Randomness of finite-state sequence machine over GF(4) and quality of hopping turbo codes

L.DE MICCO; D. PETRUZZI; J. CASTIÑEIRA MOREIRA; H. A. LARRONDO

IET COMMUNICATIONS

INST ENGINEERING TECHNOLOGY-IET

Año: 2013 vol. 7 p. 783 - 790

1751-8628

In this paper we study a turbo-coding (TC) scheme, whose constituent codes are designed using convolutional encoders. These encoders are Finite State Sequence Machines (FSSMs) operating over the Galois Field GF(4). The scheme includes encryption polynomials whose coeficients are selected every L steps, from the set of optimal polynomials of GF(4). Two cases are considered for the polynomial selection: periodical and random. This kind of encoder was studied in a previous paper and a correspondence between the randomness of the encoded sequence and performance of the TC was conjectured. The main contribution of this paper is to systematically confirm this correspondence, by analyzing the randomness of the output and performance of the TC using several randomness quantifiers. Three of the quantifiers are defined on the basis of Recurrence Plots (RP). Other two quantifiers are dened on the basis of the Information Theory. All the quantifiers allow one to justify why the proposed TC works better with random selection of the optimal polynomials and with small values of L. In summary It is shown that a random selection of polynomials and a small L produce FSSMs with enhanced randomness properties and it is also shown that they produce the best quality of the TC, measured by means of the corresponding Bit Error Rate (BER) .