V.V. Vityazev - Dr. Sc. (Eng.), Professor, Chair of "Telecommunications and Fundamentals of Radio Engineering" Department, Ryazan State Radio Engineering University. E-mail: vityazev.v.v@rsreu.ru
E.A. Likhobabin - Research Associate of "Telecommunications and Fundamentals of Radio Engineering" Department, Ryazan State Radio Engineering University. E-mail: lichobabinea@gmail.com

LDPC codes was proposed by R.Gallager in 1963, and now they are widely used in many applications and telecommunication standards. Nowadays all modern standards such as DVB-T2, DVB-S2, DVB-C2, WiFi, WiMax, IEEE 802.15.3 used this codes. Min-sum algorithm (MSA) can be considered as a further simplification of operation for log likelihoods (LLR) summation in parity-check node decoder. The main advantage of such simplification is that outcoming message from every variable node can be computed by finding only two lowest values of reliability in the check and computation of a sign. The second valuable advantage is that decoder can operate with reliabilities received from the channel without any computations of LLRs. So this algorithm also known as uniformly most powerful belief propagation algorithm UMP-BP. Due to their advantages MSA algorithm have widespread usage in different de-coding applications, and moreover there are a lot of different modifications of this algorithm exist. Algorithm a-min* reduces complexity of check nodes update. It-s a combination of sum-product (SPA) and min-sum algorithm. For MSA in every check node only two outcoming messages computed, the first for bit with lowest reliability, and the second for all other messages. Such modification reduces computation of LLR sums 3(dr-1) to (dr-1) operations. Effectiveness of this algorithm is between SPA-based and MSA algorithms. Since algorithm used LLR summation, hence may be used any approximation of them. It can be shown that a-min* algorithm is a special case of more generalized algorithm, call them generalized a-min*. Generalized a-min* algorithm loses in effectiveness SPA algorithm, but wins in complexity, so it can be used in some special cases. Generalized a-min* representation can be used to get one more modification of a-min* decoding algorithm not so evident in common consideration, call them min generalized a-min* algorithm. Analyses of obtained results for regular PEG LDPC code N=1008, К=504 shown, that a-min* algorithm loses SPA algorithm in convergence for large signal-to-noise ratios, but achievement bit error rate is quite enough for some real applications. Also we can observe, that min generalized a-min* algorithm have an intermediate effectiveness between MSA and a-min* algorithms.