Non-systematic Turbo Codes Research Articles

Revisiting the calculation of effective free distance of turbo codes

The expression for the minimum Hamming weight of the output of a constituent convolutional encoder, when its input is a weight-2 sequence is revisited. The new expression particularly facilitates the calculation of the effective free distance of recently proposed schemes, namely non-systematic turbo codes and pseudo-randomly punctured turbo codes.

Nonsystematic Turbo Codes

In this paper, we introduce the concept of nonsystematic turbo codes and compare them with classical systematic turbo codes. Nonsystematic turbo codes can achieve lower error floors than systematic turbo codes because of their superior effective free distance properties. Moreover, they can achieve comparable performance in the waterfall region if the nonsystematic constituent encoder has a low-weight feedforward inverse. A uniform interleaver analysis is used to show that rate R=1/3 turbo codes using nonsystematic constituent encoders have larger effective free distances than when systematic constituent encoders are used. Also, mutual information-based transfer characteristics and extrinsic information transfer charts are used to show that rate R=1/3 turbo codes with nonsystematic constituent encoders having low-weight feedforward inverses achieve convergence thresholds comparable to those achieved with systematic constituent encoders. Catastrophic encoders, which do not possess a feedforward inverse, are shown to be capable of achieving low convergence thresholds by doping the code with a small fraction of systematic bits. Finally, we give tables of good nonsystematic turbo codes and present simulation results comparing the performance of systematic and nonsystematic turbo codes.

The Effect of Narrowband Interference on Wideband Wireless Communication Systems

In this paper, we introduce the concept of nonsystematic turbo codes and compare them with classical systematic turbo codes. Nonsys- tematic turbo codes can achieve lower error floors than systematic turbo codes because of their superior effective free-distance properties. More- over, they can achieve comparable performance in the waterfall region if the nonsystematic constituent encoder has a lower weight feedforward in- verse. A uniform inteleaver analysis is used to show that rate turbo codes using nonsystematic constituent encoders have larger effective free distance than when systematic constituent encoders are used. Also, mutual information-based transfer characteristics and EXIT charts are used to show that rate turbo codes with nonsystematic con- stituent encoders having low-weight feedforward inverses achieve conver- gence thresholds comparable to those achieved with systematic constituent encoders. Catastrophic encoders, which do not possess a feedforward in- verse, are shown to be capable of achieving low convergence thresholds by doping the code with a small fraction of systematic bits. Finally, we give tables of good nonsystematic turbo codes and present simulation results comparing the performance of systematic and nonsystematic turbo codes. Abstract—This paper evaluates the performance of wideband commu- nication systems in the presence of narrowband interference. In partic- ular, we derive closed bit-error probability expressions for spread-spec- trum systems by approximating narrowband interferers as independent asynchronous tone interferers. The scenarios considered include additive white Gaussian noise channels, flat-fading channels, and frequency-selec- tive multipath fading channels. For multipath fading channels, we develop a new analytical framework based on perturbation theory to analyze the per- formance of a Rake receiver in Nakagami- channels. Simulation results for narrowband interference such as GSM and Bluetooth are in good agree- ment with our analytical results, showing the approach developed is useful for investigating the coexistence of ultrawide bandwidth systems with ex- isting wireless systems.

Transmission of Nonuniform Memoryless Sources via Nonsystematic Turbo Codes

We investigate the joint source-channel coding problem of transmitting nonuniform memoryless sources over binary phase-shift keying-modulated additive white Gaussian noise and Rayleigh fading channels via turbo codes. In contrast to previous work, recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources. We prove that under certain conditions, and when the length of the input source sequence tends to infinity, the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform, regardless of the degree of source nonuniformity. We also give a conjecture (which is empirically validated) on the condition for the higher order distribution of the encoder output to be asymptotically uniform, irrespective of the source distribution. Consequently, these conditions serve as design criteria for the choice of good encoder structures. As a result, the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input, since a uniformly distributed input maximizes the channel mutual information, and hence, achieves capacity. Simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes; furthermore, their performance is within 0.74-1.17 dB from the Shannon limit. Finally, we compare our joint source-channel coding system with two tandem schemes which employ a fourth-order Huffman code (performing near-optimal data compression) and a turbo code that either gives excellent waterfall bit-error rate (BER) performance or good error-floor performance. At the same overall transmission rate, our system offers robust and superior performance at low BERs (< 10/sup -4/), while its complexity is lower.