Mitigating Correlation Problems in Turbo Decoders

Abstract

In this paper, new interleaver design criteria for turbo codes are proposed, targeting the reduction of the correlation between component decoders. To go beyond the already known correlation girth maximization, we propose several additional criteria that limit the impact of short correlation cycles and increase code diversity. Two application examples are elaborated, targeting an 8-state binary turbo code and a non-binary turbo code defined over GF(64). The proposed design criteria are shown to improve the error correcting performance of the code, especially in the error floor region. Index Terms-Turbo codes, correlation in decoding, interleaving, asymptotic performance.

Channel Coding Toward 6G: Technical Overview and Outlook

“…The other one is the local information exchange between neighboring symbols within each component decoder due to the convolutional nature of the component codes. These two types of exchanges create some dependency loops between sets of symbols, which can be represented by cycles in a correlation graph [89], [90], in the same way as in the Tanner graph for LDPC codes [91].…”

Union Bound Evaluation for Non-Binary Turbo Coded Modulations

“…Effect of short cycles in the Tanner graph of NB-TCs: type-A turbo-DC sequences Due to iterative decoding, short cycles in the Tanner graph of a turbo code [17] induce a high level of correlation between the extrinsic information sequences exchanged by the constituent decoders. This was shown to hinder the effectiveness of iterative processing for error correction [18], [12]. In the case of the NB-TCs under study, short cycles have a greater effect on performance than for conventional binary TCs, due to the fully connected trellises.…”

“…equivalent to 180 bits, for the codes mapped to 4-QAM. The symbol interleaver is based on almost regular permutation (ARP) [19] designed according to minimum spread and girth criteria as in [12] and whose parameters are given in Table II. TABLE II ARP INTERLEAVER PARAMETERS FOR THE SIMULATED NB-TCS ( To estimate the ED spectrum, only type-A sequences corresponding to the minimum girth achieved by the interleaver (given in Table II) are enumerated.…”

“…Recently, new NB recursive systematic convolutional codes over GF(q), q > 2, were proposed in [11]. The study of the interleaver and the introduction of a low-complexity decoder were then presented in [12] and [13], respectively, to complement [11] towards the construction of practical NB-TCs outperforming previously published NB FEC codes.…”

“…The union bound analysis is then only used to select the constituent convolutional codes and no TUB is derived for the actual resulting NB-TC. In this work, we propose a different and low-complexity method to enumerate error events and to compute TUBs for the NB-TCs studied in [11] and [12].…”