This paper studies expurgated random coding bounds and exponents for source coding with side information with a given (possibly mismatched) decoding rule. We propose an expurgation technique that is an iterative version of Gallager’s expurgation method for channel coding and enables a direct dual domain derivation of non-asymptotic bounds for discrete sources with arbitrary side information alphabets and decoding metrics. Specializing the bounds to memoryless models a dual domain achievable error exponent for type-by-type random coding is derived and shown to coincide with the Csiszár-Körner exponent obtained via graph decomposition.

We introduce an expurgation method for source coding with side information that enables direct dual-domain derivations of expurgated error exponents. Dual-domain methods yield optimization problems over few parameters, with any sub-optimal choice resulting in an achievable exponent, as opposed to primal-domain optimization over distributions. In addition, dual-domain methods naturally allow for general alphabets and/or memory. We derive two such expurgated error exponents for different random-coding ensembles in the case where the decoder is possibly mismatched with respect to the source and side information joint distribution. We show the better of the exponents coincides with the Csiszár-Körner exponent obtained via a graph decomposition lemma. We show some numerical examples that illustrate the differences between the two exponents and show that in the case of source coding without side information, the expurgated exponent coincides with the error exponent of the source optimal code.

The optimal quantization of output binary-input discrete memoryless channels is considered, whereby the optimal quantizer preserves at least a constant$\alpha $-fraction of the original mutual information, with the smallest output cardinality. Two recursive methods with top-down and bottom-up approaches are developed; these methods lead to a new necessary condition for the recursive quantizer design. An efficient algorithm with linear complexity, based on dynamic programming and the new necessary optimality condition, is proposed.

Channel output quantization to a smaller number of outputs is modeled as a mismatched decoding problem. The conditions that a mismatched decoding metric should satisfy in order to represent an output quantizer are derived. In addition, a mismatched decoding metric and hypothesis test that minimizes the average error probability are found. It is shown that the best possible mismatched decoder is equivalent to maximum-likelihood decoding for the channel between the channel input and the quantized output. This gives a class of mismatched decoding problems where the mismatch capacity is known. This result supports previous studies on quantizer design and optimization over the quantized channel.

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis‐based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error‐rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi‐static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point‐to‐point (P2P) trellis‐based codes and off‐the‐shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

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.

We consider a binary energy harvesting communication system with a finite battery transmitter over a noisy channel, and design explicit and implementable codes based on concatenation of a nonlinear trellis code (NLTC) with an outer low density parity check (LDPC) code. We propose two different decoding methods where the simplified one ignores the memory in the battery state while the more sophisticated one utilizes the memory. Numerical results demonstrate that the designed codes outperform other reference schemes. The results also show the superiority of the improved decoding approach over the naive solution.

We focus on short block length code design for Gaussian interference channels (GICs) using trellis-based codes. We employ two different decoding techniques at the receiver side, namely, joint maximum likelihood (JML) decoding and single user (SU) minimum distance decoding. For different interference levels (strong and weak) and decoding strategies, we derive error-rate bounds to evaluate the code performance. We utilize the derived bounds in code design and provide several numerical examples for both strong and weak interference cases. We show that under the JML decoding, the newly designed codes offer significant improvements over the alternatives of optimal point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check (LDPC) codes with the same block lengths.

Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios, such as radio frequency identification (RFID) systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for the use in such systems taking into account both energy transmission and error rate requirements. In particular, we propose using concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. We design the NLTC based on maximization of its free distance. We give necessary and sufficient conditions for its catastrophicity; in order to avoid catastrophic codes, we connect each designed NLTC to a corresponding linear convolutional code allowing for the use of simpler conditions for verification. Furthermore, we use EXIT charts to design the outer LDPC code while fixing the inner NLTC. Via examples, we demonstrate that our designed codes operate at ~0.8 dB away from the information theoretic limits, and they outperform both regular LDPC codes and optimized irregular LDPC codes for additive white Gaussian noise (AWGN) channels. In addition, we show that the proposed scheme outperforms the reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode.

Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios such as RFID systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for use in such systems taking into account both energy transmission and error rate requirements. Specifically, we propose using concatenation of a nonlinear trellis code with an outer low density parity check code. Via examples, we observe that our designed codes operate at SNRs 2.4dB away from information theoretic limits, and they outperform reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode. We note that it is possible to close the gap to the information theoretic limits further by more sophisticated receiver designs and more complex encoders.