Engineering topics
Publications and source records attributed to Divsalar, D..
In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained.
In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained. Based on this analysis, design criteria for the selection of component trellis codes for MPSK modulation, and a suitable bit-by-bit iterative decoding structure are proposed. Examples are given for throughput of 2 bits/sec/Hz with 8PSK modulation. The parallel concatenation example uses two rate 4/5 8-state convolutional codes with two interleavers. The convolutional codes' outputs are then mapped to two 8PSK modulations. The serial concatenated code example uses an 8-state outer code with rate 4/5 and a 4-state inner trellis code with 5 inputs and 2 x 8PSK outputs per trellis branch. Based on the above mentioned design criteria for fading channels, a method to obtain he structure of the trellis code with maximum diversity is proposed. Simulation results are given for AWGN and an independent Rayleigh fading channel with perfect Channel State Information (CSI).
Concatenated coding schemes consist of the combination of two or more simple constituent encoders and interleavers.
Concatenated coding schemes with interleavers consist of the combination of two simple constituent encoders and an interleaver. The parallel concatenation known as.
In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.
In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.
We propose a new solution to parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2 bits/sec/Hz with 8PSK and 16QAM signal constellations.
In this article, we design new turbo codes that can achieve near-Shannon-limit performance. The design criterion for random interleavers is based on maximizing the effective free distance of the turbo code, i.e., the minimum output weight of codewords due to weight-2 input sequences. An upper bound on the effective free distance of a turbo code is derived. This upper bound can be achieved if the feedback connection of convolutional codes uses primitive polynomials. We review multiple turbo codes (parallel concatenation of q convolutional codes), which increase the so-called 'interleaving gain' as q and the interleaver size increase, and a suitable decoder structure derived from an approximation to the maximum a posteriori probability decision rule. We develop new rate 1/3, 2/3, 3/4, and 4/5 constituent codes to be used in the turbo encoder structure. These codes, for from 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b/n (b = 1, 2, 3, 4 and n = 2, 3, 4, 5, 6), and include random interleavers for better asymptotic performance. These codes are suitable for deep-space communications with low throughput and for near-Earth communications where high throughput is desirable. The performance of these codes is within 1 dB of the Shannon limit at a bit-error rate of 10(exp -6) for throughputs from 1/15 up to 4 bits/s/Hz.
A description is given of multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders.
It is shown how turbo codes and decoders can be used to improve the coding gain for deep-space communications, while decreasing the decoding complexity with respect to the large constraint length convolutional codes currently in use. Similar code constructions were used to build multiple-encoder turbo codes. This generalizes the turbo decoding concept to a truly distributed decoding system.
In this article we apply transfer function bounding techniques to obtain upper bounds on the bit-error rate for maximum likelihood decoding of turbo codes constructed with random permutations. These techniques are applied to two turbo codes with constraint length 3 and later extended to other codes. The performance predicted by these bounds is compared with simulation results. The bounds are useful in estimating the 'error floor' that is difficult to measure by simulation, and they provide insight on how to lower this floor. More refined bounds are needed for accurate performance measures at lower signal-to-noise ratios.
This article takes a preliminary look at the weight distributions achievable for turbo codes using random, nonrandom, and semirandom permutations. Due to the recursiveness of the encoders, it is important to distinguish between self-terminating and non-self-terminating input sequences. The non-self-terminating sequences have little effect on decoder performance, because they accumulate high encoded weight until they are artificially terminated at the end of the block. From probabilistic arguments based on selecting the permutations randomly, it is concluded that the self-terminating weight-2 data sequences are the most important consideration in the design of constituent codes; higher-weight self-terminating sequences have successively decreasing importance. Also, increasing the number of codes and, correspondingly, the number of permutations makes it more and more likely that the bad input sequences will be broken up by one or more of the permuters. It is possible to design nonrandom permutations that ensure that the minimum distance due to weight-2 input sequences grows roughly as the square root of (2N), where N is the block length. However, these nonrandom permutations amplify the bad effects of higher-weight inputs, and as a result they are inferior in performance to randomly selected permutations. But there are 'semirandom' permutations that perform nearly as well as the designed nonrandom permutations with respect to weight-2 input sequences and are not as susceptible to being foiled by higher-weight inputs.
A number of the claims for turbo codes as a great advance in coding theory are confirmed, and a complete description is presented of an encoder/decoder pair that could be suitable for PCS applications. A new simple method for trellis termination is described, the effect of interleaver choice on the weight distribution of the code is analyzed, and unequal rate components (which yield better performance) are introduced.
In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We analyze the effect of interleaver choice on the weight distribution of the code, and we describe simulation results on the improved performance of these new codes.
Turbo codes were recently proposed by Berrou, Glavieux, and Thitimajshima, and it has been claimed these codes achieve near-Shannon-limit error correction performance with relatively simple component codes and large interleavers. A required E(b)/N(o) of 0.7 dB was reported for a bit error rate of 10(exp -5), using a rate 1/2 turbo code. However, some important details that are necessary to reproduce these results were omitted. This article confirms the accuracy of these claims, and presents a complete description of an encoder/decoder pair that could be suitable for deep-space applications, where lower rate codes can be used. We describe a new simple method for trellis termination, analyze the effect of interleaver choice on the weight distribution of the code, and introduce the use of unequal rate component codes, which yield better performance.
Code division multiple-access spread spectrum has been proposed for use in future multiprobe/multispacecraft missions. This article considers a general parallel interference-cancellation scheme that significantly reduces the degradation effect of probe (user) interference but with a lesser implementation complexity than the maximum-likelihood technique. The scheme operates on the fact that parallel processing simultaneously removes from each probe (user) the total interference produced by the remaining most reliably received probes (users) accessing the channel. The parallel processing can be done in multiple stages. The proposed scheme uses tentative decision devices with different optimum thresholds at the multiple stages to produce the most reliably received data for generation and cancellation of probe/spacecraft interference. The one-stage interference cancellation was analyzed for two types of tentative decision devices, namely, hard and null zone decisions. Simulation results are given for one- and two-stage interference cancellation for equal as well as unequal received power probes.
This paper introduces a trellis coded modulation (TCM) scheme for non-coherent multiple full response M-ary CPFSK with modulation index 1/M. A proper branch metric for the trellis decoder is obtained by employing a simple approximation of the modified Bessel function for large signal to noise ratio (SNR). Pairwise error probability of coded sequences is evaluated by applying a linear approximation to the Rician random variable.
This paper considers a general parallel interference cancellation scheme that significantly reduces the degradation effect of user interference but with a lesser implementation complexity than the maximum-likelihood technique. The scheme operates on the fact that parallel processing simultaneously removes from each user the total interference produced by the remaining most reliably received users accessing the channel. The parallel processing can be done in multiple stages. The proposed scheme uses tentative decision devices with different optimum thresholds at the multiple stages to produce the most reliably received data for generation and cancellation of user interference.