Algorithm For Linear Block Codes Research Articles

Особливості програмної реалізації біоінспірованого методу м’якого декодування лінійних блокових кодів

The important part of many telecommunication technologies are linear block codes. The use of soft decoding can increasing the effectiveness of these codes. The expediency of application bioinspired approach for soft decoding relatively long linear block codes is grounded. The general principles bioinspired approach to soft decoding of linear block codes is considered. The basic steps and flowchart of the bioinspired method of decoding linear block codes are presented. A distinctive feature of the proposed method of decoding linear block codes is the use of generalized bioinspired search to determine the most likely base information vector and corresponding bipolar codeword. It is noted that the choice of a particular procedure bioinspired search should be carried out according to the parameters of the code, channel characteristics and performance requirements decoding. The ways of software implementation bioinspired method of decoding linear block codes are determined. Bioinspired decoding algorithm for linear block codes and features its implementation are presented. The list of input and output data for this algorithm is presented. Principles of the subprocess of the most reliable basis generative matrix and subprocess bioinspired search basic information word (and the corresponding bipolar codeword) are presented.

A Novel Decoder Based on Parallel Genetic Algorithms for Linear Block Codes

Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.

Correction to “An Efficient Maximum-Likelihood-Decoding Algorithm for Linear Block Codes With Algebraic Decoder” [Mar 94 320-327

Correction to “An Efficient Maximum-Likelihood-Decoding Algorithm for Linear Block Codes With Algebraic Decoder” [Mar 94 320-327

Mean field and mixed mean field iterative decoding of low-density parity-check codes

In this paper, the mean field (MF) and mixed mean field (MMF) algorithms for decoding low-density parity-check (LDPC) codes are considered. The MF principle is well established in statistical physics and artificial intelligence. Instead of using a single completely factorized approximated distribution as in the MF approach, the mixed MF algorithm forms a weighted average of several MF distributions as an approximation of the true posterior probability distribution. The MF decoding algorithm for linear block codes is derived and shown to be an approximation of the a posteriori probability (APP) decoding algorithm. The MF approach is then developed in the context of iterative decoding and presented as an approximation of the popular belief propagation decoding method. These results are extended to iterative decoding with the MMF algorithm. Simulation results show that the MF and MMF decoding algorithms yield a good performance-complexity tradeoff, especially when employed for decoding LDPC codes based on finite geometries.

A New Adaptive Two-Stage Maximum-Likelihood Decoding Algorithm for Linear Block Codes

In this paper, we propose a new two-stage (TS) structure for computationally efficient maximum-likelihood decoding (MLD) of linear block codes. With this structure, near optimal MLD performance can be achieved at low complexity through TS processing. The first stage of processing estimates a minimum sufficient set (MSS) of candidate codewords that contains the optimal codeword, while the second stage performs optimal or suboptimal decoding search within the estimated MSS of small size. Based on the new structure, we propose a decoding algorithm that systematically trades off between the decoding complexity and the bounded block error rate performance. A low-complexity complementary decoding algorithm is developed to estimate the MSS, followed by an ordered algebraic decoding (OAD) algorithm to achieve flexible system design. Since the size of the MSS changes with the signal-to-noise ratio, the overall decoding complexity adaptively scales with the quality of the communication link. Theoretical analysis is provided to evaluate the potential complexity reduction enabled by the proposed decoding structure.

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.

Improvement of iterative decoding algorithm for linear block codes

Two parameters are introduced into a popular algorithm for the iterative decoding of information encoded with a binary linear code and transmitted over the additive white Gaussian noise channel to improve the coding gain. Theoretical justification supported by simulation results are presented.

A Maximum Likelihood Decoding Algorithm for Wireless Channels

A new maximum likelihood decoding (MLD) algorithm for linear block codes is proposed. The new algorithm uses the algebraic decoder in order to generate the set of candidate codewords. It uses the exact probability for each codeword as a new likelihood metric and a method to generate the appropriate set of codewords similar to Kaneko, et al., and Tanaka-Kakigahara algorithms. The performance of the proposed algorithm is the same as that of MLD as it is proved theoretically and verified by simulation results. The comparison with these similar algorithms shows that the new one always requires less average decoding complexity than those of the other algorithms. Finally, we compare the algorithms for terrestrial and satellite channels.

Novel near maximum likelihood soft decision decoding algorithm for linear block codes

The authors present a novel near maximum likelihood (ML) soft decision decoding (SDD) algorithm for linear block codes. The proposed algorithm can be subdivided into three distinct algorithms, each achieving a specific objective. The first algorithm achieves near ML decoding performance by utilising channel measurement information. The second and third algorithms maintain the improved decoding performance achieved, while at the same time reducing both the number of decodings and complexity required. The resultant algorithm is both general in nature and able to offer significant performance improvements. The theoretical results are verified by computer simulation.

Decoding linear block codes using a priority-first search: performance analysis and suboptimal version

An efficient maximum-likelihood soft-decision decoding algorithm for linear block codes using a generalized Dijkstra's algorithm was proposed by Han, Hartmann, and Chen (1993). We prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10/sup -3/ by finding an upper bound of the computational effort of the algorithm. A suboptimal decoding algorithm is also proposed. The performance of this suboptimal decoding algorithm is within 0.25 dB of the performance of an optimal decoding algorithm for the (104, 52) binary extended quadratic residue code, and within 0.5 dB of the optimal performance for the (128, 64) binary BCH code, respectively.

A unified method for evaluating the error-correction radius of reliability-based soft-decision algorithms for linear block codes

This paper presents a unified method for evaluating the error-correction radii of many reliability-based soft-decision decoding algorithms for binary linear block codes. Based on this unified method, these decoding algorithms as well as their potential improvements can be compared directly. The error-correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft-decision decoder to the transmitted signal sequence. It is shown that this problem can be formulated as a constrained optimization problem. Although no general closed-form expression is possible, a simple algorithm that always converges to the optimum solution of this optimization problem is presented. Based on these results, the error-correction radii of some well-known reliability-based soft-decision decoding algorithms are revisited and compared.

Efficient heuristic search algorithms for soft-decision decoding of linear block codes

Efficient new algorithms are presented for maximum-likelihood and suboptimal soft-decision decoding algorithms for linear block codes. The first algorithm, MA*, improves the efficiency of the A* decoding algorithm, conducting the heuristic search through a code tree while exploiting code-specific properties. The second algorithm, H*, reduces search space by successively estimating the cost of the minimum-cost codeword with a fixed value at each of the most reliable and linearly independent components of the received message. The third algorithm, directed search, finds the codeword closest to the received vector by exploring a continuous search space. The strengths of these three algorithms are combined in a hybrid algorithm, applied to the (128,64), the (256,131), and the (256,139) binary-extended Bose-Chaudhuri-Hocquenghem (BCH) codes. Simulation results show that this hybrid algorithm can efficiently decode the (128,64) code for any signal-to-noise ratio, with near-optimal performance. Previously, no practical decoder could have decoded this code with such a performance for all ranges of signal-to-noise ratio.

A simple one-sweep algorithm for optimal APP symbol decoding of linear block codes

Soft-input/soft-output symbol decoding plays a significant role in iterative decoding. We propose a simple optimal soft-input/soft-output symbol decoding algorithm for linear block codes which requires one forward recursion using a trellis. For many codes the decoding complexity is lower than previous methods, such as the algorithm by Bahl et al. (1974), and the decrease is shown at its most when decoding Hamming codes.

An efficient maximum-likelihood-decoding algorithm for linear block codes with algebraic decoder

A new soft decoding algorithm for linear block codes is proposed. The decoding algorithm works with any algebraic decoder and its performance is strictly the same as that of maximum-likelihood-decoding (MLD). Since our decoding algorithm generates sets of different candidate codewords corresponding to the received sequence, its decoding complexity depends on the received sequence. We compare our decoding algorithm with Chase (1972) algorithm 2 and the Tanaka-Kakigahara (1983) algorithm in which a similar method for generating candidate codewords is used. Computer simulation results indicate, for some signal-to-noise ratios (SNR), that our decoding algorithm requires less average complexity than those of the other two algorithms, but the performance of ours is always superior to those of the other two.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient priority-first search maximum-likelihood soft-decision decoding of linear block codes

The authors present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here converts the decoding problem into a search problem through a graph that is a trellis for an equivalent code of the transmitted code. A generalized Dijkstra's algorithm, which uses a priority-first search strategy, is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to reduce drastically the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. For example, for most real channels of the 35 000 samples tried, simulation results for the (128,64) binary extended BCH code show that the proposed decoding algorithm is fifteen orders of magnitude more efficient in time and in space than that proposed by Wolf (1978). Simulation results for the (104, 52) binary extended quadratic residue code are also given. >