Carl Fredrik Leanderson

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.

The max-log list algorithm (MLLA)-a list-sequence decoding algorithm that provides soft-symbol output

We present a soft decoding algorithm for convolutional codes that simultaneously yields soft-sequence output, i.e., list sequence (LS) decoding, and soft-symbol output. The max-log list algorithm (MLLA) introduced in this paper provides near-optimum soft-symbol output equal to that of the max-log maximum a posteriori (MAP) probability algorithm. Simultaneously, the algorithm produces an ordered list containing LS-MAP estimates. The MLLA exists in an optimum and a suboptimum version that are different in that the optimum version produces optimum LS-MAP decoding for arbitrary list lengths, while the suboptimum low-complexity version only provides the MAP, the second-order MAP, and the third-order MAP sequence estimates. For lists with more than three elements, MAP decoding is not guaranteed, but the LS decoding is close to the optimal. It is demonstrated that the suboptimum/optimum MLLA can be used to obtain the combination of soft-symbol and soft-sequence outputs at lower complexity than a previously published algorithm. Furthermore, the suboptimum MLLA is well suited for operation in an iterative list (turbo) decoder, since it is obtained by only minor modifications of the well-known Max-Log-MAP algorithm frequently used for decoding of the component codes of turbo codes. Another potential area of application for the suboptimum/optimum MLLA is joint source-channel LS decoding. Estimates of complexity and memory use, as well as performance evaluations of the suboptimum/optimum MLLA, are provided in this paper.

On the design of low rate turbo codes

Low rate codes can be used to achieve coding gain in spread spectrum applications such as direct-sequence code division multiple access. Super-orthogonal- and maximum free distance convolutional codes as well as super-orthogonal turbo codes have previously been reported to be suitable for such systems. We focus on the design of component codes for low rate turbo coding schemes targeting the frame-error rate at low signal-to-noise ratios. We present code search criteria which yield high performing turbo codes on the additive white Gaussian noise channel. Simulation results show that these codes perform better than other low rate turbo codes previously reported in the literature.

On list sequence turbo decoding

An algorithm for decoding Turbo codes that combines conventional Turbo decoding and list sequence maximum a posteriori probability decoding is presented and evaluated. Compared to previous results on this theme, performance improvements in the order of 0.7 dB are obtained for Turbo codes with 514-b pseudorandom interleaving at a frame error rate of 10/sup -4/ on the additive white Gaussian noise channel.

Performance evaluation of list sequence MAP decoding

List-sequence (LS) decoding has the potential to yield significant coding gain additional to that of conventional single-sequence decoding, and it can be implemented with full backward compatibility in systems where an error-detecting code is concatenated with an error-correcting code. LS maximum-likelihood (ML) decoding provides a list of estimated sequences in likelihood order. For convolutional codes, this list can be obtained with the serial list Viterbi algorithm (SLVA). Through modification of the metric increments of the SLVA, an LS maximum a posteriori (MAP) probability decoding algorithm is obtained that takes into account bitwise a priori probabilities and produces an ordered list of sequence MAP estimates. The performance of the resulting LS-MAP decoding algorithm is studied in this paper. Computer simulations and approximate analytical expressions, based on geometrical considerations of the decision domains of LS decoders, are presented. We focus on the frame-error performance of LS-MAP decoding, with genie-assisted error detection, on the additive white Gaussian noise channel. It is concluded that LS-MAP decoding exploits a priori information more efficiently, in order to achieve performance improvements, than does conventional single-sequence MAP decoding. Interestingly, LS-MAP decoding can provide significant improvements at low signal-to-noise ratios, compared with LS-ML decoding. In this environment, it is furthermore observed that feedback convolutional codes offer performance improvements over their feedforward counterparts. Since LS-MAP decoding can be implemented in existing systems at a modest complexity increase, it should have a wide area of applications, such as joint source-channel decoding and other kinds of iterative decoding.

A comparison of turbo codes using different trellis terminations

This paper investigates the incidence of trellis termination on the performance of turbo codes and accounts for the performance degradation often experienced in the absence of trellis termination. Analytical upper bounds on the performance for the ensemble of turbo codes using different trellis termination strategies as well as performance results obtained by computer simulation are presented. In the case of uniform interleaving, the performance differences between various termination methods are relatively small, except when using no trellis termination at all.RésuméOn étudie l’influence de la terminaison du treillis sur les performances de turbocodes et on rend compte de la dégradation souvent observée en l’absence de terminaison. On présente des bornes supérieures analytiques de la probabilité d’erreur sur l’ensemble des turbocodes pour différentes manières de terminer le treillis, ainsi que l’évaluation de ces performances par simulation sur ordinateur. Dans le cas où l’entrelacement est uniforme, les performances varient assez peu d’un type de terminaison à un autre, excepté quand aucun des treillis n’est terminé.

On the performance of turbo codes and convolutional codes of low rate

Recently two new classes of low-rate codes have been presented. The first class is the super-orthogonal turbo codes (SOTCs) and the second is the maximum free distance (MFD) convolutional codes. In this paper we present an evaluation of the performance vs. arithmetic decoding complexity for these codes and compare them with the previously reported super-orthogonal convolutional codes (SOCCs). For all classes of codes, the arithmetic decoding complexity is estimated, and the error performance on the additive white Gaussian noise channel is simulated. The SOCCs offer performance comparable to that of the MFD codes. However, the existence of good SOCCs is restricted to a small number of rates while the MFD codes give high performance for a multitude of rates. For the parameters used in this investigation the SOTCs yield higher performance at lower arithmetic decoding complexity than the MFD codes.

List sequence turbo decoding techniques

An algorithm for decoding turbo codes that combines conventional turbo decoding and list sequence (LS) maximum a posteriori probability (MAP) decoding is presented and evaluated. Compared to previous results on this theme, a reduction in the order of 0.7 dB of the signal-to-noise ratio (SNR) is obtained for turbo codes with 514-bit pseudo-random interleaving at frame error rate (FER) 10/sup -4/ on the additive white Gaussian noise (AWGN) channel.

Joint source-channel list sequence decoding

We evaluate the performance of list sequence (LS) maximum a posteriori probability (MAP) decoding on the additive white Gaussian noise (AWGN) channel and the fully interleaved flat Rayleigh fading channel. In particular, we focus on the frame error rate (FER) of LS-MAP decoding with genie-assisted error detection. It is demonstrated that LS-MAP decoding yields significant performance improvements relative to single sequence MAP decoding on the AWGN channel as well as the fully interleaved flat Rayleigh fading channel. Furthermore, feedback convolutional codes have been observed to have the potential to yield improved FER performance with both single sequence MAP and IS-MAP decoding, compared to feedforward convolutional codes. Based on these performance improvements, we propose a joint source-channel IS decoding scheme. The scheme is based on the max-log list algorithm for simultaneous soft symbol and IS decoding of convolutional codes. In existing systems where a cyclic redundancy check for error mitigation is concatenated with a convolutional code for error correction, this scheme can be implemented in a fully backward compatible receiver.

Simultaneous soft symbol and list sequence decoding

We present a soft output decoding algorithm for convolutional codes, yielding both list sequence (LS) decoding and soft symbol output. Potential applications are to be found in turbo decoding.