Constraint Length Convolutional Codes Research Articles

Research on Error Correction Coding Closed Set Recognition Technology Based on Deep Learning Method

It is very difficult to obtain information in non-cooperative areas. Error correction coding analysis is one of the key and difficult links. The general analysis is highly demanding and highly dependent on the level of personal analysis. For this reason, we mainly study various deep learning methods, which are applied to scrambling codes, short constraint length convolutional codes, and short constraint length block codes and we also I want to rely on the development of deep learning now, to study and realize intelligence and automated analysis.

Interleaved Concatenations of Polar Codes With BCH and Convolutional Codes

We analyze interleaved concatenation schemes of polar codes with outer binary BCH codes and convolutional codes. We show that both BCH-polar and Conv-polar codes can have a frame error rate that decays exponentially with the code length for all rates up to capacity, which is a substantial improvement in the error exponent over stand-alone polar codes. Interleaved concatenation with long constraint length convolutional codes is an effective way to leverage the fact that polarization increases the cutoff rate of the channel. Simulation results show that Conv-polar codes when decoded with the proposed soft-output multistage iterative decoding algorithm can outperform stand-alone polar codes decoded with successive cancellation or belief propagation decoding. It may be comparable to stand-alone polar codes with list decoding in the high SNR regime. In addition to this, we show that the proposed concatenation scheme requires lower memory and decoding complexity in comparison to belief propagation and list decoding of polar codes. Practically, the scheme enables rate compatible outer codes which ease hardware implementation. Our results suggest that the proposed method may strike a better balance between performance and complexity compared to existing methods in the finite-length regime.

Performance of convolutional codes in asynchronous CDMA communications under imperfect phase-tracking conditions

In this paper, the performance of short constraint length convolutional codes in imperfect phase tracking conditions is discussed. Convolutional codes are used to provide error protection to a particular user in an Asynchronous CDMA (A- CDMA) system undergoing slow Rician fading. Maximum likelihood decoding with a Viterbi algorithm recovers the information symbols. A Phase Locked Loop (PLL) depicting the variations in the phase error for abrupt phase changes in the input signal is considered. Analytical bounds, which are useful in predicting the performance of the A-CDMA system are derived and plotted for the cases of infinite and finite channel memory. The upper bounds on the unconditional Bit Error Rate (BER) with Viterbi decoding are derived and plotted for the various convolutional codes considered. The simulated BERs are found to agree well with their upper bounds.

A new sequential decoding algorithm based on branch metric

A new sequential decoding algorithm with an adjustable threshold and a new method of moving through the decoding tree is proposed. Instead of the path metric of the conventional sequential decoding algorithms, the proposed algorithm uses a branch metric based on maximum-likelihood criterion. Two new parameters, the jumping-back distance and going-back distance, are also introduced. The performance of the algorithm for long constraint length convolutional codes is compared to those of the other sequential decoding algorithms and the Viterbi algorithm. The results show that the proposed algorithm is a good candidate for decoding of convolutional codes due to its fast decoding capability and good bit error rate (BER) performance.

The performance of incremental redundancy schemes based on convolutional codes in the block-fading Gaussian collision channel

The throughput performance of incremental redundancy (INR) schemes, based on short constraint length convolutional codes, is evaluated for the block-fading Gaussian collision channel. Results based on simulations and union bound computations are compared to estimates of the achievable throughput performance with random binary and Gaussian coding in the limit of large block lengths, obtained through information outage considerations. For low channel loads, it is observed that INR schemes with binary convolutional codes and limited block length may provide throughput close to the achievable performance for binary random coding. However, for these low loads, compared to binary random coding, Gaussian random coding may provide significantly better throughput performance, which prompts the use of larger modulation constellations. For high channel loads, a relatively large gap in throughput performance between binary convolutional codes and binary random codes indicates a potential for extensive performance improvement by alternative coding strategies. Only small improvements of the throughput have been observed by increasing the complexity through increased state convolutional coding.

Sequential Decoding of Convolutional Codes for Rayleigh Fading Channels

The performance of sequential decoding of long constraint length convolutional codes is evaluated for Rayleigh fading channels. Sequential decoding is not practical below a certain theoretical signal-to-noise ratio, and these theoretical limits are calculated for a number of modulation methods and code rates. As an example, with BPSK modulation, soft decisions and code rate 1/2, the theoretical signal-to-noise ratio per information bit is 5.7 dB. Above this limit the bit error rate can be made arbitrarily small by increasing the constraint length at no significant complexity cost. Furthermore, it is shown that with carefully chosen quantization steps, 8 level uniform quantization gives a negligible loss also for sequential decoding on a Rayleigh fading channel. Simulation results using 8 level quantization correspond well with the theoretical performance bounds. Also, the performance on a correlated channel with finite interleaving has been obtained. With an interleaver depth of 50×50 and a normalized doppler frequency equal to 0.01 we are only 0.5 dB away from the performance with perfect interleaving. Finally, bit error rate results show this scheme to compete well with Turbo codes.

Multiple differential detection of parallel concatenated convolutional (turbo) codes in correlated fast Rayleigh fading

A new technique for iterative decoding of parallel concatenated convolutional (turbo) codes (PCCCs) for the correlated fast Rayleigh fading channel is proposed and evaluated. This technique is based upon the use of a multiple differential detector (MDD) receiver structure which exploits the statistical characteristics of the fading process to overcome the effects of the rapid phase and amplitude variations. Since traditional MDD receivers cannot be used with PCCCs because they do not produce soft output and are not compatible with channel interleaving, a novel MDD receiver structure is derived which overcomes these shortfalls. In addition, with careful use of extrinsic information related to the a posteriori probability distribution function of the transmitted symbols, the receiver is designed in such a fashion as to allow channel estimation to improve with each iteration. Evaluation of the proposed receiver by means of computer simulation has shown dramatic performance improvements in fast Rayleigh fading channels as compared to long constraint-length conventional convolutional codes using both single and traditional MDD receiver structures.

Modified multiple stack algorithm for decoding convolutional codes

The multiple stack algorithm (MSA), devised by Chevillat and Costello, is an efficient algorithm for erasurefree decoding of long constraint length convolutional codes. In the MSA, substack size and the number of transferred survivors (or successors) are assumed to be small. Lower error probabilities can be achieved by increasing the first stack size and/or increasing the computational limit. A large storage capacity for survivors is required to prevent memory overflow and achieve a low error probability. The authors present a modified MSA, in which the storage capacity for survivors is kept as a constant, while the substacks are arranged in a ring-like structure to handle the overflow problem of storage for survivors. In addition, the substack size and the number of transferred survivors are made large to improve performance. The performance of the modified MSA in decoding a convolutional code with constraint length m = 23 is investigated and compared with the performance of the unmodified MSA.

Improved rate 1/4 convolutional codes

The performance of parallel architectures for generating rate 1/4 high constraint length convolutional codes is examined via information weight distributions. It is found that these codes offer a significant decoding advantage, while having a comparable bit error rate (BER) performance to classical codes.

A two-dimensional product code with robust soft-decision decoding

The performance of a relatively simple two-dimensional (2-D) product code is considered. The row code is a short constraint length convolutional code, and the column code is a high-rate block code. Both the rows and columns are decoded with soft-decision maximum likelihood decoding. The soft output Viterbi algorithm (SOVA) is used to decode the rows. In one case, the same decoder may be used for the rows and the columns. It is shown that, depending on the rate of the row code, reliable signaling is achieved within about 1.0 to 1.5 dB of the R/sub 0/ limit. Results are given for a particular impulsive noise channel; it is seen that performance is robust over a wide range of channel conditions.

Bidirectional decoding of convolutional codes for indoor cellular radio

Bidirectional suboptimal breadth-first decoding of convolutional codes is an attractive technique for slowly varying and quasi-static fading channels as it restricts the extent of decoding errors due to correct path loss to very heavy noise or interference regions. This paper compares the performance of such a decoding scheme to the Viterbi algorithm over wideband TDMA indoor radio links where equalization and space diversity are also used to combat dispersive fading and cochannel interference. On the basis of equal computational complexity and equal decoding delay, suboptimal, breadth-first, bidirectional decoding of a long constraint length convolutional code is shown to be superior to Viterbi decoding of a shorter constraint length code. Furthermore, this advantage increases as the outage criterion (in terms of bit error rate) becomes more stringent which makes bidirectional decoding particularly attractive for data applications and makes channel coding a more attractive alternative to increasing the space diversity order at the receiver.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On unit constraint-length convolutional codes

Unit constraint length convolutional codes are codes that can be generated by encoders with a single delay element. The maximal free distances of these codes are determined in terms of the maximal minimum distances of linear block codes. A formula for the weight enumerator of unit constraint-length convolution codes is derived and a MacWilliams identity to determine the weight enumerator state diagram of a code from the weight enumerator state diagram of its dual code is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of convolutional codes with multipulse signaling in optical channels

AbstractMultipulse signaling has recently become an attractive alternative format to single pulse position modulation (PPM) utilized in optical communication systems [1]. In Ref. 2, the author analyzed the performance of short constraint length convolutional codes (CC) with the standard PPM model. In this article, CC are extended to multipulse signaling applied to both self‐noise limited, and degraded optical channels. Using this scheme, it is seen that gains in bandwidth expansion and peak‐to‐average power ratios are attainable.

Performance evaluation of convolutional codes with MPSK on Rician fading channels

It is known that convolutional coding and Viterbi decoding together with high-level modulation can provide error-control protection without sacrificing bandwidth efficiency on additive white Gaussian noise (AWGN) channels. Bearing this in mind, the paper is concerned with the performance of short constraint length convolutional codes in conjunction with M-ary phase-shift-keyed modulation and maximum-likelihood Viterbi decoding on the fully interleaved Rician fading channels. The primary interest is in the bit error probability performance as a function of system parameters and channel parameters. The generating function union bounding approach is applied, and fairly general analytic upper bounds on the event and bit error probability performance are developed. The bit error probability performance of selected rate-1/2 optimum codes with QPSK and of selected rate-2/3 Ungerbock codes and the Hui code with 8PSK are evaluated using the developed bound. The tightness of the analytic upper bound on bit error probability is also checked by means of computer simulation.

New short constraint length convolutional code constructions for selected rational rates (Corresp.)

New short constraint length convolutional code constructions are tabulated for rates R=(n-k)/n, k=1,2, \cdots ,n-1 with n=2, 3,\cdots ,8 , and for constraint lengths K=3,4, \cdots,8 . These codes have been determined by iterative search based upon a criterion of optimizing the free distance profile. Specifically, these codes maximize the free distance d_{f} while minimizing the number of adversaries in the distance, or weight, spectrum. In several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length. These codes are expected to have a number of applications, including combined source-channel coding schemes as well as coding for burst or impulsive noise channels.

Convolutionally Encoded Memory Protection

A memory protection technique is described in which individually code-protected memory cells are supplemented with redundant memory cells derived from the basic cells according to the rules of a short constraint length convolutional code. The technique is found to be far more protective against faults than memory duplication. The method of clearing up faults is extremely simple—only slightly more complex than with memory duplication.

On a method of calculating the event error probability of convolutional codes with maximum likelihood decoding (Corresp.)

Maximum likelihood (ML) decoding of short constraint length convolutional codes became feasible with the invention of the Viterbi decoder. Several authors have since upper bounded the performance of ML decoders. A method to calculate the event error probability of an ML decoder for convolutional codes is described.

Convolutional Code Performance in the Rician Fading Channel

The performance of short constraint length convolutional codes in conjunction with binary phase-shift keyed (BPSK) modulation and Viterbi maximum likelihood decoding on the classical Rician fading channel is examined in detail. Primary interest is in the bit error probability performance as a function of E_{b}/N_{0} parameterized by the fading channel parameters. Fairly general upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results in the two extremes of zero channel memory and infinite channel memory. The efficacy of simple block interleaving in combating the memory of the channel is thoroughly explored. Results include the effects of fading on tracking loop performance and the subsequent impact on overall coded system performance. The approach is analytical where possible; otherwise resort is made to digital computer simulation.