Recursive Convolutional Encoders Research Articles

TURBO CODE RE-ANALYSIS USING DIFFERENT ALGORITHMS

Turbo codes are a novel type of forward error correcting codes that have proved to give a perfor- mance close to the channel capacity as proposed by C. Shannon. The parallel concatenation of two identical recursive convolutional encoders that are spaced apart by an interleaver results in a turbo code encoder. The two cascaded decoding blocks used by the turbo code decoder pass along a priori knowledge generated by each block in turn. The decoding approach has the advantage of working iteratively, allowing for an increase in total performance. This study does a performance analysis of turbo codes. The performance study includes two decoding methods: the soft output Viterbi algo- rithm (SOVA), which uses the log-likelihood ratio to produce soft outputs, and the log maximum a posteriori probability (Log-MAP) algorithm. Both punctured and unpunctured codes are studied to determine the impact of utilizing various decoding algorithms. The performance of the two various decoding techniques is then contrasted in terms of bit error rate. MATLAB tools are utilized to per- form simulations.

SP-DSTS-MIMO Scheme-Aided H.266 for Reliable High Data Rate Mobile Video Communication

With the ever growth of Internet users, video applications, and massive data traffic across the network, there is a higher need for reliable bandwidth-efficient multimedia communication. Versatile Video Coding (VVC/H.266) is finalized in September 2020 providing significantly greater compression efficiency compared to Highest Efficient Video Coding (HEVC) while providing versatile effective use for Ultra-High Definition (HD) videos. This article analyzes the quality performance of convolutional codes, turbo codes and self-concatenated convolutional (SCC) codes based on performance metrics for reliable future video communication. The advent of turbo codes was a significant achievement ever in the era of wireless communication approaching nearly the Shannon limit. Turbo codes are operated by the deployment of an interleaver between two Recursive Systematic Convolutional (RSC) encoders in a parallel fashion. Constituent RSC encoders may be operating on the same or different architectures and code rates. The proposed work utilizes the latest source compression standards H.266 and H.265 encoded standards and Sphere Packing modulation aided differential Space Time Spreading (SP-DSTS) for video transmission in order to provide bandwidth-efficient wireless video communication. Moreover, simulation results show that turbo codes defeat convolutional codes with an averaged Eb/N0 gain of 1.5 dB while convolutional codes outperform compared to SCC codes with an Eb/N0 gain of 3.5 dB at Bit Error Rate (BER) of . The Peak Signal to Noise Ratio (PSNR) results of convolutional codes with the latest source coding standard of H.266 is plotted against convolutional codes with H.265 and it was concluded H.266 outperform with about 6 dB PSNR gain at Eb/N0 value of 4.5 dB.

A novel method for identifying recursive systematic convolutional encoders based on the cuckoo search algorithm

The existing methods for identifying recursive systematic convolutional encoders with high robustness require to test all the candidate generator matrixes in the search space exhaustively. With the increase of the codeword length and constraint length, the search space expands exponentially, and thus it limits the application of these methods in practice. To overcome the limitation, a novel identification method, which gets rid of exhaustive test, is proposed based on the cuckoo search algorithm by using soft-decision data. Firstly, by using soft-decision data, the probability that a parity check equation holds is derived. Thus, solving the parity check equations is converted to maximize the joint probability that parity check equations hold. Secondly, based on the standard cuckoo search algorithm, the established cost function is optimized. According to the final solution of the optimization problem, the generator matrix of recursive systematic convolutional code is estimated. Compared with the existing methods, our proposed method does not need to search for the generator matrix exhaustively and has high robustness. Additionally, it does not require the prior knowledge of the constraint length and is applicable in any modulation type.

Low-Power VLSI Implementation of Novel Hybrid Adaptive Variable-Rate and Recursive Systematic Convolutional Encoder for Resource Constrained Wireless Communication Systems

In the modern wireless communication system, digital technology has tremendous growth, and all the communication channels are slowly moving towards digital form. Wireless communication has to provide the reliable and efficient transfer of information between transmitter and receiver over a wireless channel. The channel coding technique is the best practical approach to delivering reliable communication for the end-users. Many conventional encoder and decoder units are used as error detection and correction codes in the digital communication system to overcome the multiple transient errors. The proposed convolutional encoder consists of both Recursive Systematic Convolutional (RSC) Encoder and Adaptive Variable-Rate Convolutional (AVRC) encoder. Adaptive Variable-Rate Convolutional encoder improves the bit error rate performance and is more suitable for a power-constrained wireless system to transfer the data. Recursive Systematic Convolutional encoder also reduces the bit error rate and improves the throughput by employing the trellis termination strategy. Here, AVRC encoder ultimately acquires the channel state information and feeds the data into a fixed rate convolutional encoder and rate adaptor followed by a buffer device. A hybrid encoder combines the AVRC encoder and RSC encoder output serially and parallel, producing the solid encoded data for the modulator in the communication system. A modified turbo code is also obtained by placing interleaver between the two encoder units and building the stronger code word for the system. Finally, the conventional encoder system is compared and analyzed with the proposed method regarding the number of LUT’s, gates, clock cycle, slices, area, power, bit error rate, and throughput.

Verilog HDL using LTE Implementation MAP Algorithm

In many communication systems, turbo coding Techniques for Encoding and Decoding are employed to repair errors. As compared to other error correction codes, turbo codes provide great error correcting capabilities. For the implementation of the Turbo decoder, a Very Large Scale Integration (VLSI) architecture is suggested in this study. The Maximum-a-Posteriori (MAP) algorithm is employed at the decoder side, where soft-in-soft-out decoders, interleaves, and deinterleavers are all used. The usage of the MAP algorithm reduces the quantity of iterations necessary to decode the information bits being transferred. This research employs a system for the encoder component that consists of two recursive convolutional encoders and a pseudorandom interleaver on the encoder side. Tools from Octave and Xilinx Vivado are used for the Turbo encoding and decoding. The system is synthesised and implemented using a specialised integrated circuit.

A High Throughput Hardware Architecture for Parallel Recursive Systematic Convolutional Encoders

During the last years, recursive systematic convolutional (RSC) encoders have found application in modern telecommunication systems to reduce the bit error rate (BER). In view of the necessity of increasing the throughput of such applications, several approaches using hardware implementations of RSC encoders were explored. In this paper, we propose a hardware intellectual property (IP) for high throughput RSC encoders. The IP core exploits a methodology based on the ABCD matrices model which permits to increase the number of inputs bits processed in parallel. Through an analysis of the proposed network topology and by exploiting data relative to the implementation on Zynq 7000 xc7z010clg400-1 field programmable gate array (FPGA), an estimation of the dependency of the input data rate and of the source occupation on the parallelism degree is performed. Such analysis, together with the BER curves, provides a description of the principal merit parameters of a RSC encoder.

Some Extended Results on the Design of Punctured Serially Concatenated Convolutional Codes

The aim of this paper is twofold. On one hand, it presents the results of the search for good punctured systematicrecursive convolutional encoders suitable for application in serially concatenated convolutional codes (SCCCs) operating in two different target regions: at low-to moderate signal-to-noise ratios (SNRs), i.e., in the so called waterfall region, and at high SNRs. On the other hand, it provides some useful design guidelines for choosing the constituent encoders in an SCCC. The results of the search for good SCCCs operating in the waterfall region rely upon an effective algorithm, based on density evolution technique, first proposed in a companion paper. Good punctured SCCCs were obtained through considerationsdeduced by the behaviour of the bit error probability of an SCCC for high values of both SNR and interleaver length, i.e., through asymptotic considerations. The mother codes in the serial concatenation are rate 1/2 recursive convolutional encoders (RCC) found by an exhaustive search for encoders tailored to SCCC schemes, using two different selection criteria. Extensive tables of optimized puncturing patterns for various mother codes and SCCCs are presented along with sample simulation results.

Capacity-Approaching TQC-LDPC Convolutional Codes Enabling Power-Efficient Decoders

In this paper, we develop a new capacity-approaching code, namely, parallel-concatenated (PC)-Low Density Parity Check (LDPC) convolutional code that is based on the parallel concatenation of trellis-based quasi-cyclic LDPC (TQC-LDPC) convolutional codes. The proposed PC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing the trellis-based convolutional dependency to the code. The capacity-approaching PC-LDPC convolutional codes are encoded through parallel concatenated trellis-based QC recursive systematic convolutional (RSC) encoder (namely, QC-RSC encoder) that is also proposed in this paper. The proposed PC-LDPC convolutional code and the associated encoder retain a fine input granularity on the order of the lifting factor of the underlying block code. We also describe the corresponding trellis-based QC maximum a posteriori probability (namely, QC-MAP) decoder that efficiently decodes the PC-LDPC convolutional code. Performance and hardware implementation results show that the PC-LDPC convolutional codes with the QC-MAP decoder have two times lower complexity for a given bit-error-rate (BER), signal-to-noise ratio, and data rate, than conventional QC-LDPC block codes and LDPC convolutional codes. Moreover, the PC-LDPC convolutional code with the QC-MAP decoder outperforms the conventional QC-LDPC block codes by more than 0.5 dB for a given BER, complexity, and data rate and approaches Shannon capacity limit with a gap smaller than 1.25 dB. This low decoding complexity and the fine granularity make it feasible to efficiently implement the proposed capacity-approaching PC-LDPC convolutional code and the associated trellis-based QC-MAP decoder in next generation ultra-high data rate mobile systems.

Design and Simulation of Turbo Encoder in Quantum-Dot Cellular Automata

Quantum-dot cellular automata (QCA) is a potential nanoelectronic technology for information processing. To be considered as a suitable CMOS candidate, QCA must be able to implement complex real-time applications of bit-serial information processing, which lacks of enough investigation. Turbo encoding is one of such applications, which refers to three representative issues of bit-serial circuits: convolution computation, feedback, and serial data permutation. The inherent shift-register nature of QCA offers an advantage to performing convolution computation but poses handicaps to resolve the latter two issues. How to manage the ambivalent effects of shift-register nature is investigated in this paper, which determines the efficient design of Turbo encoder. A strobe scheme based on main-branch wire crossing is proposed to efficiently make data choosing that is the communally key procedure of the implementation of feedback and serial data permutation. On this basis, a method of implementing recursive convolutional encoder with multifeedback is proposed. A two-stage pipelining interleaver is presented. Finally, a Turbo encoder is implemented using QCA based on these approaches and simulation demonstrates that it performs well.

Distributed Turbo Coding Schemes for Receive Diversity: A Modified Matched S-Random Interleaver for Half-Duplex Wireless Relay Channels

It is known that one of the essential building blocks of distributed turbo codes is the interleaver and its design uses random, semi-random (S-Random) and deterministic permutations. In this paper, a new modified matched S-random interleaver for turbo code is proposed. Then we extend the effect of this new interleaver to the relay channel to evaluate the interleaving gain in two different distributed turbo-coding schemes: distributed turbo codes and distributed multiple turbo codes for half-duplex relay system. For these schemes with half- duplex constraint, the source node transmits its information with the parity bit sequence(s) to both the relay and the destination nodes during the first phase. The relay receives the data from the source and processes it by using decode and forward protocol. For the second transmission period, the decoded systematic data at relay is interleaved and re-encoded by a recursive systematic convolutional encoder and forwarded to the destination. At destination node, the signals which are received from the source and relay nodes are processed by using turbo log-MAP iterative decoding for retrieving the original information bits. We demonstrate via simulations that the new interleaving gain has a large effect with distributed turbo coding scheme when we use only one recursive systematic convolutional encoder at both the source and relay. Index Terms—Distributed turbo codes, interleaver, semi- random, relay channel

8 States Triple Binary Convolutional Encoders for the Construction of Turbo Codes

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.

Analysis of recursive convolutional codes and turbo codes as sources with memory

The paper proposes a general method to analyze discrete sources with memory. Besides the classical entropy, we define new information measures for discrete sources with memory, similar to the information quantities specific to discrete channels. On the base of this method, we show for the first time that, as result of convolutional and turbo encoding, sources with memory are obtained. We apply this information analysis method for the general case of a recursive convolutional encoder of rate RCC=1/n0 and memory of order m, and for a turbo encoder of rate RTC=1/3, with two systematic recursive convolutional component encoders. Each component encoder has memory of order m, and is built based on the same primitive feedback polynomial. For the convolutional and turbo codes, the information quantities H(Y/S), H(S,Y), H(S/Y), H(Y), H(S) and I(S,Y) have been computed, where S and Y denote the set of states and the set of messages of the encoder, respectively. The analysis considered two cases: n0≤m+1 and n0>m+1. When n0=m+1, the mutual information I(S,Y) is maximum and equal to m, as is the entropy of the set of states. For turbo codes, the quantity I(S,Y) also depends on the input bit and on its probability.

Novel Blind Encoder Parameter Estimation for Turbo Codes

A novel blind parameter-estimation method, which identifies a turbo encoder, is proposed in this paper. The blind estimator is designed using an iterative expectation-maximization (EM) algorithm. To facilitate this innovative blind estimation scheme, we transform the recursive systematic convolutional (RSC) encoder into a non-systematic convolutional encoder preceded by a feedback encoder. The effect of the separate feedback encoder on the state sequence of the forward convolutional encoder will be studied. Besides, the effectiveness of our proposed new scheme will be evaluated by Monte Carlo simulations.

High-rate systematic recursive convolutional encoders: minimal trellis and code search

Abstract We consider high-rate systematic recursive convolutional encoders to be adopted as constituent encoders in turbo schemes. Douillard and Berrou showed that, despite its complexity, the construction of high-rate turbo codes by means of high-rate constituent encoders is advantageous over the construction based on puncturing rate-1/2 constituent encoders. To reduce the decoding complexity of high-rate codes, we introduce the construction of the minimal trellis for a systematic recursive convolutional encoding matrix. A code search is conducted and examples are provided which indicate that a more finely grained decoding complexity-error performance trade-off is obtained.

ПрогрАмнА реалізаціЯ тА дослідженнЯ сИстемИ турбокодуваннЯ нА базІ рекурсивнО систематичниХ кодеріВ

For the research, the turbo-encoding method was chosen. It refers to the method of the direct correction of errors. We have implemented and studied programmatically the turbo-encoding and decoding systems, according to the method of maximum final probability. The model of a turbo-encoder is based on the use of the recursive systematic convolutional encoders and the use of interleaver for the connection of the encoders. We have implemented and calculated the decoding model by the method of maximum final probability using feedback and the decoder of the output hard decision. The simulated operation of the system was implemented in the hardware description language VHDL, which allows its implementation on the EPLD structures. The special features of the system turbo-encoding development in VHDL (Very high integrated circuits Hardware Description Language) include the possibility of using the system as a whole or partitioning the system into separate components. The turbo-encoding system can increase the speed of information transfer without requiring an increase of a transmitter power, or can be used to reduce the required power in the transmission with given rate. An important advantage of the system is an independence of the decoding complexity from the length of the information block that allows the reduction of the possibility of the decoding error by increasing its length

Improving the structure of multiple dimension turbo codes using multiple identical component encoders

In this paper, we propose an improved structure for M-dimension(M ⩾ 2) turbo codes using M identical component encoders. The presented structure only applies single recursive convolutional encoder to encode M interleaved versions of information sequence and single tail sequence to operate termination. For the commonly used two-dimension (M = 2) turbo codes, two cascade soft input soft output (SISO) decoders are detailed to decode the corresponding codes. With the two cascade SISO decoders, this coding structure obviously outperforms traditional turbo codes at high code rates, especially, about 0.3 dB gain can be obtained at code rate 0.9 in additive white Gaussian noise channel with quadrature phase shift keying modulation. This makes the proposed coding structure very attractive for future radio communication systems with high throughput requirements.

Recursive GF(2 N) encoders using left-circulate function for optimum PSK–TCM schemes

In this paper, phase shift keying–trellis coded modulation (PSK–TCM) schemes are designed using recursive convolutional encoders over Galois field GF(2 N ). These encoders are designed using the nonlinear left-circulate (LCIRC) function. The LCIRC function performs a bit left circulation over the representation word. Different encoding rates are obtained for these encoders when using different representation wordlengths at the input and the output, denoted as N in and N, respectively. A generalized 1-delay GF(2 N ) encoder scheme using LCIRC is proposed for performance analysis and optimization, for any possible encoding rate, N in / N. The minimum Euclidian distance is estimated for these PSK–TCM schemes and a general expression is found as a function of the wordlengths N in and N. The symbol error rate (SER) is estimated by simulation for PSK–TCM transmissions over an additive white Gaussian noise (AWGN) channel.

Performance Analysis of Serial Concatenation Convolutional Codes Based on Amplitude Matrix

Serial Concatenation Convolutional Codes (SCCCs) encoder is built using a serial concatenation of two Recursive Systematic Convolutional (RSC) encoders, separated by an interleaver. These two RSC encoders depending on the trellis termination criteria are software implemented and the performance of each one of them is analyzed under different conditions and circumstances. The output data from the encoder are multiplied by an amplitude matrix (AM) at the transmitter side and the Inverse of Amplitude Matrix (IAM) at the receiver side. The reliability estimation, log-likelihood algebra, and soft channel outputs for Soft Output Viterbi Algorithm (SOVA) are examined. Then the modified Viterbi metric that incorporates a-priori information used for SOVA decoding is derived. A low memory implementation of the SOVA decoder is presented. The iterative SOVA for SCCCs is described with illustrative examples. The behavior of the SCCCs encoder-decoder scheme is tested under different circumstances with AM and without AM at the AWGN and Rayleigh fading channels with unlike frame sizes (FS) and constraint length (K). The results show that the performance of system with AM outperforms the other conventional system that worked without AM.

Quantum Serial Turbo Codes

In this paper, we present a theory of quantum serial turbo codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum low-density parity-check (LDPC) codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Second, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular, its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoders have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be noncatastrophic and nonrecursive. While the resulting families of turbo codes have bounded minimum distance, from a pragmatic point of view, the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well-chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.

Improved Frey Chaotic Digital Encoder for Trellis-Coded Modulation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this brief, nonlinear digital filters with finite precision are analyzed as recursive systematic convolutional (RSC) encoders. An infinite-impulse-response (IIR) digital filter with finite precision (wordlength of <formula formulatype="inline"><tex Notation="TeX">$N$</tex></formula> bits) is a rate-1 RSC encoder over a Galois field <formula formulatype="inline"><tex Notation="TeX">$GF(2^{N})$</tex></formula>. The Frey chaotic filter is analyzed for different wordlengths <formula formulatype="inline"><tex Notation="TeX">$N$</tex></formula>, and it is demonstrated that the trellis performances can be enhanced by proper filter design. Therefore, a modified definition for the encoding rate is provided, and a trellis design method is proposed for the Frey filter, which consists of reducing the encoding rate from 1 to 1/2. This trellis optimization partially follows Ungerboeck's rules, i.e., increasing the performances of the encoded chaotic transmission in the presence of noise. In fact, it is demonstrated that for the same spectral efficiency, the modified Frey encoder outperforms the original Frey encoder only for <formula formulatype="inline"> <tex Notation="TeX">$N = 2$</tex></formula>. To show the potential of these nonlinear encoders, it is demonstrated that a particular nonlinear digital filter over <formula formulatype="inline"><tex Notation="TeX">$GF(4)$</tex></formula> is equivalent to a <formula formulatype="inline"><tex Notation="TeX">$GF(2)$</tex></formula> conventional optimum RSC encoder. The symbol error rate (SER) is estimated for all the proposed schemes, and the results show the expected coding gains as compared to their equivalent nonencoded and linear versions. </para>