Browsing by Subject "Concatenated codes"

Now showing 1 - 3 of 3

Open Access
Capacity bounds and concatenated codes over segmented deletion channels
(IEEE, 2013) Wang, F.; Duman, T. M.; Aktas, D.
We develop an information theoretic characterization and a practical coding approach for segmented deletion channels. Compared to channels with independent and identically distributed (i.i.d.) deletions, where each bit is independently deleted with an equal probability, the segmentation assumption imposes certain constraints, i.e., in a block of bits of a certain length, only a limited number of deletions are allowed to occur. This channel model has recently been proposed and motivated by the fact that for practical systems, when a deletion error occurs, it is more likely that the next one will not appear very soon. We first argue that such channels are information stable, hence their channel capacity exists. Then, we introduce several upper and lower bounds with two different methods in an attempt to understand the channel capacity behavior. The first scheme utilizes certain information provided to the transmitter and/or receiver while the second one explores the asymptotic behavior of the bounds when the average bit deletion rate is small. In the second part of the paper, we consider a practical channel coding approach over a segmented deletion channel. Specifically, we utilize outer LDPC codes concatenated with inner marker codes, and develop suitable channel detection algorithms for this scenario. Different maximum-a-posteriori (MAP) based channel synchronization algorithms operating at the bit and symbol levels are introduced, and specific LDPC code designs are explored. Simulation results clearly indicate the advantages of the proposed approach. In particular, for the entire range of deletion probabilities less than unity, our scheme offers a significantly larger transmission rate compared to the other existing solutions in the literature.
Open Access
Code design for discrete memoryless interference channels
(Institute of Electrical and Electronics Engineers, 2018) Dabirnia, Mehdi; Tanc, A. K.; Sharifi S.; Duman, Tolga M.
We study the design of explicit and implementable codes for the two-user discrete memoryless interference channels (DMICs). We consider Han-Kobayashi (HK) type encoding where both public and private messages are used and propose coding techniques utilizing a serial concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. Since exact analytical treatment of the BCJR decoder for the inner trellis-based code appears infeasible, we analytically investigate the iterative decoding process in the asymptotic regime where the probability of decoding error tends to zero. Based on this approximate analysis, we derive a stability condition for this type of a concatenated coding scheme for the first time in the literature. Furthermore, we use an extrinsic information transfer analysis to design the outer LDPC code while fixing the inner NLTC, and utilize the derived stability condition to accelerate the design process and to avoid code ensembles that potentially produce high error floors. Via numerical examples, we demonstrate that our designed codes achieve rate pairs close the optimal boundary of the HK subregion, which cannot be obtained without the use of nonlinear codes. Also, we verify that the estimated thresholds of the designed codes via finite block length simulations and show that our designs significantly outperform the point-to-point optimal codes, hence demonstrating the need for designs specifically tailored for DMICs.
Open Access
Deep learning based decoders for concatenated codes over insertion and deletion channels
(2025-01) Kargı, Eksal Uras
Channels with synchronization errors, including insertion/deletion channels, are of significant importance, as they are encountered in various systems, such as communication networks and various storage technologies, including DNA data storage. Serially concatenated codes where the outer code is a powerful channel code, such as a low-density parity-check (LDPC) or convolutional code, and the inner code is a watermark or marker code, are shown to be effective solutions over such channels. In particular, the use of marker codes, referring to insertion of preselected sequences in the transmitted data stream periodically, are shown to work well in regaining synchronization at the receiver and achieving improved error rate performance compared to other alternatives. In the current literature, maximum a posteriori (MAP) detector realized by the well-known forward-backward algorithm is commonly employed to decode the inner marker code and estimate the log-likelihood ratios (LLRs) of the bits encoded by the outer code, and the resulting log-likelihood estimates are fed to the outer decoder to estimate the transmitted data. Alternative to the MAP detector, this thesis proposes deep learning-based solutions to estimate the LLRs of the coded bits in the paradigm of concatenated codes, exploiting the marker information and addressing some limitations of conventional methods. Bit-level deep learning-based detectors offer good alternatives when the channel statistics are not perfectly available at the decoder, degrading of the performance of the MAP detector. They can also be employed for one-shot decoding when the outer code is a convolutional code. Also developed are symbol-level deep learning-based detectors to exploit the correlations among adjacent bits at the detector output. Contrary to the existing symbol-level decoders for insertion/deletion channels, the newly proposed approaches can go beyond the case of combining three bits, offering further enhancements in performance while keeping the complexity tolerable. As a final contribution, deep learning-based detectors are developed for insertion and deletion channels that are further exacerbated by inter-symbol interference, e.g., modeling bit-patterned media recording channels, and their performance is studied via numerical examples.