Design of Chaotic Interleaver Based on Duffing Map for Turbo Code

Abstract

This article presents the performance analysis and comparison of turbo codes for several interleavers with short blockchains. According to the symmetry concept, turbo codes consist of two symmetric convolutional codes preceded by an interleaver. Some interleavers can be described by symmetric 3 × 3 generator matrices, whereas others are represented through symmetric matrices in which the nonzero terms in the matrix are monomials. Interest in short blockchains has grown over the years because of their use in emerging applications that require the transmission of data units in the order of hundred bits. In this research, interleavers used are random interleaver, semi-random interleaver, quadratic polynomial permutation (QPP) interleaver, and chaotic Lozi map interleaver. For each interleaver, the turbo code is assessed with at least two short data distances; then, the interleavers are compared against each other. The performance of turbo codes is assessed based on bit error rate, particularly with lengths between 64 and 512 bits. Additionally, an interleaver based on Duffing chaotic maps is proposed, whose deterministic nature provides an advantage, and the performance results are presented, achieving excellent BER values for 64 bits. With these results, the effect of the interleaver on turbo codes and particularly on short block length interleavers, is studied.

Modification of chaotic interleaver for turbo codes with a change to the duffing equation and accounting for the distance spectrum of the code

“…The peculiarity of the proposed modification is not only in the selection of a more successful Duffing equation, which gives a more random distribution than the Lozi equation, for example, as in [11], as well as in the application of the analysis of the distance spectrum of the code and the condition of choosing a greater distance between elements by permutations by code words with a small by weight.…”

“…We proposed using one of the Duffing equations in the chaotic interleaver instead of the Lozi equations, which also gives the chaotic distribution dynamics. Analyzing works with a chaotic interleaver based on the Duffing equations [11] and considering many other Duffing equations, several Duffing equations as part of turbo codes were considered and their characteristics were analyzed. They made it possible to obtain different minimum distances between elements.…”

“…In the work, the random distribution law is based on the Lozi equation. But there are many mathematical works that indicate that, under certain circumstances, the Duffing equation better forms a random sequence [11]. To date, very few works have studied interleavers with the Duffing equation as part of turbo codes.…”

Survey of Recent Applications of the Chaotic Lozi Map

“…Sahnoune and Berkani concluded that, compared with a random interleaver and dithered Golden interleaver, a chaotic interleaver has low latency, low complexity of implementation, and improves the security of the encoded data. Urrea et al [54] compared the performances of a chaotic interleaver with short block lengths to a new chaotic interleaver based on the Duffing map, which showed slightly better performance.…”