Class of double terminating turbo code interleavers

Abstract

The class of interleavers is identi ed, which possesses the following property: both Turbo Code component scramblers are terminated in the same state, independent of the encoder information word. It is proven that the presented class contains all interleavers with the above property. Introduction: Turbo Codes 4] represent the most power-e cient binary channel codes of the present time. Their encoder consists of three parallel branches: one systematic branch and two (recursive) scramblers (in the following denoted by scr1 and scr2, respectively), both of which are joined by an interleaver. In the article we always assume identical scramblers of memory. Scrambler properties: Throughout the article, we use the following terminology. Variables with a superscript index (1) and (2) are associated with scr1 and scr2, respectively. The input of length K to the scramblers is denoted by the vector u (j) = (u (j) 0 ; u (j) 1 ; ::; u (j) K?1); j 2 f1; 2g with u (j) i 2 GF(2) = f0; 1g. The interleaver function u (2) = (u (1)) performs transpositions i ! i of the input bit positions i = 0::K ? 1 of scr1 to those of scr2, i.e. u (2) i = u (1)

Analysis and design of punctured rate-1/2 turbo codes exhibiting low error floors

“…The transfer function B P (W, U, Z) of P enumerates all code sequences that correspond to trellis paths of length N , which start from the zero state, can re-visit it more than once and can remain at it for an indefinite period of time. Tail-bits, appended to each input sequence, and a double terminating interleaver [13] ensure that trellis paths return to the zero state. A generic form for the transfer function is…”