We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the received sequence and all symbols are corrupted by additive white Gaussian noise. To this end, we utilize the inherent redundancy achievable in non-binary symbol sets by first expanding the symbol set and then allocating part of the bits associated with each symbol to watermark symbols. The watermark sequence, known at the receiver, is then used by a forward-backward algorithm to provide soft information for an outer code which decodes the transmitted sequence. Through numerical results and discussions, we evaluate the performance of the proposed solution and show that it leads to significant system ability to detect and correct insertions/deletions. We also provide estimates of the maximum achievable information rates of the system, compare them with the available bounds, and construct practical codes capable of approaching these limits.

Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance loss compared to true LLRs.

An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

On a fading channel with no channel state information at the receiver, true log-likelihood ratios (LLR) are complicated functions of the channel output. It is assumed in the literature that the power of the additive noise is known and the expected value of the fading gain is used in a linear function of the channel output to find approximate LLRs. This approach, however, is not optimal in the sense of bit error rate performance. In this paper, we introduce a measure of accuracy for the approximate LLRs based on their probability density function and we show that this measure provides a very convenient tool for finding good approximate LLRs. Assuming that the power of the additive noise is known, and using the proposed measure, we find a linear LLR approximation whose performance is extremely close to that of the true LLR calculation on an uncorrelated Rayleigh fading channel. These results are then extended to the case that the noise power is also unknown and a performance almost identical to the previous case is obtained.

An efficient method for finite-length low-density parity-check (LDPC) code analysis is proposed. This method is based on studying the channel variations when observed during a finite-length codeword. To this end, channel parameters are interpreted as random variables and their distributions are found. Assuming that a decoding failure is the result of an observed channel worse than the code's decoding threshold, the block error probability of finite-length LDPC codes is estimated. Using an extrinsic information transfer chart analysis, bit error probability is obtained from the block error probability. Our results suggest that by considering only the channel variations around its expected behavior and even ignoring the effects of cycles, one can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

The time-varying nature of wireless channels poses a challenge for using soft-decision iterative decoders on such channels. Even if the channel gain is perfectly known to the receiver, inaccurate estimation of the additive noise power, results in incorrect log-likelihood computation at the receiver and hence significant performance degradation in the decoder. Through a detailed study of the effects of channel estimation errors on the performance of soft-decision iterative decoders in uncorrelated block-fading channels, we propose a solution which does not need a knowledge of the power of the additive noise. We show that this solution performs almost identical to the case for which a perfect knowledge of the power of the additive noise exists at the receiver. The choice of the block-fading channel reflects a situation where the equivalent variance of the additive Gaussian noise can change in a wide range and thus the decoder performance seriously relies on the knowledge of the noise power at the receiver.

On a fading channel with no channel state information at the receiver, calculating true log-likelihood ratios (LLR) is complicated. Existing work assume that the power of the additive noise is known and use the expected value of the fading gain in a linear function of the channel output to find approximate LLRs. In this work, we first assume that the power of the additive noise is known and we find the optimum linear approximation of LLRs in the sense of maximum achievable transmission rate on the channel. The maximum achievable rate under this linear LLR calculation is almost equal to the maximum achievable rate under true LLR calculation. We also observe that this method appears to be the optimum in the sense of bit error rate performance too. These results are then extended to the case that the noise power is unknown at the receiver and a performance almost identical to the case that the noise power is perfectly known is obtained.

Irregular decoding of low-density parity-check codes, i.e., using different algorithms in one iteration of the decoding of a single word, is studied. We formulate density evolution for irregular decoders. Using a one-dimensional representation of density evolution, we then jointly optimize irregular codes and irregular soft decoders for minimizing the decoding complexity. More specifically, for a given set of soft algorithms, a given channel, and a given code-rate, we find an irregular code-decoder pair which is capable of achieving a desired error performance with minimal decoding complexity. Robustness of irregular decoders when there exist channel estimation errors is also shown via an example