Performance comparison of turbo codes with LDPC codes and with BCH codes for forward error correcting codes

Author(s):  
Mohammed Hasan Alwan ◽  
Mandeep Singh ◽  
Hussain Falih Mahdi
Author(s):  
Issam Abderrahman Joundan ◽  
Said Nouh ◽  
Mohamed Azouazi ◽  
Abdelwahed Namir

<span>BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity.  ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper.</span>


Sensors ◽  
2019 ◽  
Vol 19 (21) ◽  
pp. 4793 ◽  
Author(s):  
Bushra Bashir Chaoudhry ◽  
Syed Ali Hassan ◽  
Joachim Speidel ◽  
Haejoon Jung

This paper presents cooperative transmission (CT), where multiple relays are used to achieve array and diversity gains, as an enabling technology for Internet of Things (IoT) networks with hardware-limited devices. We investigate a channel coding aided decode-and-forward (DF) relaying network, considering a two-hop multiple-relay network, where the data transmission between the source and the destination is realized with the help of DF relays. Low density parity check (LDPC) codes are adopted as forward error correction (FEC) codes to encode and decode the data both at the source and relays. We consider both fixed and variable code rates depending upon the quality-of-service (QoS) provisioning such as spectral efficiency and maximum energy efficiency. Furthermore, an optimal power allocation scheme is studied for the cooperative system under the energy efficiency constraint. We present the simulation results of our proposed scheme, compared with conventional methods, which show that if decoupled code rates are used on both hops then a trade-off has to be maintained between system complexity, transmission delay, and bit error rate (BER).


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