Multi-non-binary turbo codes

International audienceThis paper presents a new family of turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes (PCCC). An MNBTC incorporates, as component encoders, recursive and systematic multi-non-binary convolutional encoders. The more compact data structure for these encoders confers some advantages on MNBTCs over other types of turbo codes, such as better asymptotic behavior, better convergence, and reduced latency. This paper presents in detail the structure and operation of an MNBTC: MNB encoding, trellis termination, Max-Log-MAP decoding adapted to the MNB case. It also shows an example of MNBTC whose performance is compared with the state-of-the-art turbo code adopted in the DVB-RCS2 standard

8 states triple binary convolutional encoders for the construction of turbo codes

Abstract. This paper presents the rate 3/4 (triple-binary) memory 3 recursive and systematic convolutional encoders with a single shift register (TBEm3) implemented in the observer canonical form with the best frame error rate (FER) versus signal to noise ratio (SNR) performance in configuration turbo (parallel concatenated) The triple-binary turbo-codes (TBTC) were compared in terms of performance with the turbo-codes (TC) from the actual standards of communications, at the same turbo-coding rates of 3/5 and 3/4. Besides the very good FER/SNR performance, the TBTC present several other advantages that recommend them: an effect "error floor" low, latency diminution, more compact blocks -lower delay caused by interleaving, the possibility to connect the encoder TBTC to modulation blocks of higher order

8 states triple binary convolutional encoders for the construction of turbo codes

Abstract. This paper presents the rate 3/4 (triple-binary) memory 3 recursive and systematic convolutional encoders with a single shift register (TBEm3) implemented in the observer canonical form with the best frame error rate (FER) versus signal to noise ratio (SNR) performance in configuration turbo (parallel concatenated) The triple-binary turbo-codes (TBTC) were compared in terms of performance with the turbo-codes (TC) from the actual standards of communications, at the same turbo-coding rates of 3/5 and 3/4. Besides the very good FER/SNR performance, the TBTC present several other advantages that recommend them: an effect "error floor" low, latency diminution, more compact blocks -lower delay caused by interleaving, the possibility to connect the encoder TBTC to modulation blocks of higher order

On the equivalence between canonical forms of recursive systematic convolutional transducers based on single shift registers

International audienceStandardized turbo codes (TCs) use recursive systematic convolutional transducers of rate $b/(b{+}d)$ , having a single feedback polynomial $(b{+}d{rm RSCT})$ . In this paper, we investigate the realizability of the $b{+}d{rm RSCT}$ set through two single shift register canonical forms (SSRCFs), called, in the theory of linear systems, constructibility, and controllability. The two investigated SSRCF are the adaptations, for the implementation of $b{+}d{rm RSCT}$ , of the better-known canonical forms controller (constructibility) and observer (controllability). Constructibility is the implementation form actually used for convolutional transducers in TCs. This paper shows that any $b{+}1{rm RSCT}$ can be implemented in a unique SSRCF observer. As a result, we build a function, $xi:{{cal H}}to{cal G}$ , which has as definition domain the set of encoders in SSRCF constructibility, denoted by ${cal H}$ , and as codomain a subset of encoders in SSRCF observer, denoted by ${cal G}$ . By proving the noninjectivity and nonsurjectivity properties of the function $xi$ , we prove that ${cal H}$ is redundant and incomplete in comparison with ${cal G}$ , i.e., the SSRCF observer is more efficient than the - SRCF constructibility for the implementation of $b{+}1{rm RSCT}$ . We show that the redundancy of the set ${cal H}$ is dependent on the memory $m$ and on the number of inputs $b$ of the considered $b{+}1{rm RSCT}$ . In addition, the difference between ${cal G}$ and $xi({cal H})$ contains encoders with very good performance, when used in a TC structure. This difference is consistent for $mapprox b>1$ . The results on the realizability of the $b{+}1{rm RSCT}$ allowed us some considerations on $b{+}d{rm RSCT}$ , with $b$ , $d>1$ , as well, for which we proposed the SSRCF controllability. These results could be useful in the design of TC based on exhaustive search. So, the proposed implementation form permits the design of new TCs, which cannot be conceived based on the actual form. It is possible, even probable, among these new TCs to find better performance than in the current communication standards, such as LTE, DVB, or deep-space communications

Performance Prediction of Double-Binary Turbo Codes with High Order Modulations in AWGN Channel

International audienceIn this paper, we present a method for turbo codes (TC) performance prediction, in terms of bit error rate (BER) and frame error rate (FER) versus signal to noise ratio (SNR), when they are used with high-order modulations (HOM). The method is based on two simplifying hypotheses and assumes that the BER/FER vs. SNR performance, in the case of BPSK modulation, is known. For the simulations we have chosen the double-binary turbo codes (DBTC) used in the DVB-RCS standard. The experimental results confirm the good accuracy of the proposed prediction method and validate our assumptions. The method has been applied in the case of 16-Quadrature Amplitude Modulation (16-QAM), but it can be easily extended to any other type of modulation