A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> International Siberian Conference on Control and Communications (SIBCON) <s> A process for the preparation by sintering of molybdenum based alloys containing at least one reinforcing element, characterized in that at least one addition compound is introduced in the liquid state into molybdenum used in the form of at least one of the members belonging to the group consisting of the salts of molybdenum, the oxides of molybdenum and metallic molybdenum, and in that carbon is then added in sufficient quantity and the intimate member, after reduction of the matrix to the metallic state of molybdenum was used in the form of at least one molybdenum salt or at least one molybdenum oxide, is sintered at a temperature at which the said carbon at least partially reduces the addition compound. <s> BIB001 </s> A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> International Siberian Conference on Control and Communications (SIBCON) <s> For decades, the de facto standard for forward error correction was a convolutional code decoded with the Viterbi algorithm, often concatenated with another code (e.g., a Reed-Solomon code). But since the introduction of turbo codes in 1993, much more powerful codes referred to collectively as turbo and turbo-like codes have eclipsed classical methods. These powerful error-correcting techniques achieve excellent error-rate performance that can closely approach Shannon's channel capacity limit. The lure of these large coding gains has resulted in their incorporation into a widening array of telecommunications standards and systems. This paper will briefly characterize turbo and turbo-like codes, examine their implications for physical layer system design, and discuss standards and systems where they are being used. The emphasis will be on telecommunications applications, particularly wireless, though others are mentioned. Some thoughts on the use of turbo and turbo-like codes in the future will also be given. <s> BIB002 </s> A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> International Siberian Conference on Control and Communications (SIBCON) <s> In this paper, a new suboptimal modification for the log-MAP turbo decoding algorithm is proposed. This method (PL-log-MAP) based on the piecewise linear approximation of the the compensation term (correction function) in the Jacobian logarithm used by the MAP (BCJR) decoder. Using the proposed approximation, the complex functions ln(.) and exp(.) in the log-MAP algorithm can be estimated with high accuracy and lower computational complexity. The efficacy of the proposed approximation is investigated and demonstrated by applying it to digital communication system. The performance of the PL-log-MAP algorithm is shown to have the closest performance to the original log-MAP solution. <s> BIB003
An overview of the log-MAP algorithm will be presented. Detailed description is given in [4-9, 11, 15, 16] . The BCJR algorithm for convolutional codes was first presented in the fundamental work BIB001 . Nowadays in modern coding theory this algorithm has several names: MAP (maximum a posteriori probability), APP (for a posteriori probability), BCJR (the first letters of the authors surnames), FBA (forward-backward algorithm), SPA (sum-product algorithm). MAP or BCJR decoders show better energy efficiency, but they are more difficult to implement, than SOVA decoders  . The basis of the mathematical apparatus for turbo decoding is some computational procedure for assessing the solutions reliability, which is called logarithm of the likelihood ratio or LLR. , 0  is forward path metric on the trellis for recursive systematic convolutional (RSC) code; path metric on the trellis for RSC code; Efficient modification is log-MAP algorithm. It works in logarithmic area (natural logarithm of relevant MAP metrics is calculated and some simplifications is performed), has a lower computational complexity and achieves performance of MAP turbo decoding algorithm. For example, the forward path metric is given as Similarly, we present the backward path metric in the next equation Calculation of the logarithm of the exponential components sum is performed using Jacobian logarithm formula [7-9, 11, 15, 16] ). Note that in (6) can be neglected calculation of the correction function f cor . In this case we lose of about 10% efficiency compared to the MAP method. Such suboptimal turbo decoding algorithm is called max-log-MAP  . To calculate a posteriori solutions for log-MAP decoding algorithm the logarithm of the N exponential components sum is presented recursively. So the formula BIB002  There is a need to complement this algorithm with using some approximation of the correction to improve the efficiency of the turbo decoder. The authors of this paper proposed an effective PL-log-MAP algorithm   BIB003  , which is not used complex functions (logarithm, exponential components sum) in the recursive process. This feature reduces the computational complexity. Next section gives some numerical results and simulation for PL-log-MAP algorithm.