A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> I. INTRODUCTION <s> Iterative decoding of two-dimensional systematic convolutional codes has been termed "turbo" (de)coding. Using log-likelihood algebra, we show that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 2/3. Any combination of block and convolutional component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of 10/sup -4/ the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations. <s> BIB001 </s> A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> I. INTRODUCTION <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> I. INTRODUCTION <s> This tutorial paper gives an overview of the implementation aspects related to turbo decoders, where the term turbo generally refers to iterative decoders intended for parallel concatenated convolutional codes as well as for serial concatenated convolutional codes. We start by considering the general structure of iterative decoders and the main features of the soft-input soft-output algorithm that forms the heart of iterative decoders. Then, we show that very efficient parallel architectures are available for all types of turbo decoders allowing high-speed implementations. Other implementation aspects like quantization issues and stopping rules used in conjunction with buffering for increasing throughput are considered. Finally, we perform an evaluation of the complexities of the turbo decoders as a function of the main parameters of the code. <s> BIB003 </s> A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> I. INTRODUCTION <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> BIB004
One of the most interesting and most promising direction in the development of an error correction theory is data protection, which is based on cascaded parallel code structures (often with convolutional component codes) or turbo codes. The term "turbo" and important mathematical apparatus for the turbo code was first proposed in the fundamental work  . It is shown that at the high bit error rate (BER = 10 -5 -10 -7 from 0 to 3 dB) the best of the considered codes is turbo code (power gain of about 7-9 dB), what is very close to Shannon limit  . Thus, turbo code is the most effective method for information transmission in channels with low energy consumption. The results of original work  gave a powerful impetus to scientists to perform detailed research in the turbo decoding field with using of complex computational algorithms with high degree of error correction BIB002 . High turbo code efficiency is caused by special iterative decoding algorithms SOVA, Bi-SOVA, MAP or BCJR, log-MAP and other modifications [4-9, 12, 14] . All turbo decoding algorithms can be interpreted as the implementation of techniques known as message passing algorithm or belief propagation algorithm. To describe the strategy, that is embodied in an iterative decoding of turbo codes, a German scientist J. Hagenauer introduced the concept of "turbo"-principle: supply output data back to the entrance, which is similar with turbocharger engine; concept of probability iterative decoders with soft input and soft output; parallel working of elementary coders BIB001 BIB003 . Turbo codes can be implemented in software, hardware or mixed (software and hardware) manner. Often turbo codes implemented in mixed manner on digital signal processors. Detailed researches of turbo decoding complexity is given in  as well as comparative analysis for implementation complexity of turbo decoding algorithms. Turbo codes with probabilistic decoding algorithms are used for high performance data transmission in almost any communication system: television (DVB-RCS, DVB-RCT, DVB-SSP), telemetry, wireless local area networks (WiMAX), SDR systems (software defined radio), mobile (3G, 4G, Inmarsat) and space (CCSDS) communication  . Since there is no adequate mathematical tools that would calculate the practical error correction characteristics for turbo code, then computer simulation with Monte-Carlo method is used. So the purpose of this work is to conduct simulation for data transmission process in channels with low energy consumption for research an important experimental dependencies for the turbo code using developed by us in BIB004 piecewise-linear log-MAP decoding algorithm (PL-log-MAP). This algorithm helped to reduce computational complexity without significantly reducing of decoding quality. The paper is structured as follows. Section II is connected with the basic of iterative turbo decoding with MAP and log-MAP algorithms and their modifications. In Section III we compare some numerical results of PL-log-MAP decoding algorithm with other existing algorithms. At final we simulate the work of digital communication system with turbo codec and using PL-log-MAP to decode images in MatLab. The paper is finally concluded in Section IV.