A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> III. RESEARCH EXPERIMENTS FOR PL-LOG-MAP ALGORITHM <s> We provide an overview of the novel class of channel codes referred to as turbo codes, which have been shown to be capable of performing close to the Shannon limit. We commence with a discussion on turbo encoding, and then move on to describing the form of the iterative decoder most commonly used to decode turbo codes. We then elaborate on various decoding algorithms that can be used in an iterative decoder, and give an example of the operation of such a decoder using the so-called soft output Viterbi (1996) algorithm (SOVA). Lastly, the effect of a range of system parameters is investigated in a systematic fashion, in order to gauge their performance ramifications. <s> BIB001 </s> A brief overview and experimental researches of novel PL-log-MAP turbo decoding algorithm <s> III. RESEARCH EXPERIMENTS FOR PL-LOG-MAP ALGORITHM <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> BIB002
In log-MAP algorithm at the stages of metrics and "soft" decisions calculation the important element is decreasing nonlinear function f cor (z). It have been proposed to simplify calculations using standard linear functions in sub-ranges, which have been found via computer search by the least squares method  . So we take 6 sub-ranges: z 0 ∈[0;1), z 1 ∈[1;1.5), z 2 ∈[1.5; 2), z 3 ∈[2; 3), z 4 ∈[3; 4], z 5 ∈(4; +∞). If z is greater than 4, the compensation term takes a small constant value, for example we set this measure on 0.01. So we see (Table 1) , that our correction function is very precise on sub-ranges. The accuracy of our function is verified through the comparison against different approximations in table 2 for test range, where MAE is Mean Absolute Error, RMSE − Root-Mean-Square Error, r is correlation coefficient,  -difference between r for piecewise linear approximation and r for other existing approximations in percents. Figure 1 shows the graphical comparisons for different correction function approximations. The proposed function has high accuracy on the test range of the argument z values (from 0 to 10 with step of 0.01) compared to existing analogs, such as fractional (by 0.11 %), quadratic (by 0.2 %), combined hybrid (by 0.37 %), Robertson lookup table (by 0.54 %), Zaytsev-linear (by 0.65 %), hybrid (by 0.69 %) and others BIB002   . Also we calculate the number of elementary mathematical operations (or computational complexity) for turbo decoding of one binary information symbol on digital signal processor  . The equation is presented in the next form where m is RSC coder memory; h is total number of binary symbols from the output of the RSC coder. For simulation the work of digital communication system we use the turbo codec  with two identical RSC codes with generator polynomial  BIB001  , implemented in 1, 4 and 8 iterations, with overall rate of 1/3; random interleaver (S. Park-K. Miller random generator) with m = 2 tail bits; AWGN channel for data modulated using BPSK; the energy per bit to noise power spectral density ratio Eb/N 0 = [0:3] with step 0.25 dB; 8 decoding iterations; 1024 binary symbols in frame. Ziggurat algorithm was used for modeling standard normally distributed random variables. Stopping rule for turbo decoder is 10 frames with errors. The comparison with popular turbo decoding algorithms is presented in the Fig. 2 The results of these experiments confirm the high efficiency of PL-log-MAP turbo decoding algorithm. So it can be used in digital communication systems.