Construction Of Encodable QC-LDPC Codes Using Particle Swarm Optimization Algorithm

Low-Density Parity-Check (LDPC) codes have been the subject of intense research lately because of their capacity-achieving performance and linear decoding complexity by using an iterative decoding algorithm, the so called belief propagation or sum-product algorithm. Ever since their construction, decoding, efficient encoding and applications in digital communication have become focal points of research. Gallager considered only regular LDPC, i.e., codes that are represented by a sparse parity-check matrix with a constant number of ones (weight) in each column and in each row.Methods for constructing LDPC codes can be classified into two categories:one is random or pseudorandom constructions; where the generator G or parity check matrix H of an LDPC has been generated randomly, which requires large power and storage space because of its larger size. Long random LDPC codes in general perform closer to the Shannon limit than their equivalent algebraic constructed LDPC codes; however, they usually do not have sufficient structure to allow simple encoding. The other disadvantage is that the general LDPC codes need amount of memory to store the parity check matrix.The other category is algebraic constructions. QC-LDPC codes may be a good candidate for solving the memory and encoding problem of LDPC codes for their parity check matrix consists of circulant permutation matrix or zero matrix. Tanner code and array code are two reprehensive QC-LDPC codes. The significant benefit of the QC-LDPC lies in the code construction where the rows of the generator matrix are just cyclic shifts of the first row. These structured QC-LDPC codes having a relatively simple algebraic construction that can be implemented with an inexpensive shift register generator which greatly simplifies the encoder design.Particle Swarm Optimization (PSO) is an evolution method proposed by Kennedy and Eberhart. PSO algorithm learned from bird-flocking scenario, and used it to solve the optimization problems. In PSO algorithm, each single solution is a "bird" in the search space. We call it "particle". All of particles have cost values which are evaluated by the cost function to be optimized, and have velocities which direct the flying of the particles. The particles fly through the problem space by following the current optimum particles. We can obtain good performance in optimization of encodable QC-LDPC codes. Tanner-LDPC codes is an example of QC-LDPC codes. In this paper, we take PSO algorithm to optimize the construction of Tanner-LDPC codes, and solve encoding problem. In the system simulation, the bits'stream is modulated by a binary phase-shift keying (BPSK), and through the AWGN channel. Generally, random LDPC codes are regarded as good codes. the simulation results show that the new LDPC codes have similar BER performance as random codes,and the new Tanner-LDPC codes have much better BER performance than basic Tanner-LDPC codes. From the simulation results we know that the codes constructed based on the proposed method have a good performance.