Protograph-Based Interleavers for Punctured Turbo Codes

Abstract

A method to design efficient puncture-constrained interleavers for turbo codes (TCs) is introduced. Resulting TCs profit from a joint optimization of puncturing pattern and interleaver to achieve an improved error rate performance. First, the puncturing pattern is selected based on the constituent code Hamming distance spectrum and on the TC extrinsic information exchange under uniform interleaving. Then, the interleaver function is defined via a layered design process taking account of several design criteria such as minimum span, correlation girth, and puncturing constraints. We show that applying interleaving with a periodic cross connection pattern that can be assimilated to a protograph improves error-correction performance when compared to the state-of-the-art TCs. An application example is elaborated and compared with the long term evolution (LTE) standard: a significant gain in performance can be observed. An additional benefit of the proposed technique resides in the important reduction of the search space for the different interleaver parameters.

Efficient error-correcting codes in the short blocklength regime

“…The small size of the information word permits an efficient interleaver optimization. Codematched [82] and protograph-based [83] interleavers in particular turn out to be very effective in lowering error floors. The performance of two (128,64) turbo codes with memory-3 and memory-4 component codes is provided in Figure 7.…”

Dual Trellis Construction for High-Rate Punctured Convolutional Codes

“…The information frame length is K = 400 bits. The puncturing patterns of the parity bits (Table I) (ARP) interleaver have been jointly optimized according to the method described in [10]. The interleaver is defined by…”

“…The search for good puncturing patterns has been intensively studied in [8], [9] for feedforward convolutional codes and in [3], [10] for recursive systematic convolutional (RSC) codes, employed in turbo codes. In [10], the authors investigated the joint optimization of puncturing patterns and interleavers for turbo codes.…”

25 Years of Turbo Codes: From Mb/s to beyond 100 Gb/s

“…In [34], it was observed that the puncturing of well-chosen systematic bits can improve the performance of turbo codes at high and low error rates especially for high coding rates. Lately in [35], it was shown that the reliability of extrinsic information related to an information bit depends on the position of the considered bit in the puncturing period and the puncturing or not of the corresponding parity. Moreover, it was observed that the extrinsic information computed from unpunctured parity positions is more reliable than the one generated from punctured parity positions.…”

“…Moreover, it was observed that the extrinsic information computed from unpunctured parity positions is more reliable than the one generated from punctured parity positions. These observations led to the proposal of protograph-based interleavers [35], where a periodic strategy is applied through the interleaver, by connecting the positions with highly reliable extrinsic information to the positions with unreliable extrinsic information, more prone to errors. In addition to the associated error correction improvements, the introduced additional regularity through periodicity of both connection and puncturing patterns largely facilitates the support of code rate flexibility for hardware implementation.…”