Abstract
This chapter presents performance of a new technique for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) encrypted codes based on a row division method. The new QC-LDPC encrypted codes are flexible in terms of large girth, multiple code rates, and large block lengths. In the proposed algorithm, the restructuring of the interconnections is developed by splitting the rows into subrows. This row division reduces the load on the processing node and ultimately reduces the hardware complexity. In this method of encrypted code construction, rows are used to form a distance graph. They are then transformed to a parity-check matrix in order to acquire the desired girth. In this work, matrices are divided into small sub-matrices, which result in improved decoding performance and reduce waiting time of the messages to be updated. Matrix sub-division increases the number of sub-matrices to be managed and memory requirement. Moreover, Prototype architecture of the LDPC codes has been implemented by writing Hardware Description Language (VHDL) code and targeted to a Xilinx Spartan-3E XC3S500E FPGA chip.
TopIntroduction
The means by which people correspond has radically changed since the early days of communication. At the moment, wireless networks and devices communicate far more than conventional verbal conversations. It has been noted that the cellular phone industry is facing revenue losses every year due to illegal handling of their services. As the cellular systems are developed, newly employed security features cut down the possibility of technical hoaxs. Nevertheless, as third generation (3G) cellular systems become the main part of omnipresent wireless communication, the security of cellular systems confronts new challenges. Integration and interfacing of these systems into packet switching networks will expose them to all kinds of intentional and unintentional attacks, and will require an advanced level of security. Security and encryption are necessary concerns in this computer age.
This chapter explores the research and development of new encryption codes and systems. The term code has a number of different meanings and in this chapter where it is used to refer to a computer program or software those terms will be used everywhere else the term code or coding will be used to refer to encryption and digital security systems. A secure system constrains from doing anything that it is not supposed to do. The key prospects of security are Confidentiality, Integrity and Availability. These three views also are named as Computational Intelligence (CI). Confidentiality is all about asserting privacy and Integrity is about ascertaining the precision and completeness of information while Availability is about guaranteeing the availability of information to authorized hands.
This chapter presents a new technique for designing and implementing QC-LDPC encrypted codes based on a row division method. The new encrypted codes offer more flexibility in terms of large girth, multiple code rates and large lengths. In this method of encrypted code construction, the rows are used to form the distance graph. In the proposed algorithm, the restructuring of the interconnections is developed by splitting the rows into subrows. This row division reduces the load on processing nodes and ultimately reduces the hardware complexity.
Channel coding is a broadly used term mostly referring to the forward error correction code and bit interleaving in communication and storage where the communication media or storage media is viewed as a channel and plays a key role in providing a reliable communication method that can overcome signal degradation in practical channels. The breakthrough of convolutional codes (Charles, 1997) led a new field of study into non-algebraic codes based on linear transformations using generator and parity-check matrices. These use error-correcting that firstly transforms each m-bit information symbol (each m-bit string) into an n-bit symbol, where m/n is the code rate (n ≥ m) and secondly the transformation is a function of the last k information symbols, where k is the constraint length of the code. Convolutional codes are encoded using a finite-state process, which generates a linear order encoding scheme. Since then convolutional codes have led to the discovery of a new class of codes called Turbo codes (Berrou et al., 1993), which are a class of concatenated convolutional codes that randomize the order of some of the bits by using an interleaver.
Key Terms in this Chapter
Code Weights and Rate: The rate of a code, is the number of information bits over the total number of bits transmitted. Higher row and column weights result in extra computation at each node because of the large number of incoming messages. Nevertheless, if many nodes contribute in estimating the probability of a bit the node accomplishes a consensus faster. Higher rates indicate fewer redundancy bits. Namely, more information data is transmitted per block resulting in high throughput. Though, low redundancy implies less protection of bits and thus less decoding performance or higher error rate. Low rate codes have more redundancy with less throughput. More redundancy results in more decoding performance. But, low rate may have poor performance with a small number of connections. LDPC codes with column-weight of two have their minimum distance increasing logarithmically with code size as compared to a linear increase for codes with column-weight of three or higher. Column weights higher than two are generally employed but carefully designed irregular codes could have better performance.
Cycle: A cycle in a distance graph is formed by a path edges or vertices starting from a vertex and ending at. No more than two vertices forming the cycle belong to the same column. See also distance graph and girth.
Minimum Sistance: The Hamming weight of a codeword is the number of 1’s of the codeword. The Hamming distance between any two codewords is the number of bits with which the words differ from each other, and the minimum distance of a code is the smallest Hamming distance between two code words. The larger the distance the better the performance of a code. Very long and large girth LDPC codes tend to have larger minimum distances. Minimum distance can be used as a measure to rank these codes.
Codeword: A codeword is an element of an error-correcting code C. If C has length n, then a codeword in C has the form (c1,c2……cn), where each ci is a letter in the alphabet of C
Code Structure: The structure of a code is ascertained by the pattern of connection between rows and columns. The connection pattern ascertains the complexity of the communication interconnect between check and variable processing nodes in the encoder and decoder hardware implementations. Random codes do not chase any predefined or known pattern in row-column connections. Structured codes on the hand have a known interconnection pattern.
Code Size: The code size defines the dimensions of the parity check matrix. Occasionally the term ‘code length’ is given as n. Usually a code is defined by employing its length and row column weight in the form. can be deduced from the code parameters, and . It has been determined that long codes execute better than shorter codes but need more hardware implementation resources.
Distance Graph: Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns.
Girth: The girth g, is the smallest cycle in the graph. A cycle of length of gin the graph corresponds to a cycle of length 2g in the matrix form.