Computation of Parity Check Matrices for Binary EG-LDPC Codes used in Communication Systems

Author Name(s): J. Chinna Babu, C.Chinnapu Reddy, M.N.Giri Prasad
Author Email: jchinnababu@gmail.com

Abstract

The Low Density Parity Check (LDPC) are direct codes, which are true block and Shannon Limit codes. These codes are attained least error floors of data bits for data transfer applications used in communication systems. However, the proposed LDPC codes are more beneficial than Turbo codes because of reduction in the decoding complexity and detection of the errors in less cycle time. This results the reduction of decoding time, low decoding latency, complexity and as well as least error floorings in communication, when the transmitted data contains multiple error bits. This paper is proposed to represent the majority logic decoding/detecting of LDPC codes. This paper proposes the Generation of Originator and Parity estimated matrices for the Binary LDPC Codes. Here, the proposed techniques are hard decision decrypting and soft decision decrypting schemes. These schemes uses majority logic decoding based on the data transmission and reception in communication channel. This paper also elaborates the effective calculation of Euclidean distance and algorithm for constructing the LDPC codes.

Introduction

Correcting Error Codes The terminated data or parity bits is auxiliary to the novel coded data, therefore that the exact coded data can be recovered at the destination end without the requirement for the data re-transmission and similarly the faults can be discovered and rectified, if any faults are existing. For this, we are using sophisticated codes, which are called error-correcting odes. Shannon’s Theorem: For the consistent broadcasting of data over a given communication medium, the data transmission rate should not exceed the channel capacity, which is proved by Shannon theorem. LDPC Codes: LDPC codes are established by R.G. Gallagher, hence these are also identified as Gallagher codes. Due to unbearable practical comprehension, these codes are abandoned, although these codes were designed in the early 1960’s. These LDPC codes are direct error improving codes and methodologies near Shannon capability. These LDPC codes are the better blunder improving codes, used for encoding and decoding at present scenario [1]-[3]. Here are binary categories of LDPC codes are of two types. LDPC Regular Codes: Regular type of codes take equivalent row masses (π‘Šπ‘Ÿ) and equivalent column masses (π‘Šπ‘) (Equivalent number of ones in rows and columns)

Conclusion

The LDPC codes have the near Shannon limit presentation and the creation of the equivalence check matrices is clarified in this paper for the binary LDPC codes. Where the methodology of creating the LDPC Codes and its corresponding general decoding block diagram of LDPC codes is also explained. General Decoding scheme for bit flipping algorithms is also elaborated. Hence, these LDPC codes have higher coding rates compared to other conventional codes available. From these construction, we conclude that these codes are used in Security and Signal processing applications which provides authentication between source and destination

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