Karin Engdahl

On the Theory of Low-Density Convolutional Codes

We introduce and analyze a new statistical ensemble of low-density parity-check convolutional (LDC) codes. The result of the analysis are bounds, such as a lower bound for the free distance and upper bounds for the burst error probability of the LDC codes.

Tighter bounds on the error probability of fixed convolutional codes

We introduce new upper bounds for the bit and burst error probabilities, when a convolutional code is used for transmission over a binary input, additive white Gaussian noise (AWGN) channel, and the decoder performs maximum-likelihood decoding. The bounds are tighter than existing bounds, and nontrivial also for signal-to-noise ratios below the computational cutoff rate.

On the calculation of the error probability for a multilevel modulation scheme using QAM-signalling

We analyze the quadrature amplitude modulation (QAM) version of multilevel modulation with multistage decoding using a suboptimal metric, when transmission takes place over a memoryless Gaussian channel. The upper bounds for decoding error probabilities are functions of the Chernoff bounding parameter Z. We argue that the conventional approximation of Z is not adequate; new values of Z that tightens the error bounds without causing them to lose their validity are given. The capacity for this system is also calculated, and we conclude that the use of a suboptimal metric in multistage decoding causes very little degradation in capacity compared to when the optimal metric is used in each decoding stage.

Analytical approach to low-density convolutional codes

A statistical analysis of low-density convolutional (LDC) codes is performed. This analysis is based on the consideration of a special statistical ensemble of Markov scramblers and the solution to a system of recurrent equations describing this ensemble. The results of the analysis are lower bounds for the free distance of the codes and upper bounds for the maximum likelihood decoding error probability. For the case where the size of the scrambler tends to infinity some asymptotic bounds for the free distance and the error probability are derived. Simulation results for iterative decoding of LDC codes are also presented.

New Decoding Error Probability Bounds for Fixed Convolutional Codes used in BSC

Abstract New upper bounds for the bit and burst error probabilities are derived for the case, when a fixed convolutional code is used for communication over the binary symmetric channel (BSC) and the decoder performs maximum likelihood decoding. These bounds are tighter than existing bounds.

A comparison analysis of two multilevel QAM systems

Two multilevel modulation systems are compared in terms of capacity, under the condition that the average energy per channel use is the same for the two systems. We consider the suboptimal multistage receiver for the Gaussian channel. We conclude that, under these conditions, the capacity for the hexagonal system is close to 1 dB better than the capacity for the rectangular system.

How large is the coding gain for multilevel modulation systems

It is well known that Ungerboecks and Imai/Hirokawas multilevel coded modulation systems give essential gain in comparison to a conventional coded modulation system, but as we know a rigorous analysis of this gain has not yet been done. We present the results of an asymptotical analysis and a comparison of two coded modulation systems, conventional modulation and multilevel modulation, using q-PSK signaling and transmission over the AWGN channel.