code. We examine the proposed method for synchronous as well as asynchronous frequency-hopped systems in both AWGN and fading channels.     

Twin-stack decoding of recursive systematic convolutional codes

We present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes. The proposed decoder, the twin-stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative “turbo” configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs). Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R=1/3, recursive code, but this difference narrows progressively at higher SNRs. The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques     

Soft Decoding Assisted SNR Estimation Under Block Fading Channels for Orthogonal Modulations

The performance of the coded orthogonal modulation (OM) system under slow fading channels heavily depends on the estimation of the signal-to-noise ratio (SNR), including the fading amplitude and the noise spectral density. However, a relatively long packet of pilot symbols is often required to guarantee the accuracy of the SNR estimation, which makes it impractical in some situations. To address this problem, this paper proposes an iterative SNR estimation algorithm using the soft decoding information based on the expectation-maximization algorithm. In the proposed method, a joint iterative loop between the SNR estimator and decoder is performed, where the extrinsic information generated by the soft decoder is employed to enhance the estimation accuracy and the SNR estimated by the estimator is used to generate the soft information to the decoder. Also, no pilot symbols are needed to estimate the SNR in the proposed estimator. The Cramer–Rao lower bound (CRLB) of fully data-aided (FDA) estimation is derived to works as the final benchmark. The performance of the proposed algorithm is evaluated in terms of the normalized mean square errors (NMSEs) and the bit error rates (BERs) under block fading channels. Simulation results indicate that the NMSE of the proposed estimator reaches the CRLB of the FDA estimator and outperforms that of the approximate ML (ML-A) estimator proposed by Hassan et al. by 4.1 dB. The BER performance of coded OM system with the proposed estimation algorithm is close to the ideal case where the channel fading and the noise spectral density are known at the receiver.     

Carrier Synchronization for Very Low SNR

The Turbo decoding performance will suffer serious degradation under low signal-to-noise ratios (SNR) conditions for the reason of residual frequency and phase offset in the carrier. In this paper, an improved residual carrier frequency offset estimation algorithm based on u priori probability aided (APPA) phase estimation is proposed. A carrier synchronization loop that combines the iterative turbo decoder and the phase estimator together is constructed, where the extrinsic information obtained from the Turbo decoder is used to aid an iterative phase estimation process. The simulation results show that the algorithm performs successfully under very low SNR conditions (for example, less than -7.4 dB) with large frequency offset and phase error and the performance of this algorithm is very close to the optimally synchronized system.     

Design of Irregular LDPC Codes for BIAWGN Channels with SNR Mismatch

Belief propagation (BP) algorithm for decoding lowdensity parity-check (LDPC) codes over a binary input additive white Gaussian noise (BIAWGN) channel requires the knowledge of the signal-to-noise ratio (SNR) at the receiver to achieve its ultimate performance. An erroneous estimation or the absence of a perfect knowledge of the SNR at the decoder is referred to as ?SNR mismatch?. SNR mismatch can significantly degrade the performance of LDPC codes decoded by the BP algorithm. In this paper, using extrinsic information transfer (EXIT) charts, we design irregular LDPC codes that perform better (have a lower SNR threshold) in the presence of mismatch compared to the conventionally designed irregular LDPC codes that are optimized for zero mismatch. Considering that min-sum (MS) algorithm is the limit of BP with infinite SNR over-estimation, the EXIT functions generated in this work can also be used for the efficient analysis and design of LDPC codes under the MS algorithm.     

SNR mismatch and online estimation in turbo decoding

Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires knowledge of the signal-to-noise ratio (SNR) of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. We study the sensitivity of decoder performance to misestimation of the SNR, and propose a simple online scheme that estimates the unknown SNR from each code block, prior to decoding. We show that this scheme is sufficiently adequate in accuracy to not appreciably degrade the performance     

Joint turbo decoding and estimation of hidden Markov sources

We describe a joint source-channel scheme for modifying a turbo decoder in order to exploit the statistical characteristics of hidden Markov sources. The basic idea is to treat the trellis describing the hidden Markov source as another constituent decoder which exchanges information with the other constituent decoder blocks. The source block uses as extrinsic information the probability of the input bits that is provided by the constituent decoder blocks. On the other hand, it produces a new estimation of such a probability which will be used as extrinsic information by the constituent turbo decoders. The proposed joint source-channel decoding technique leads to significantly improved performance relative to systems in which source statistics are not exploited and avoids the need to perform any explicit source coding prior to transmission. Lack of a priori knowledge of the source parameters does not degrade the performance of the system, since these parameters can be jointly estimated with turbo decoding     

Bit-Level Extrinsic Information Exchange Method for Double-Binary Turbo Codes

Nonbinary turbo codes have many advantages over single-binary turbo codes, but their decoder implementations require much more memory, particularly for storing symbolic extrinsic information to be exchanged between two soft-input–soft-output (SISO) decoders. To reduce the memory size required for double-binary turbo decoding, this paper presents a new method to convert symbolic extrinsic information to bit-level information and vice versa. By exchanging bit-level extrinsic information, the number of extrinsic information values to be exchanged in double-binary turbo decoding is reduced to the same amount as that in single-binary turbo decoding. A double-binary turbo decoder is designed for the WiMAX standard to verify the proposed method, which reduces the total memory size by 20%.      

Code characteristic matching for iterative decoding of serially concatenated codes

The design of serially concatenated codes has yet been dominated by optimizing asymptotic slopes of error probability curves. We propose mutual information transfer characteristics for soft in/soft out decoders to design serially concatenated codes based on the convergence behavior of iterative decoding. The exchange of extrinsic information is visualized as a decoding trajectory in the Extrinsic Information Transfer Chart (exit chart). By finding matching pairs of inner and outer decoder transfer characteristics we are able to construct serially concatenated codes whose iterative decoder converges towards low bit error rate at signal- to- noise ratios close to the theoretical limits.     

Turbo codes for image transmission-a joint channel and sourcedecoding approach

This paper studies an application of turbo codes to compressed image/video transmission and presents an approach to improving error control performance through joint channel and source decoding (JCSD). The proposed approach to JCSD includes error-free source information feedback, error-detected source information feedback, and the use of channel soft values (CSV) for source signal postprocessing. These feedback schemes are based on a modification of the extrinsic information passed between the constituent maximum a posteriori probability (MAP) decoders in a turbo decoder. The modification is made according to the source information obtained from the source signal processor. The CSVs are considered as reliability information on the hard decisions and are further used for error recovery in the reconstructed signals. Applications of this joint decoding technique to different visual source coding schemes, such as spatial vector quantization, JPEG coding, and MPEG coding, are examined. Experimental results show that up to 0.6 dB of channel SNR reduction can be achieved by the joint decoder without increasing computational cost for various channel coding rates     

Predicting Approximate Performance Bounds for Space–Time Codes Over Quasi-Static Fading Channels

This paper provides a useful method for predicting the approximate performance of space time codes over quasi-static fading channels. Based on evaluating the signal-to-noise ratios (SNR) of the extrinsic information in the minimum mean-square error (MMSE) detector, we obtain upper and lower bounds on SNR, which are the convergent limits of the SNR evolution of the extrinsic information between the MMSE detector and the a posteriori probability decoder. Based on the SNR bounds the upper and lower bounds of frame-error-rate and bit-error-rate can be assessed by averaging over the fading coefficients. The results of numerical simulations are found to be in excellent agreement with the semi-analytic bounds.     

Architectural strategies for low-power VLSI turbo decoders

The use of "turbo codes" has been proposed for several applications, including the development of wireless systems, where highly reliable transmission is required at very low signal-to-noise ratios (SNR). The problem of extracting the best coding gains from these kind of codes has been deeply investigated in the last years. Also the hardware implementation of turbo codes is a very challenging topic, mainly due to the iterative nature of the decoding process, which demands an operating frequency much higher than the data rate; in the case of wireless applications, the design constraints became even more strict due to the low-cost and low-power requirements. This paper first presents a new architecture for the decoder core with improved area and power dissipation properties; then partitioning techniques are proposed to reduce the power consumption of the decoder memories. It is proven that most of the power is dissipated by the large RAM units required by the decoder, so the described technique is very efficient: an average power saving of 70% with an area overhead of 23% has been obtained on a set of analyzed architectures.