Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?

Abstract

Abstract-In this paper we concentrate on rate-1/3 systematic parallel concatenated convolutional codes and their rate-1/2 punctured child codes. Assuming maximum-likelihood decoding over an additive white Gaussian channel, we demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error floor than that of its rate-1/3 parent code, if a particular condition is met. However, assuming iterative decoding, convergence of the non-systematic code towards low bit-error rates is problematic. To alleviate this problem, we propose rate-1/2 partially-systematic codes that can still achieve a lower error floor than that of their rate-1/3 parent codes. Results obtained from extrinsic information transfer charts and simulations support our conclusion. I. INTRODUCTIONA punctured convolutional code is obtained by the periodic elimination of symbols from the output of a low-rate parent convolutional code. Extensive analyses on the structure and performance of punctured convolutional codes has shown that their performance is always inferior than the performance of their low-rate parent codes (e.g.The performance of punctured parallel concatenated convolutional codes (PCCCs), also known as punctured turbo codes, has also been investigated. Design considerations have been derived by analytical [3]-[5] as well as simulation-based approaches [6]-[8], while upper bounds to the bit error probability (BEP) were evaluated in [5], [9]. The most recent papers [7]- [9] demonstrate that puncturing both systematic and parity outputs of a rate-1/3 turbo code results in better high-rate turbo codes, in terms of BEP performance, than puncturing only the parity outputs of the original turbo code.The aim of this paper is to explore whether rate-1/2 punctured turbo codes can eventually achieve better performance than their parent rate-1/3 systematic turbo codes on additive white Gaussian (AWGN) channels. Assuming maximum-likelihood (ML) decoding, we demonstrate that, contrary to punctured convolutional codes, punctured turbo codes yielding lower error floors than that of their parent code can be constructed. Nevertheless, we cannot be conclusive when suboptimal iterative decoding is used. For this reason, we also study the convergence behavior of iterative decoding and we investigate whether the performance of the proposed rate-1/2 punctured turbo codes converges towards the theoretical error floor, at low bit error probabilities.

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

“…A moderate interleaver size of N = 1000 has been chosen, so as to allow the performance curves of the PCCCs to approach the corresponding bound approximations at BEPs in the region of 10 −6 . As expected [20], iterative decoding of the rate-1/2 NS-PCCC hits an error floor, which is much higher than that defined by the bound approximation. On the other hand, transmission of all systematic bits helps the iterative decoder converge to the error floor region at low E b /N 0 ratios.…”

“…For comparison, the bound approximation for the parent rate-1/3 PCCC(1,5/7,5/7) has also been plotted. We observe that the parent rate-1/3 PCCC performs better than the rate-1/2 S-PCCC but both PS and NS codes exhibit lower ) and an impractical number of decoding iterations are required to drive the BEP performance of NS-PCCCs into the error floor region [20]. On the other hand, the performance of iteratively decoded PS-PCCCs converges to low BEPs for practical interleaver sizes (N ≈ 1000) after 8 iterations [20]; nevertheless, PS-PCCCs yielding low BEPs can be found only by means of an exhaustive search, for a given parent code.…”

“…However, it is important to note that puncturing influences the convergence behavior of a turbo code [20]; thus we also need to investigate whether the performance of the suboptimal iterative decoder eventually converges to the error floor region at high E b /N 0 values, using analysis tools such as EXIT charts [22].…”

Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications

“…There has also been significant interest in partially systematic turbo codes (PSTCs), where higher code rates are achieved by puncturing both parity and data bits. This approach can substantially improve performance and has been applied to 4-state [38]- [42], 8-state [43], [44], and 16-state [45], [46] codes.…”

Convergence performance and EXIT analysis of 4-state partially-systematic Turbo codes

“…If some data symbols (i.e., information plus termination) as well as some parity symbols are eliminated, the result is a partially-systematic Turbo code (PSTC). PSTCs have been studied by numerous researchers for 4-, 8-, and 16-state codes [3], [4], [5], [6], [7], [8].…”