Hard Decoding Research Articles

Fast Decoding Algorithms for First Order Reed-Muller and Related Codes

Fast decoding algorithms for short codes based on modifications of maximum likelihood decoding algorithms of first order Reed-Muller codes are described. Only additions-subtractions, comparisons and absolute value calculations are used in the algorithms. Soft and hard decisions maximum likelihood decoding algorithms for first order Reed-Muller and the Nordstrom-Robinson codes with low complexity are proposed.

Soft syndrome decoding of binary convolutional codes

We present an efficient recursive algorithm for accomplishing maximum likelihood (ML) soft syndrome decoding of binary convolutional codes. The algorithm consists of signal-by-signal hard decoding followed by a search for the most likely error sequence. The number of error sequences to be considered is substantially larger than in hard decoding, since the metric applied to the error bits is the magnitude of the log likelihood ratio rather than the Hamming weight. An error-trellis (alternatively, a decoding table) is employed for describing the recursion equations of the decoding procedure. The number of its states is determined by the states indicator, which is a modified version of the constraint length of the check matrix. Methods devised for eliminating error patterns and degenerating error-trellis sections enable accelerated ML decoding. In comparison with the Viterbi algorithm, the syndrome decoding algorithm achieves substantial reduction in the average computational complexity, particularly for moderately noisy channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Erasing gains for concatenated codes

The optimal strategy for erasing symbols in a concatenated coding system, in which the outer code is decoded once, is considered. In general, the strategy involves comparison of a posteriori symbol likelihoods to nonuniform thresholds. The performance of a greedy version of such a rule is evaluated for a number of specific short inner codes, over both memoryless and bursty channels, with hard and soft decisions. It is shown that the gains achievable via erasing can be substantial when hard decision inner decoders are used and when short inner codes are used, but are less so otherwise. It is shown that erasing gains can be very large when applied over channels with memory, with interleaving at the symbol level.

Demodulation and decoding for diversity mobile radio systems

In mobile communication systems, channel coding and equalisation are required to achieve high-quality signals. The channel degradation owing to multipath fading, time spread and Doppler spread can be further reduced by using diversity techniques, where the receiver is provided with multiple independently faded replicas of the same information signal. The information coming from the diversity channels can be properly combined to improve the system performance. In the paper a new diversity receiver which performs demodulation and decoding of mobile-radio signals is described. The proposed demodulation scheme uses a new distance-combination technique based on the classical MLSE Viterbi algorithm. A new soft-decoding algorithm combining the signals coming from the diversity channels is proposed. The experimental results obtained by computer simulations show a significant improvement of the bit-error rate with respect to hard decoding in return for a modest increase in receiver complexity.

A performance comparison of the binary quadratic residue codes with the 1/2-rate convolutional codes

The 1/2-rate binary quadratic residue (QR) codes, using binary phase-shift keyed (BPSK) modulation and hard decoding, are presented as an efficient system for reliable communication. Performance results of error correction are obtained both theoretically and by means of computer calculations for a number of binary QR codes. These results are compared with the commonly used 1/2-rate convolutional codes with constraint lengths from 3 to 7 for the hard-decision case. The binary QR codes of different lengths are shown to be equivalent in error-correction performance to some 1/2-rate convolutional codes, each of which has a constraint length K that corresponds to the error-control rate d/n and the minimum distance d of the QR codes. >

Performance of combined diversity reception and convolutional coding for QDPSK land mobile radio

Diversity reception and error correction coding are powerful techniques to combat multipath fading encountered in mobile radio communications. In order to improve the transmission performance of the /spl pi//4-shift QDPSK signal in mobile radio channels, the authors propose a new scheme of combined coding and diversity reception, i.e., combination of diversity reception employing code combining (CC) and convolutional coding employing error-and erasure correction Viterbi decoding. They also consider another combination scheme, i.e., combination of diversity reception employing postdetection maximal ratio combining (MRC) and convolutional coding employing hard decision Viterbi decoding. They theoretically analyze the performance of the schemes taking into account the additive white Gaussian noise (AWGN), random FM noise, co-channel interference (CCI), and intersymbol interference (ISI) due to multipath propagation delay spread. Numerical calculations are presented for the required average signal energy per bit-to-noise power spectral density ratio (E/sub b//N/sub 0/), required average signal-to-interference power ratio (SIR), tolerable maximum Doppler frequency, and tolerable rms delay spread needed to achieve a certain average BER. The spectrum efficiency of the cellular system is also calculated. >

A model for local/mobile radio communications with correct packet capture

The performance of a local/mobile radio communications system utilizing the slotted ALOHA multiple random access protocol is analyzed. The probability of correct packet capture is evaluated for a local/mobile packet radio system using ideal coherent binary phase-shift keying (BPSK) modulation. Both the near/far effect and the effect of Rayleigh fading on the probability of correct packet capture are taken into account, but the effect of thermal noise is neglected since the interference due to competing packets is dominant in practical systems. The probability of correct packet reception is evaluated for a system using spatial diversity. In addition, the effect on system performance of either convolutional coding with hard decision Viterbi decoding or binary linear block coding with hard decision decoding is evaluated. The pseudo-Bayesian algorithm that has been developed to stabilize a packet system based on the slotted ALOHA protocol at maximum channel throughput is found to be adaptable to the local mobile operating environment. For the system considered here, channel throughputs as high as 0.66 can be obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New approaches to reduced-complexity decoding

We examine new approaches to the problem of decoding general linear codes under the strategies of full or bounded hard decoding and bounded soft decoding. The objective is to derive enhanced new algorithms that take advantage of the major features of existing algorithms to reduce decoding complexity. We derive a wide range of results on the complexity of many existing algorithms. We suggest a new algorithm for cyclic codes, and show how it exploits all the main features of the existing algorithms. Finally, we propose a new approach to the problem of bounded soft decoding, and show that its asymptotic complexity is significantly lower than that of any other currently known general algorithm. In addition, we give a characterization of the weight distribution of the average linear code and thus show that the Gilbert-Varshamov bound is tight for virtually all linear codes over any symbol field.

Developments in Error Control Coding Techniques and some Results on Concatenated Codes

Error control coding has gained significant importance in most of the digital communication systems since a few decades. As a result, a large variety of coding and decoding techniques, suitable for different applications and to meet different requirements, have emerged. In this paper, we have made an attempt to present an overview of the error control coding techniques by suitably classifying them and drawing a qualitative comparison between them in order to provide a design tool to the researcher. Some simulated and practically achieved performance results of some of the popular codes have been included to emphasize their utility and suitability. We have also presented here some of the important results of our studies on concatenated coding schemes which have become very important recently. The structure of codes, algorithms, the hard and soft-decision decoding and their complexities have been discussed. The parameters like bandwidth, data-rate, types of errors, BER vs SNR, coding gain and buffer requirements have also been considered in this paper.

Optimum threshold soft decision decoding of linear block codes in impulsive noise

The union and upper bounds of the probability of error Pc for soft decision (unquantised) optimum threshold decoding of binary phase-shift keying (PSK) with the Golay (23, 12) code are found. Even though soft decision decoding performs better, as expected, than hard decision-bounded distance decoding, the difference in performance between the two decoding schemes decreases as the data sample size N becomes large, while the difference between the upper and union bounds remains almost constant For example, for Pc˜ 10−5 improvement greater than 3dB can be achieved when going from N = 100 to 400. This result is in direct contrast with the equivalent result in white Gaussian noise where a 2dB difference exists between hard and soft-decision decoding for all coded digital communications.

Systolic array processing of the Viterbi algorithm

Results on efficient forms of decoding convolutional codes based on the Viterbi algorithm by using systolic arrays are presented. Various properties of convolutional codes are discussed. A technique called strongly connected trellis decoding is introduced to increase the efficient utilization of all the systolic array processors. Issues dealing with the composite branch metric generation, survivor updating, overall system architecture, throughput rate, and computational overhead ratio are also investigated. The scheme is applicable to both hard and soft decoding of any rate b/n convolutional code. It is shown that as the length of the code becomes large, the systolic Viterbi decoder maintains a regular and general interconnection structure as well as moderate throughput rate gain over the sequential Viterbi decoder.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>