Rate allocation for serial concatenated convolutional codes

In this paper, we focus on the design of optimized binary convolutional codes (CCs) and serially concatenated convolutional codes (SCCCs) in the presence of a-priori information (API) at the receiver. For large signal-to-noise ratios (SNRs), we first propose a CC design criterion based on the minimization of a union bound on the bit error probability (BEP). In this case, relevant performance gains, with respect to previously proposed CCs, are obtained. These gains persist even in the presence of estimation errors on the API. Then, we apply the same union bound-based design criterion to SCCCs. Since the BEP of SCCCs is characterized by a typical waterfall shape, the proposed union bound-based design criterion is accurate only at large SNR, to estimate the BEP floor. In order to complement this analysis, we propose a density evolution-based approach to optimize the SCCC design in terms of minimization of the SNR of the knee of the BEP curve. The obtained simulation results show substantial gains with respect to previously proposed parallel concatenated convolutional coding (PCCCing) schemes optimized under the assumption of no API at the decoder. Moreover, in the presence of strong API the proposed SCCCs allow to approach the Shannon limit (SL) more than any previously proposed turbo coding scheme.

International audience

We compare the asymptotic performance of parallel concatenated codes (PCCs) and serial concatenated codes (SCCs) over GF(4). We construct such codes using optimal nonbinary convolutional codes where optimality is in the sense of achieving the largest minimum distance for a fixed number of encoder states. Code rates of the form K/sub 0//(K/sub 0/ + 1) for K/sub 0/ = 1, 8, and 64 are considered. For all of these code rates, we find the minimum distance and its multiplicity for both concatenated code systems. This is accomplished by feeding the encoder with all possible weight-two and weight-three input information patterns and monitoring, at the output of the encoder, the weight of the corresponding codewords and their multiplicity. Our analytical results indicate that the SCC codes outperform their counterpart PCC codes with much lower complexity.

A coded wideband MC-CDMA system is considered for high-bit-rate data transmission in a typical outdoor environment with Rayleigh multipath fading. First, two powerful interleaved concatenated coding techniques, turbo and serially concatenated convolutional codes (SCCC) codes are applied in the downlink system and important conclusions are derived on their relative performance behavior in this type of system. Simulation results indicate some of the relative merits of SCCC on achieving very low error rates, with relative mitigation of error floor behavior at the typical BER range of interest for wireless data applications. Next, the more critical uplink system is considered, which requires a multiuser detection technique in combination with powerful coding to achieve similar performance. Successive interference cancellation with SCCC coding is presented, with computation of optimal log-likelihood ratios required for this type of interference cancellation followed by SCCC decoding. Application of SCCC coding and interference cancellation has improved the system performance significantly even in the fully loaded case. Based on these results, the combination of SCCC coding and successive cancellation is found to be attractive for high-rate data transmission in the uplink MC-CDMA.

An analysis of performance of Serially Concatenated Convolutional Codes (SCCC) is evaluated on Additive White Gaussian Noise model channel, which is used as a basis, and actions of SCCC on Raleigh flat slow and flat fast faded channels are evaluated in this research work. In DCS the SCCC are utilized to reduce the bit error rates. SCCC encoder consists of RSCC. The major thrust is iterative decoding. This research has utilized BCJR and TDA decoding algorithms. This research analyzed SCCC with interleaved scheme. The BPSK modulation was considered. Performance metric for SCCC over Memory less AWGN channel, and memory based channels i.e. Rayleigh slow and fast Faded Channel is BER verses SNR.

In this letter, we propose and compare some new rate-compatible serially concatenated convolutional code (SCCC) families. To obtain them, inner coded bits only are punctured. However, and this is the novelty proposed in the letter, the puncturing is not limited to inner parity bits, but extended also to inner systematic bits, thus obtaining high rate SCCCs (i.e., beyond the outer code rate). The two main applications of this technique are its use in hybrid Automatic-Repeat-reQuest/Forward-Error Correction (ARQ/FEC) schemes and to achieve unequal error protection (UEP) of an information sequence.

When channel state information (CSI) is not available, unitary space-time symbol-based parallel concatenated convolutional code (UST-SB-PCCC) can give a good performance and remain an acceptable calculation complexity, however it also meet with the error floor phenomenon. We propose a scheme utilizing UST-SB serial concatenated convolutional code (SCCC) for multiple-antenna wireless communication systems over rapid fading channels which can avoid the error floor. We also give the corresponding multi-ary MAP decoding algorithm for both the systematic and the parity symbols. With iterative decoding and/or multi-antennas, it can further improve the system performance, which helps to give an acceptable bit error rate (BER).

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. We focus on the ubiquitous inner differential encoder (used, in particular, to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum-likelihood (ML) coherently detected antipodal modulation over the additive white Gaussian noise (AWGN) channel for this construction are advantageous as compared to the stand-alone outer convolutional code. This is in spite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of an ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a rather dramatic decrease, as demonstrated here, in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand-alone convolutional code. The advantage of the examined serially interleaved concatenated code, given in terms of bit and/or block error probability which is decoded by a practical suboptimal decoder, over the optimally decoded standard convolutional code is demonstrated by simulations, and some insights into the performance of the iterative decoding algorithm are also discussed. Though we have investigated only specific constructions of constituent inner (rate 1) and outer codes, we trust, hinging on the rational of the arguments here, that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes.

The paper presents a novel cooperative coding scheme using punctured serial concatenated convolutional codes (SCCC). We evaluate its performance in terms of frame error rate (FER) under two cooperation protocols: a decode-and-forward protocol in conjunction with automatic repeat request (ARQ), by which the relay sends an acknowledge bit (ACK) back to the source to indicate whether its data packet is correctly decoded; an adaptive amplify-and-forward protocol, where the amplifying relay node cooperates to forward the message only when the inter-user link gain is above a certain threshold. In both cases, the destination makes the decision on each transmitted bit after appropriately combining signals and performing iterative decoding. Simulation results show that SCCC-based cooperative coding achieves full spatial diversity and exhibits a similar FER performance to that using parallel concatenated convolutional codes (PCCC). At the price of channel feedback, the adaptive decode-and-forward algorithm demonstrates a relatively lower FER than the adaptive amplify-and-forward scheme. Amplified cooperation experiences severe performance degradation due to the inefficiency of repetition coding and error propagation, especially when the quality of the source-relay link deteriorates; however, if the threshold for carrying cooperation is carefully selected, the adaptive amplify-and-forward protocol can perform comparably to the decode-and-forward protocol.

We provide a performance analysis of a new class of serial concatenated convolutional codes (SCCC) where the inner encoder can be punctured beyond the unitary rate. The puncturing of the inner encoder is not limited to inner coded bits, but extended to systematic bits. We derive analytical upper bounds to the error probability of this particular code structure and address suitable design guidelines for the inner code puncturing patterns. We show that the proportion of systematic and parity bits to be deleted strongly depends on the SNR region of interest. Furthermore, we show that puncturing of the inner code systematic bits should be interleaver dependent. Based on these considerations, we derive design guidelines to obtain well-performing rate-compatible SCCCs families. Throughout the paper, the performance of the proposed codes are compared with analytical bounds, and with the performance of PCCC and SCCC proposed in literature

This paper considers detection and error control coding for the two-dimensional magnetic recording (TDMR) channel modeled by the two-dimensional (2D) four-rectangular-grain model proposed by Kavcic, Huang et. al. in 2010. This simple model captures the effects of different 2D grain sizes and shapes, as well as the TDMR grain overwrite effect: grains large enough to be written by successive bits retain the polarity of only the last bit written. We construct a row-by-row BCJR detection algorithm that considers outputs from two rows at a time over two adjacent columns, thereby enabling consideration of more grain and data states than previously proposed algorithms that scan only one row at a time. The proposed algorithm employs soft-decision feedback of grain states from previous rows to aid the estimation of current data bits and grain states. Simulation results using the same average coded bit density and serially concatenated convolutional code (SCCC) as a previous paper by Pan, Ryan, et. al. show gains in user bits/grain of up to 6.7% over the previous work when no iteration is performed between the TDMR BCJR and the SCCC, and gains of up to 13.4% when the detector and the decoder iteratively exchange soft information.

We give an overview of iterative techniques for bit‐interleaved coded modulation. We start with simple methods where a convolutional code is concatenated with a standard QAM modulation scheme. The mapping is carefully chosen different from Gray mapping such that significant gains can be obtained by an iterative (turbo) receiver. The idea can also be applied to transmit antenna diversity as well as spatial multiplexing (MIMO). We then consider various powerful iterative coding schemes which are under discussion in standardisation for wireless systems beyond 3G such as serial or parallel concatenated convolutional codes, repeat accumulate codes and LDPC codes. We give a comparison in terms of complexity and performance.The main intention is to provide an illustrative overview over relevant applications of the turbo principle in demodulation and decoding. It is a summary of results which have been obtained in collaboration between the Institute of Communications Engineering, TUM and DoCoMo Euro‐Labs. Copyright © 2007 John Wiley & Sons, Ltd.

Concatenation is a method of building long codes out of shorter ones, it attempts to meet the problem of decoding complexity by breaking the required computation into manageable segments. Concatenated Continuous Phase Frequency Shift Keying (CPFSK) facilitates powerful error correction. CPFSK also has the advantage of being bandwidth efficient and compatible with non-linear amplifiers. Bandwidth efficient concatenated coded modulation schemes were designed for communication over Additive White Gaussian noise (AWGN), and Rayleigh fading channels. An analytical bounds on the performance of serial concatenated convolutional codes (SCCC), and parallel concatenated convolutionalcodes (PCCC), were derived as a base of comparison with the third category known as hybrid concatenated trellis codes scheme (HCTC). An upper bound to the average maximum-likelihood bit error probability of the three schemes were obtained. Design rules for the parallel, outer, and inner codes that maximize the interleaver's gain were discussed. Finally, a low complexity iterative decoding algorithm that yields a better performance is proposed.

We develop a method called binary shaping for transmitting low-duty-cycle sequences robustly over binary-input channels, that employs a convolutional shaping code and a serially-concatenated convolutional code (SCCC) for forward error correction. Binary shaping is closely related to the nested linear coding scheme for coding over channels with known interference.

In this paper, we derive feedback power control strategies for block-faded multiple access schemes with correlated sources. In particular, upon the derivation of the feasible signal-to-noise ratio (SNR) region for the considered multiple access schemes, i.e., the multidimensional SNR region where error-free communications are, in principle, possible, two feedback power control strategies are proposed: (i) a “classical” feedback power control strategy, which aims at “equalizing” the SNRs at the AP over all communication links, and (ii) an “optimal” feedback power control strategy, which tries to make the network operational point fall in the feasible SNR region at the lowest energy consumption. These strategies will be referred to as balanced SNR and unbalanced SNR, respectively. While they require unlimited power control range at the sources (the sensors), we then propose “practical” implementations by limiting the power control range. We evalute the benefits brought by the use of the proposed feedback power control strategies considering joint channel decoding (JCD) schemes, where the sensors use channel coding and a proper iterative decoding algorithm is considered at the AP. The analysis is carried out considering the use of low-density parity-check (LDPC) codes and a serially concatenated convolutional code (SCCC).