Bahl-Cocke-Jelinek-Raviv Algorithm Research Articles

BNET: A Neural Network Approach for LLR-Based Detection in the Presence of Bursty Impulsive Noise

Ensuring reliable wireless communications is often a major challenge in environments characterized by bursty impulsive noise. Unfortunately, effective receivers adapted to this problem employ recursive techniques that are computationally complex and challenging to implement where computing and battery resources are limited. As a solution, we propose a computationally efficient neural network-based framework to approximate the log-likelihood ratio function produced by the Bahl Cocke Jelinek Raviv (BCJR) algorithm for single-carrier communication systems. The results show that our method can match the BCJR algorithm’s BER performance in many scenarios and even outperform it when some noise model parameters change over time.

Turbo decoding of simple product codes in a two user binary adder channel employing the Bahl–Cocke–Jelinek–Raviv algorithm

The main goal in this paper is an investigation of the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm applied in a turbo decoding scheme. Binary product codes are employed in a turbo coding scheme and the channel model considered is the two user binary adder channel (2-BAC) with additive white Gaussian noise. A trellis for two users is constructed for a pair of product codes tailored for use in the 2-BAC in order to employ the BCJR decoding algorithm. Computer simulation is employed to show that product codes on the 2-BAC, employing low-complexity component codes, produces considerable gain with few iterations under iterative BCJR decoding.

An Information-Spectrum Approach to the Capacity Region of the Interference Channel

In this paper, a general formula for the capacity region of a general interference channel with two pairs of users is derived, which reveals that the capacity region is the union of a family of rectangles. In the region, each rectangle is determined by a pair of spectral inf-mutual information rates. The presented formula provides us with useful insights into the interference channels in spite of the difficulty of computing it. Specially, when the inputs are discrete, ergodic Markov processes and the channel is stationary memoryless, the formula can be evaluated by the BCJR (Bahl-Cocke-Jelinek-Raviv) algorithm. Also the formula suggests that considering the structure of the interference processes contributes to obtaining tighter inner bounds than the simplest one (obtained by treating the interference as noise). This is verified numerically by calculating the mutual information rates for Gaussian interference channels with embedded convolutional codes. Moreover, we present a coding scheme to approach the theoretical achievable rate pairs. Numerical results show that the decoding gains can be achieved by considering the structure of the interference.

Interference cancellation and signal detection technique based on QRD‐M algorithm for FTN signalling

This Letter presents interference cancellation and signal detection technique for faster-than-Nyquist (FTN) signalling. The proposed scheme uses QR decomposition (QRD)-M algorithm to execute interference cancellation and signal detection. Based on the Toeplitz structure of the inter-symbol interference coefficient matrix, the QRD-M algorithm is adopted to detect the transmitted symbols from an FTN signal. The computational complexity comparisons and numerical results demonstrate that the proposed technique can achieve the complexity <10% of Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm while maintaining BER performance similar to that of BCJR algorithm.

Equivalent Discrete-Time Channel Modeling for Molecular Communication With Emphasize on an Absorbing Receiver.

This paper introduces the equivalent discrete-time channel model (EDTCM) to the area of diffusion-based molecular communication (DBMC). Emphasis is on an absorbing receiver, which is based on the so-called first passage time concept. In the wireless communications community the EDTCM is well known. Therefore, it is anticipated that the EDTCM improves the accessibility of DBMC and supports the adaptation of classical wireless communication algorithms to the area of DBMC. Furthermore, the EDTCM has the capability to provide a remarkable reduction of computational complexity compared to random walk based DBMC simulators. Besides the exact EDTCM, three approximations thereof based on binomial, Gaussian, and Poisson approximation are proposed and analyzed in order to further reduce computational complexity. In addition, the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is adapted to all four channel models. Numerical results show the performance of the exact EDTCM, illustrate the performance of the adapted BCJR algorithm, and demonstrate the accuracy of the approximations.

Bahl–Cocke–Jelinek–Raviv decoding algorithm applied to the three‐user binary adder channel

The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is a well-known maximum a posteriori probability decoding algorithm which has been proposed earlier for point to point communication applications, employing block codes or convolutional codes and turbo codes. This study describes an application of the BCJR algorithm for decoding the output of a multiple-access channel called the noisy three-user binary adder channel, in the presence of additive white Gaussian noise. The computer simulation results are presented for the overall coding performance in terms of bit error rate against signal-to-noise ratio.

Low-Complexity Iterative Row-Column Soft Decision Feedback Algorithm for 2-D Inter-Symbol Interference Channel Detection With Gaussian Approximation

In this paper, we study the complexity reduction problem of the iterative row-column soft decision feedback algorithm (IRCSDFA) for 2-D inter-symbol interference (ISI) detection. Specifically, Gaussian approximation (GA) is employed in both the component row and column detectors of the IRCSDFA in order to reduce its computational complexity. With the employment of GA, the state space dimension of the ISI trellis of either component detector can be reduced enormously (i.e., the number of branches in one ISI trellis section decreases). Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is then employed to perform detection over the GA-simplified ISI trellis. For brevity, we refer to the IRCSDFA with BCJR detection over the GA-simplified ISI trellis as “IRCSDFA-GA-BCJR”. Next, the iteration scheduling of component detectors and decoder in coded 2-D ISI channels with low density parity check (LDPC) coding and IRCSDFA-GA-BCJR detection is studied. Specifically, three iteration schemes: single detector (row or column) scheme, alternate detector scheme, and combined detector scheme, are considered, with the last scheme showing the best coded performance. Finally, the computational complexity of the proposed IRCSDFA-GA-BCJR is analyzed, and shown to have significant reduction with a cost of only about 0.3 and 0.35 dB in coded BER/FER performance loss compared to the conventional IRCSDFA without GA and the optimal symbol-based BCJR algorithm, respectively.

Application and Optimization of Factor Graph-Based Detector on 1D ISI Magnetic Recording Channel

This paper introduces the application of a factor graph (FG)-based detector on a one-dimensional (1D) intersymbol interference (ISI) magnetic recording channel. The conventional Bahl-Cocke-Jelinek-Raviv (BCJR) detection algorithm operates on a trellis, which defines an equivalence between a bit sequence and a path through the trellis, as well as all possible time evolutions of states of the channel. The BCJR algorithm outputs soft information which corresponds to the a-posteriori channel bit probabilities. Unlike the BCJR, the FG-based detector employs the use of the sum product algorithm (SPA) on a FG with the objective of calculating the same a-posteriori probabilities. Employing the binary SPA to this FG detector gives rise to a suboptimal performance due to the presence of short cycles within the channel factor graph. A nonbinary implementation of the same algorithm mitigates the effect of these cycles and thereby results in an improved performance as compared to the binary implementation. In this paper we also propose an alternative method that can be used to reduce the number of these cycles for performance enhancement. This method involves using an equalizer with a generalized partial response (GPR) target.

Exploitation of 2D binary source correlation using turbo block codes with fine-tuning

This article proposes a joint source-channel coding technique for two-dimensional (2D) binary Markov sources by using concatenated turbo block codes composed of two Bose, Chaudhuri, Hocquenghem (BCH) codes, of which output is followed by a rate-1 recursive systematic convolutional code. The source correlation of all rows and columns of the 2D source is well exploited by using a modified Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm for the decoding of the BCH codes. Simulation results show that the proposed technique outperforms in terms of bit error rate the codes that exploits one-dimensional (1D) source correlation using the modified BCJR algorithm, and obviously the conventional system without source correlation exploitation. In order to further improve the performance, this article aims to make fine-tuning of the code parameters, given the source correlation property, that can achieve performance even closer to the theoretical limit than without the fine-tuning. Finally, results of image transmission simulations using two images, one having strong and the other weak 2D correlation, are presented to demonstrate the effectiveness of our proposed technique.

The Bahl-Cocke-Jelinek-Raviv Algorithm Applied to the Two-User Binary Adder Channel

The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is a well known maximum a posteriori probability decoding algorithm which has been proposed earlier for point to point communication applications, employing block codes or convolutional codes, and turbo codes. This paper describes an application of the BCJR algorithm for decoding the output of a multiple access channel called the noisy two-user binary adder channel, in the presence of additive white Gaussian noise.

Reduced-Complexity BCJR Algorithm for Turbo Equalization

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We propose novel techniques to reduce the complexity of the well-known Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is more suitable than the original for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them being particularly effective over one of the three different classes of channels (minimum-phase, maximum-phase, and mixed-phase channels) affected by intersymbol interference. The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, which are chosen according to the maximum <emphasis emphasistype="italic">a posteriori</emphasis> criterion. Moreover, some optimization techniques for improving the effectiveness of the proposed solutions are described. Finally, we report the results of computer simulations showing the impressive performance of the proposed algorithms, and compare them with other solutions in the literature. </para>

A Generalized BCJR Algorithm and Its Use in Iterative Blind Channel Identification

The well-known Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm was generalized to compute joint posterior probabilities of arbitrary sets of symbols given noisy observations of those symbols at the output of an intersymbol interference (ISI) channel. This letter explores using pair-wise joint posterior probabilities produced by generalized BCJR together with expectation maximization for blind identification of the ISI channel impulse response and noise variance. Simulations indicate that the blind algorithm accurately estimates the channel response and noise variance and yields bit error rates comparable to a channel-informed BCJR equalizer.

On the BCJR Algorithm for Rate-Distortion Source Coding

The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is an important channel decoding method. We extend it to trellis rate-distortion data compression. Beginning from source coding principles, the derivation of the algorithm avoids channel coding or soft output ideas. The encoder does not use entropy coding; equiprobable reproducer letters are emphasized since these maximize entropy. The BCJR method is demonstrated by tests of a tail-biting variant. It performs much better than the ordinary Viterbi algorithm for short and medium blocks. However, the improvement stems from tail biting; the role of the BCJR is to achieve tail biting in a relatively simple way. Some issues that arise with tail biting are explored. It is shown that there is an optimal trellis state size for each block length.

Approximate inference in hidden Markov models using iterative active state selection

The inferential task of computing the marginal posterior probability mass functions of state variables and pairs of consecutive state variables of a hidden Markov model is considered. This can be exactly and efficiently performed using a message passing scheme such as the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. We present a novel iterative reduced complexity variation of the BCJR algorithm that uses reduced support approximations for the forward and backward messages, as in the M-BCJR algorithm. Forward/backward message computation is based on the concept of expectation propagation, which results in an algorithm similar to the M-BCJR algorithm with the active state selection criterion being changed from the filtered distribution of state variables to beliefs of state variables. By allowing possibly different supports for the forward and backward messages, we derive identical forward and backward recursions that can be iterated. Simulation results of application for trellis-based equalization of a wireless communication system confirm the improved performance over the M-BCJR algorithm.

Iterative reduced-state decoding for coded partial-response channels

The conventional iterative decoding based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm rises exponentially in terms of channel memory length. In this paper, we propose a low-complexity soft-input/soft-output (SISO) channel detector based on tentative hard estimates fed back from the outer decoder in the previous iteration. The computational complexity of the proposed detector is polynomial in terms of the channel memory length. To demonstrate the performance/complexity tradeoff of the proposed detector, we present simulation results for 9-tap, 11-tap, and 12-tap channels. We show that the proposed detector significantly reduces the computational complexity with only slight performance degradation compared to the full-complexity BCJR algorithm.

On the Application of Factor Graphs and the Sum–Product Algorithm to ISI Channels

In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth-6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of low-density parity-check (LDPC) codes is also considered and results are shown for some partial-response magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal "serial" BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified "parallel" BCJR algorithm proposed in the literature for the application to magnetic channels.

A Memory-Efficient Optimal APP Symbol-Decoding Algorithm for Linear Block Codes

We propose a simple modification of the famous Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm for linear block codes. The modified algorithm requires one forward and two backward recursions in the code trellis, but eliminates the need to store the whole trellis. Compared with the BCJR algorithm, the computational complexity is slightly increased, but the storage requirement is reduced.

Simple MAP Decoding of First-Order Reed–Muller and Hamming Codes

A maximum a posteriori (MAP) probability decoder of a block code minimizes the probability of error for each transmitted symbol separately. The standard way of implementing MAP decoding of a linear code is the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, which is based on a trellis representation of the code. The complexity of the BCJR algorithm for the first-order Reed-Muller (RM-1) codes and Hamming codes is proportional to n/sup 2/, where n is the code's length. In this correspondence, we present new MAP decoding algorithms for binary and nonbinary RM-1 and Hamming codes. The proposed algorithms have complexities proportional to q/sup 2/n log/sub q/n, where q is the alphabet size. In particular, for the binary codes this yields complexity of order n log n.