A non-iterative phase noise compensation method based on the sum-product algorithm (SPA) is applied to the outputs of intersymbol interference (ISI) channels. The outputs are modeled as independent Gaussian random variables, and the receiver applies mismatched processing with von Mises statistics. The performance is compared with that of linear minimum-mean-square-error filtering. The SPA achieves higher information rates at similar complexity for three channel types: ISI-free, standard single-mode fiber, and multipath channels with orthogonal frequency-division multiplexing.

Scalar quantization and probabilistic shaping are applied to the distributed source coding of Gaussian sources, with mean-square error distortion. A coding scheme with a modulo interval, dithering, and truncated Gaussian shaping is shown to achieve the corner points of the Berger-Tung region. The theory is illustrated by designing short-block-length multilevel 5G polar codes for Wyner-Ziv (WZ) polar coded quantization (PCQ). WZ-PCQ substantially reduces the total distortion compared to separate PCQ of the source blocks.

Scalar lattice quantization with a modulo operator, dithering, and probabilistic shaping is applied to the Wyner-Ziv (WZ) problem with a Gaussian source and mean square error distortion. The method achieves the WZ rate-distortion pairs. The analysis is similar to that for dirty paper coding but requires additional steps to bound the distortion because the modulo shift is correlated with the source noise. The results extend to vector sources by reverse waterfilling on the spectrum of the covariance matrix of the source noise. Simulations with short polar codes illustrate the performance and compare with scalar quantizers and polar coded quantization without dithering.

Joint detection and decoding (JDD) achieves rates based on information theory but is too complex to implement for many channels with memory or nonlinearities. Successive interference cancellation (SIC) at the receiver, combined with multistage encoding at the transmitter, is a method that lets one use coded modulation for memoryless channels to approach JDD rates. A SIC-based receiver is presented to compensate for inter-channel interference in long-haul optical fiber links. Simulations for 1000 km of standard single-mode fiber with ideal distributed Raman amplification, single-polarization transmission, and circularly symmetric complex Gaussian (CSCG) modulation show that SIC attains the achievable information rates (AIRs) of JDD using surrogate channel models with correlated phase and additive noise (CPAN). Moreover, the AIRs of ring constellations are compared to those of CSCG modulation. Simulations show that 32 rings, 16 SIC-stages, and Gaussian message passing on the factor graph of the CPAN surrogate model achieve the JDD rates of CSCG modulation. The computational complexity scales in proportion to the number of SIC-stages, where one stage has complexity similar to separate detection and decoding.

Reliable communication over bandlimited and nonlinear channels usually requires equalization to simplify receiver processing. Equalizers that perform joint detection and decoding (JDD) achieve the highest information rates but are often too complex to implement. To address this challenge, model-based neural network (NN) equalizers that perform successive interference cancellation (SIC) are shown to approach JDD information rates for bandlimited channels with a memoryless nonlinearity and additive white Gaussian noise. The NNs are chosen to have a periodically time-varying and recurrent structure that imitates the forward-backward algorithm (FBA) in every SIC stage. Simulations for short-haul fiber-optic links with square-law detection show that NN-SIC nearly doubles current spectral efficiencies, and bipolar or complex-valued modulations achieve energy gains of up to 3 dB compared to state-of-the-art intensity modulation. Moreover, NN-SIC is considerably less complex than equalizers that perform JDD, mismatched FBA processing, and Gibbs sampling.

The capacity-achieving input distribution of non-coherent Rayleigh fading channels with average- and peak-power constraints is known to be discrete with a finite number of points. We sharpen this result by deriving upper and lower bounds on the number of amplitude levels. The upper bounds are based on two techniques from complex analysis: counting the number of maxima of a function that characterizes the Karush-Kuhn-Tucker conditions and an oscillation theorem. The latter provides a stronger bound but applies only if the average power constraint is inactive.

A multi-input multi-output (MIMO) Gaussian chan-nel with two transmit antennas and two receive antennas is studied that is subject to an input peak-power constraint. The ca-pacity and the capacity-achieving input distribution are unknown in general. The problem is shown to be equivalent to a channel with an identity matrix but where the input lies inside and on an ellipse with principal axis length$r_{p}$and minor axis length$r_{m}$. If$r_{p}\leq\sqrt{2}$, then the capacity-achieving input has support on the ellipse. A sufficient condition is derived under which a two-point distribution is optimal. Finally, if$r_{m} < r_{p}\leq\sqrt{2}$, then the capacity-achieving distribution is discrete.

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to approach the information rates of joint detection and decoding (JDD) with considerably less complexity than JDD and other existing equalizers. Simulations for short-haul optical fiber links with square-law detection illustrate the gains.

A coding scheme for broadcast channels (BCs) is proposed that shifts the users' code blocks by different amounts of time and applies alternating Gelfand-Pinsker encoding. The scheme achieves all rate tuples in Marton's region for two receiver BCs without time-sharing or rate-splitting. Simulations with short polar codes show that the method reduces the gap to capacity as compared to time-sharing.

A coding scheme with scalar lattices is applied to K-receiver, Gaussian, vector broadcast channels with K independent messages, one for each receiver. The method decomposes each receiver channel into parallel scalar channels with known interference and applies dirty paper coding with a modulo interval, amplitude shift keying (ASK), and probabilistic shaping to each scalar channel. The achievable rate tuples include all points inside the capacity region by choosing truncated Gaussian shaping, large ASK alphabets, and large modulo intervals.

To accommodate extremely high data rates, provide high reliability, improve coverage, and meet traffic demands in future wireless communication networks, novel technologies have emerged that exploit electromagnetic waves, large multiple-antenna systems, intelligent reflective surfaces, hardware innovations, new network architectures, and higher frequency bands. Considering advances in information theory and devices, fundamental questions arise for system designers on how to develop synergies between theory and practice. Current design and analysis methods are predominantly based on scalar-quantity, far-field, planar-wavefront, monochromatic, and other non-physically consistent assumptions, which can lead to significant mismatches with systems designed based on realistic propagation models.

The maximum information rates for bandlimited channels with direct detection are achieved with joint detection and decoding (JDD), but JDD is often too complex to implement. Two receiver structures are studied to reduce complexity: separate detection and decoding (SDD) and successive interference cancellation (SIC). For bipolar modulation, frequency-domain raised-cosine pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves rates close to those of JDD, thereby attaining significant energy gains over SDD and intensity modulation. Gibbs sampling further reduces the detector complexity and achieves rates close to those of the forward-backward algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high SNR. Simulations with polar codes, higher-order modulation, and multi-level coding confirm the predicted gains.

An upper bound is derived on the secret key rates of a general multiterminal wiretap channel. The bound unifies and generalizes some of the previously known bounds. Additionally, a multivariate dependence balance bound is introduced that is of independent interest.

Stability properties of Bernstein’s characterization of Gaussian vectors are derived. Stability leads to a soft doubling argument through which one can prove capacity theorems without requiring the existence of capacity-achieving distributions.

The stability of Bernstein’s characterization of Gaussian distributions is extended to vectors by utilizing characteristic functions. Stability is used to develop a soft doubling argument that establishes the optimality of Gaussian vectors for certain communications channels with additive Gaussian noise, including two-receiver broadcast channels. One novelty is that the argument does not require the existence of distributions that achieve capacity.

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence. The additional requirement of invertibility usually leads to using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best one-to-one encoders have divergences that grow logarithmically with the block length. To overcome this limitation, an encoder is proposed that has an invertible one-to-many mapping and a low-rate random number generator (RNG). Two algorithms are developed to design the mapping by assigning strings in either a most-likely first or least-likely first order. Both algorithms give information rates approaching the entropy of the target distribution with exponentially decreasing divergence and with vanishing RNG rate in the block length.

Distribution matchers for finite alphabets are shown to have informational divergences that grow logarithmically with the block length, generalizing a basic result for binary strings.

Feedback is shown to increase the sum-rate capacity of K-user Gaussian multiple-access channels by at most a factor of approximately 1.54, improving Thomas’ doubling bound (1987). The new bound is the best possible in the sense that it can be approached as closely as desired for a massive number of users. Moreover, feedback provides unbounded power gain in K for a fixed transmit power per user.

The key agreement problem with biometric or physical identifiers and two terminals for key enrollment and reconstruction is considered. A nested convolutional code construction that performs lossy compression with side information is proposed. Nested convolutional codes are an alternative to nested polar codes and nested random linear codes that achieve all points of the key-leakage-storage regions of the generated-secret and chosen-secret models for long block lengths. Our design uses a convolutional code for vector quantization during enrollment and a subcode of it for error correction during reconstruction. Physical identifiers with small bit error probability are considered to illustrate the gains of the proposed construction. One variant of nested convolutional codes improves on all previous constructions in terms of the key vs. storage rate ratio but it has high complexity. Another variant of nested convolutional codes with lower complexity performs similarly to previously designed nested polar codes. The results suggest that the choice of convolutional or polar codes for key agreement with identifiers depends on the complexity constraints.

A framework for stealth communication with vanishing power (VP) is presented by studying binary symmetric channels. Coding theorems are proved by modifying Gallager's error exponents for VP and by applying resolvability exponents. The analysis unifies and generalizes existing rate bounds for covert and stealth communication.

Two new classes of skew codes over a finite field F are proposed, called skew convolutional codes and skew trellis codes. These two classes are defined by, respectively, left or right sub-modules over the skew fields of fractions of skew polynomials over $\mathbb{F}$. The skew convolutional codes can be represented as periodic time-varying ordinary convolutional codes. The skew trellis codes are in general nonlinear over $\mathbb{F}$. Every code from both classes has a code trellis and can be decoded by Viterbi or BCJR algorithms.

A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of Rényi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables which is of independent interest.

The feedback sum-rate capacity is established for the symmetric J -user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the factorization of a convex envelope of Geng and Nair (2014). The converse bound matches the achievable sum-rate of the Fourier-Modulated Estimate Correction strategy of Kramer (2002).

A distribution matcher (DM) encodes a binary input data sequence into a sequence of symbols with a desired target probability distribution. Several DMs, including shell mapping and constant- composition distribution matcher (CCDM), have been successfully employed for signal shaping, e.g., in optical-fiber or 5G. The CCDM, like many other DMs, is typically implemented by arithmetic coding (AC). In this work we implement AC based DMs using finite-precision arithmetic (FPA). An analysis of the implementation shows that FPA results in a rate-loss that shrinks exponentially with the number of precision bits. Moreover, a relationship between the CCDM rate and the number of precision bits is derived.

A memoryless state-dependent multiple access channel (MAC) is considered where two transmitters wish to convey a respective message to a receiver while simultaneously estimating the respective channel state via generalized feedback. The scenario is motivated by a joint radar and communication system where the radar and data applications share the same bandwidth. An achievable capacity-distortion tradeoff region is derived that outperforms a resource-sharing scheme through a binary erasure MAC with binary states.

A basic model for key agreement with biometric or physical identifiers is extended to include measurements of a hidden source through a general broadcast channel (BC). An inner bound for strong secrecy, maximum key rate, and minimum privacy-leakage and database-storage rates is proposed. The inner bound is shown to be tight for physically-degraded and less-noisy BCs.

The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of the key-leakage-storage regions of the generated-secret and chosen-secret models. The second construction uses nested polar codes for vector quantization during enrollment and for error correction during reconstruction. The simulation results show that the nested polar codes achieve privacy leakage and storage rates that improve on existing code designs. One proposed code achieves a rate tuple that cannot be achieved by existing methods.

The two-party key agreement problem with public discussion, known as the source model problem, is considered for an erasure model for Eve's side information. By relating the key agreement problem to hypothesis testing, a new coding scheme is developed that yields an upper bound on the maximum erasure probability for which the secret-key (SK) capacity is zero. The bound is shown to be tight when Alice's or Bob's source is binary, and this shows that the new code achieves larger SK rates than the best known coding scheme. A full version of this paper with extensions to general models for Eve's side information is available in [1].

A communication setup is considered where a transmitter wishes to simultaneously sense its channel state and convey a message to a receiver. The state is estimated at the transmitter by means of generalized feedback, i.e. a strictly causal channel output that is observed at the transmitter. The scenario is motivated by a joint radar and communication system where the radar and data applications share the same frequency band. For the case of a memoryless channel with i.i.d. state sequences, we characterize the capacity-distortion tradeoff, defined as the best achievable rate below which a message can be conveyed reliably while satisfying some distortion constraint on state sensing. An iterative algorithm is proposed to optimize the input probability distribution. Examples demonstrate the benefits of joint sensing and communication as compared to a separation-based approach.

The feedback sum-rate capacity is established for the symmetric three-user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the “doubling trick” of Geng and Nair (2014). The converse bound matches the achievable sum-rate of the Fourier-Modulated Estimate Correction strategy of Kramer (2002). The proof arguments extend to GMACs with more than three users.

We investigate lossy compressed sensing (CS) of a hidden, or remote, source, where a sensor observes a sparse information source indirectly. The compressed noisy measurements are communicated to the decoder for signal reconstruction with the aim to minimize the mean square error distortion. An analytically tractable lower bound to the remote rate-distortion function (RDF), i.e., the conditional remote RDF, is derived by providing support side information to the encoder and decoder. For this setup, the best encoder separates into an estimation step and a transmission step. A variant of the Blahut-Arimoto algorithm is developed to numerically approximate the remote RDF. Furthermore, a novel entropy coding based quantized CS method is proposed. Numerical results illustrate the main rate-distortion characteristics of the lossy CS, and compare the performance of practical quantized CS methods against the proposed limits.

The key-leakage-storage region is derived for a generalization of a classic two-terminal key agreement model. The additions to the model are that the encoder observes a hidden, or noisy, version of the identifier, and that the encoder and decoder can perform multiple measurements. To illustrate the behavior of the region, the theory is applied to binary identifiers and noise modeled via binary symmetric channels. In particular, the key-leakage-storage region is simplified by applying Mrs. Gerber's lemma twice in different directions to a Markov chain. The growth in the region as the number of measurements increases is quantified. The amount by which the privacy-leakage rate reduces for a hidden identifier as compared to a noise-free (visible) identifier at the encoder is also given. If the encoder incorrectly models the source as visible, it is shown that substantial secrecy leakage may occur and the reliability of the reconstructed key might decrease.

Optical fiber signals with high power exhibit spectral broadening that seems to limit capacity. To study spectral broadening, the autocorrelation function of the output signal given the input signal is derived for a simplified fiber model that has zero dispersion, distributed optical amplification (OA), and idealized spatial noise processes. The autocorrelation function is used to upper bound the output power of bandlimited or time-resolution limited receivers, and thereby to bound spectral broadening and the capacity of receivers with thermal noise. The output power scales at most as the square-root of the launch power, and thus capacity scales at most as one-half the logarithm of the launch power. The propagating signal bandwidth scales at least as the square-root of the launch power. However, in practice the OA bandwidth should exceed the signal bandwidth to compensate attenuation. Hence, there is a launch power threshold beyond which the fiber model loses practical relevance. Nevertheless, for the mathematical model an upper bound on capacity is developed when the OA bandwidth scales as the square-root of the launch power, in which case capacity scales at most as the inverse fourth root of the launch power.

The downlink of symmetric Cloud Radio Access Networks (C-RANs) with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton's coding which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow's technique to augment the system with an auxiliary random variable. The bounds are studied over scalar Gaussian C-RANs and are shown to meet and characterize the capacity for interesting regimes of operation.

A waveform channel is considered where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise. A discrete-time channel model that considers the effect of filtering on the phase noise is developed. The model is based on a multi-sample receiver, i.e., an integrate-and-dump filter whose output is sampled at a rate higher than the signaling rate. It is shown that, at high Signal-to-Noise Ratio (SNR), the multi-sample receiver achieves a rate that grows logarithmically with the SNR if the number of samples per symbol (oversampling factor) grows with the cubic root of the SNR. Moreover, the pre-log factor is at least 1/2 and can be achieved by amplitude modulation. For an approximate discrete-time model of the multi-sample receiver, the capacity pre-log at high SNR is shown to be at least 3/4 if the number of samples per symbol grows with the square root of the SNR. The analysis shows that phase modulation achieves a pre-log of at least 1/4, while amplitude modulation still achieves a pre-log of 1/2. This is strictly greater than the capacity pre-log of the (approximate) discrete-time Wiener phase noise channel with only one sample per symbol, which is 1/2. Numerical simulations are used to compute lower bounds on the information rates achieved by the multi-sample receiver. The simulations show that oversampling is beneficial for both strong and weak phase noise at high SNR. In fact, the information rates are sometimes substantially larger than when using commonly-used approximate discrete-time models.

Two discrete-time interference channel models are developed for information transmission over a single span of optical fiber using wavelength-division multiplexing (WDM) and lumped amplification. The models are derived from the nonlinear Schrödinger equation by including the nonlinear phenomena of self-phase modulation (SPM) and cross-phase modulation (XPM), but ignoring four-wave mixing, polarization effects and group velocity dispersion (GVD) within WDM bands. The first model also ignores GVD across WDM bands, referred to as group velocity mismatch (GVM). For the case of two users, a new technique called interference focusing is proposed where each carrier achieves the capacity pre-log 1, thereby doubling the pre-log of 1/2 achieved by using conventional methods. For three users, interference focusing is also useful under certain conditions. The second model captures GVM and the effect of filtering at the receivers in addition to SPM and XPM. In a 3-user system, it is shown that all users can achieve the maximum pre-log factor 1 simultaneously by using interference focusing, a time-limited pulse and a bank of filters at the receivers.

The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A uniform approximation lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. Without leakage constraints the inner bound recovers Marton's region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios.

A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semideterministic and physically degraded BCs, and the results are compared with those of the corresponding BCs without a secrecy constraint. Black well and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.

The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bit of capacity for all signal-to-noise ratios (SNRs). The 2-D bound is within 0.15 bits of capacity provably up to 4.5 dB; numerical evidence suggests a similar gap for all SNRs. As the SNR tends to infinity, these bounds are accurate and match with a volume-based lower bound. For the 2-D complex case, an analytic lower bound is derived by using a concentric constellation and is shown to be within 1 bit of capacity.

A class of two-relay diamond networks is studied where the broadcast component is modelled by two independent bit-pipes and the multiple-access component is memoryless. A new upper is derived on the capacity which generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). For binary adder MACs, the upper bound establishes the capacity for all ranges of bit-pipe capacities.

Lossy compressed sensing (CS) of a sparse source is studied. A lower bound to the best achievable compression performance in a finite rate CS setup is established by providing support side information to the encoder and decoder. The rate-distortion problem is formulated via remote source coding and conditional rate-distortion theory. The best encoder separates into an estimation step and a rate-dependent transmission step. Numerical results illustrate the rate-distortion behavior of the scheme.

A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes the bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all the ranges of bit-pipe capacities.

The Wyner-Ahlswede-Körner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques, such as Wyner-Ziv coding, binning, and superposition coding. Furthermore, a semi-deterministic (SD) broadcast channel (BC) with one-sided decoder cooperation is considered. Duality principles relating the two problems are presented, and the capacity region for the SD-BC setting is derived. The direct part follows from an achievable region for a general BC that is tight for the SD scenario. A converse is established by using telescoping identities. The SD-BC is shown to be operationally equivalent to a class of relay-BCs, and the correspondence between their capacity regions is established. The capacity region of the SD-BC is transformed into an equivalent region that is shown to be dual to the admissible region of the WAK problem in the sense that the information measures defining the corner points of both regions coincide. Achievability and converse proofs for the equivalent region are provided. For the converse, we use a probabilistic construction of auxiliary random variables that depends on the distribution induced by the codebook. Several examples illustrate the results.

Short message noisy network coding (SNNC) differs from long message noisy network coding (LNNC) in that one transmits many short messages in blocks rather than using one long message with repetitive encoding. Two properties of SNNC are developed. First, SNNC with backward decoding achieves the same rates as SNNC with offset encoding and sliding window decoding for memoryless networks where each node transmits a multicast message. The rates are the same as LNNC with joint decoding. Second, SNNC enables early decoding if the channel quality happens to be good. This leads to mixed strategies that unify the advantages of decode-forward and noisy network coding.

A concatenation of two encoders is used to construct channel resolvability codes. The code of the first encoder has large minimum distance and the second encoder is linear and has a sparse generator matrix. If the first encoder has encoding complexity O(n) or O(n log n), where n is the length of the codewords, an overall encoding complexity O(n log n) can be achieved. One can tune the sparsity to trade off the complexity of the second encoder against the minimum distance requirement of the first code, and to trade off the complexity of one of the encoders and the informational divergence scaling.

A continuous-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A lower bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. The proposed lower bound suggests that the capacity pre-log depends on the oversampling factor, and amplitude and phase modulation do not equally contribute to capacity at high SNR.

The broadcast channel (BC) with one confidential message and where the decoders cooperate via a one-sided link is considered. A pair of messages is transmitted, one message for each user. The message to the cooperative user is confidential and is kept secret from the cooperation-aided user. The secrecy level is measured by the equivocation rate. An inner bound on the secrecy-capacity region of the BC is derived. The inner bound is achieved by double-binning the codebook of the secret message. The inner bound is tight for the semi-deterministic (SD) and physically degraded (PD) cases. The secrecy results are compared to those of the corresponding BCs without a secrecy constraint. A cooperative Blackwell channel example illustrates the impact of secrecy on the rate regions.

Upper and lower bounds on the capacity of Gaussian multicast relay channels are shown to be quasi-concave in the receiver signal-to-noise ratios and the transmit correlation coefficient. The bounds considered are the cut-set bound, decode-forward (DF) rates, and quantize-forward rates. The DF rates are shown to be quasi-concave in the relay position and this property is used to optimize the relay position for example networks.

The capacity-achieving input distribution of the discrete-time additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bits of capacity for all signal-to-noise ratios (SNRs). The two-dimensional bound is within 0.15 bits of capacity provably up to 4.5 dB, and numerical evidence suggests a similar gap for all SNRs.

A discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. An upper bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. If the oversampling factor grows as SNRαfor 0 ≤ α ≤ 1, then the capacity pre-log is at most (1 + α)/2 at high SNR.

The semi-deterministic (SD) broadcast channel (BC) where the decoders cooperate via a one-sided link is considered and its capacity region is derived. The direct proof relies on an achievable region for the general BC that is tight for the SD scenario. This achievable region follows by a coding scheme that combines rate-splitting and binning with Marton and superposition coding. The SD-BC is shown to be operationally equivalent to a class of relay-BCs (RBCs) and the correspondence between their capacity regions is established. Furthermore, a dual source coding problem, referred to as the Wyner-Ahlswede-Körner (WAK) problem with one-sided encoder cooperation, is proposed. Transformation principles between the problems are presented and the optimal rate region for the AK problem is stated. The SD-BC capacity and the admissible region of the AK problem are shown to be dual to one another in the sense that the information measures defining the corner points of both regions coincide. Special cases of the two problems are inspected and shown to maintain duality.

The capacity region of deterministic, half-duplex, line networks with two sources is established. Capacity is achieved with superposition coding. The main novelty is the converse proof for which a property of optimal codes is identified, namely that the symbol input to the node immediately after the second source node may as well identify the latter node's output symbol.

An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schrödinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.

A continuous-time model for the additive white Gaussian noise (AWGN) channel in the presence of white (memoryless) phase noise is proposed and discussed. It is shown that for linear modulation the output of the baud-sampled filter matched to the shaping waveform represents a sufficient statistic. The analysis shows that the phase noise channel has the same information rate as an AWGN channel but with a penalty on the average signal-to-noise ratio, the amount of penalty depending on the phase noise statistic.

A class of diamond networks is studied where the broadcast component is modelled by two independent bit-pipes. New upper and lower bounds are derived on the capacity which improve previous bounds. The upper bound is in the form of a max-min problem, where the maximization is over a coding distribution and the minimization is over an auxiliary channel. The proof technique generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The bounds are evaluated for a Gaussian multiple access channel (MAC) and the binary adder MAC, and the capacity is found for interesting ranges of the bit-pipe capacities.

A discrete-time Wiener phase noise channel model is introduced in which multiple samples are available at the output for every input symbol. A lower bound on the capacity is developed. At high signal-to-noise ratio (SNR), if the number of samples per symbol grows with the square root of the SNR, the capacity pre-log is at least 3/4. This is strictly greater than the capacity pre-log of the Wiener phase noise channel with only one sample per symbol, which is 1/2. It is shown that amplitude modulation achieves a pre-log of 1/2 while phase modulation achieves a pre-log of at least 1/4.

The Ahlswede-Körner (AK) coordination problem with one-sided encoder cooperation is considered. Encoder co-operation refers to communication between the encoders via a finite-capacity one-sided link. For this setting, the coordination capacity region is derived. The optimal coding scheme leverages the link between the encoders to optimally handle the correlation between the sources. Moreover, the scheme incorporates several source coding techniques, such as Wyner-Ziv coding, binning and superposition coding. Furthermore, a dual semi-deterministic broadcast channel (BC) with one-sided cooperative decoders is considered. Transformation principles between the two problems are presented and an achievable rate region for the BC setting is derived. The region of the BC is shown to be dual to the optimal region of the AK problem in the sense that the information measures defining the corner points in both regions coincide. Although the optimality of the achievable region for the semi-deterministic BC setting is yet to be shown, the region is optimal in the fully-deterministic case.

A security measure called effective security is defined that includes strong secrecy and stealth communication. Effective secrecy ensures that a message cannot be deciphered and that the presence of meaningful communication is hidden. To measure stealth we use resolvability and relate this to binary hypothesis testing. Results are developed for wire-tap channels and broadcast channels with confidential messages.

Capacity computations are presented for Faster-Than-Nyquist (FTN) signaling in the presence of interference from neighboring frequency bands. It is shown that Shannon's sinc pulses maximize the spectral efficiency for a multi-access channel, where spectral efficiency is defined as the sum rate in bits per second per Hertz. Comparisons using root raised cosine pulses show that the spectral efficiency decreases monotonically with the roll-off factor. At high signal-to-noise ratio, these pulses have an additive gap to capacity that increases monotonically with the roll-off factor.

A class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks. The multiuser model is called an information network with in-block memory (NiBM). It is shown that block-fading channels, channels with state known causally at the encoder, and relay networks with delays are NiBMs. A cut-set bound is developed for NiBMs that unifies, strengthens, and generalizes existing cut bounds for discrete memoryless networks. The bound gives new finite-letter capacity expressions for several classes of networks including point-to-point channels, and certain multiaccess, broadcast, and relay channels. Cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action-dependent state available causally at the encoder and for relays without delay. Finally, quantize-forward network coding is shown to achieve rates within an additive gap of the new cut-set bound for linear, additive, Gaussian noise channels, symmetric power constraints, and a multicast session.

A waveform channel is considered where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise (AWGN). A discrete-time channel model is introduced that is based on a multi-sample receiver. Tight lower bounds on the information rates achieved by the multi-sample receiver are computed by means of numerical simulations. The results show that oversampling at the receiver is beneficial for both strong and weak phase noise at high signal-to-noise ratios. The results are compared with results obtained when using other discrete-time models.

Conditions are derived on the interference channel with single-antenna nodes to achieve maximal degrees-of-freedom with only two symbol extensions. The conditions for line-of-sight channels involve choosing only the spacing between two subcarriers of an orthogonal frequency division multiplexing (OFDM) scheme. For 3 user pairs an upper bound on the sum-rate of interference alignment is approached arbitrarily closely.

Consider a waveform channel where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise (AWGN). A discrete-time channel model that takes into account the effect of filtering on the phase noise is developed. The model is based on a multi-sample receiver which, at high Signal-to-Noise Ratio (SNR), achieves a rate that grows logarithmically with the SNR if the number of samples per symbol grows with the square-root of the SNR. Moreover, the pre-log factor is at least 1/2 in this case.

The relay positioning problem is addressed for low signal-to-noise ratio Gaussian multicast relay networks where the objective is to maximize the multicast flow. A network coding based decode-and-forward (DF) strategy is presented that achieves strictly larger rates than a previously-studied routing based DF strategy. Properties of the multicast flow function are analyzed and efficient solutions are presented.

The capacity of noncoherent regular-fading relay channels is studied where all terminals are aware of the fading statistics but not of their realizations. It is shown that if the fading coefficient of the channel between the transmitter and the receiver can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high signal-to-noise ratio (SNR), the relay does not increase capacity. It is further shown that if the fading coefficient of the channel between the transmitter and the relay can be predicted more accurately from its infinite past than the fading coefficient of the channel between the relay and the receiver, then at high SNR, one can achieve communication rates that are within one bit of the capacity of the multiple-input single-output fading channel that results when the transmitter and the relay can cooperate.

A pair of strings (X,Y) put out by a memoryless source needs to be reliably communicated over a memoryless broadcast channel. Receiver 1 hasYas side information and must reconstructXto within some distortion. Receiver 2 hasXand must reconstructYto within some distortion. The problem is motivated by the broadcast phase (downlink) of the two-way relay channel. We characterize reliable communication for Gaussian sources with quadratic distortion functions; conditionally independent sources; deterministic distortion functions; and small distortions with Hamming distortion functions. The last result is obtained by solving a new version of the broadcast problem with Steinberg's common-reconstruction decoding constraint.

In this paper, we review some recent advances in the design of ADCs that exploit system-driven metrics, such as the bit-error rate in a communication link, or mutual information in a scheme employing forward error correction. We show, for example, that ADCs can be designed that maximize the information rate between the quantized output of the channel and the input to the channel for communication links with intersymbol-interference and additive noise. These ADCs dramatically outper-form (in terms of achievable information rates) traditional ADC design methods that are based on fixed uniform quantization. Architectures are also developed for ADCs such that system-metrics can be used to dynamically adapt the structure of the ADC to optimize application meaningful criteria, such as bit-error rate for communication over intersymbol interference links.

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. In the classical discrete memoryless network (DMN), every node incurs a delay. A well-known result for the classical DMN is the cut-set outer bound. In this paper, we generalize the model of the DMN in such a way that some nodes may incur no delay, and we obtain the cut-set outer bound for the generalized DMN.

Short message noisy network coding (SNNC) transmits independent short messages in blocks rather than using long message repetitive encoding. SNNC is shown to achieve the same rates as noisy network coding (NNC) for discrete memoryless networks where each node transmits a multicast message. One advantage of SNNC is that backward decoding may be used which simplifies the analysis and understanding of the achievability proof. The analysis reveals that each decoder may ignore certain other nodes rather than including their message in the decoding procedure. Additionally, SNNC enables early decoding at nodes if the channel quality happens to be good.

A network with in-block memory (NiBM) is a generalization of a discrete memoryless network (DMN) where blocks of symbols may have memory inside each block. A cut-set bound is developed for NiBMs that generalizes and strengthens existing cut bounds. This bound gives the capacity for point-to-point channels with iBM.

Binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio (L-value) domain. A hard decision results in the Gallager B algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 dB in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

Analog-to-digital converters that maximize the information rate between the quantized channel output sequence and the channel input sequence are designed for discrete-time channels with intersymbol-interference, additive noise, and for independent and identically distributed signaling. Optimized scalar quantizers with Λ regions achieve the full information rate of log2(Λ) bits per channel use with a transmit alphabet of size Λ at infinite signal-to-noise ratio; these quantizers, however, are not necessarily uniform quantizers. Low-precision scalar and two-dimensional analog-to-digital converters are designed at finite signal-to-noise ratio, and an upper bound on the information rate is derived. Simulation results demonstrate the effectiveness of the designed quantizers over conventional quantizers. The advantage of the new quantizers is further emphasized by an example of a channel for which a slicer (with a single threshold at zero) and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal-to-noise ratio, in contrast to memoryless binary signaling and an optimized quantizer.

A discrete-time two-user interference channel model is developed that captures non-linear phenomena that arise in optical fiber communication employing wavelength-division multiplexing (WDM). The effect of non-linearity is that an amplitude variation on one carrier induces a phase variation on the other carrier. Moreover, the model captures the effect of group velocity mismatch that introduces memory in the channel. It is shown that both users can achieve the maximum pre-log factor of 1 simultaneously by using an interference focusing technique introduced in an earlier work.

The rate-distortion (RD) function for source coding with complementary side-information is characterised for several special cases of the general problem. These include Steinberg's common-reconstruction setting, small distortions for both sources, zero distortion for one source, conditionally independent sources, and deterministic distortion measures.

We consider the discrete-time channel with intersymbol-interference and additive noise under output analog-to-digital conversion (quantization) at the receiver. The analog-to-digital converter is optimized so as to maximize the information rate between the quantized channel output sequence and the channel input sequence, where the input sequence has independent and identically distributed symbols. An upper bound on the information rate is derived. Simulation results demonstrate the effectiveness of the designed quantizers over conventional quantizers at 1-bit/sample precision. The advantage of those quantizers is further emphasized by an example of a channel for which a simple slicer and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal-to-noise ratio, in contrast to memoryless binary signaling and an optimized quantizer.

Quantize-map-forward (QMF) and noisy network coding (NNC) differ primarily from compress-forward relaying in that relays do not hash their quantization bits. Two further differences are that source nodes use “long”-message repetitive encoding and destination nodes use simultaneous joint decoding. Recent work has shown that classic “short”-message encoding combined with backward decoding achieves the same rates as QMF and NNC. A simplified proof of this result is given.

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called “spectral loss” is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels.

A recent inner bound on the capacity region of the two-receiver discrete memoryless broadcast channel is shown to be equivalent to the Marton-Gelfand-Pinsker region. The proof method is based on a result of Gelfand and Pinsker concerning channel input distributions.

The sum-rate capacity of the parallel Gaussian interference channel is shown to be achieved by independent transmission across subchannels and treating interference as noise if the channel coefficients and power constraints satisfy a certain condition. The condition requires the interference to be weak, a situation commonly encountered, e.g., in digital subscriber line transmission. The optimal power allocation is characterized by using the concavity of the sum-rate capacity as a function of the power constraints.

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.

A memoryless interference network model is introduced that is based on non-linear phenomena observed when transmitting information over optical fiber using wavelength-division multiplexing. The main characteristic of the model is that amplitude variations on one carrier wave are converted to phase variations on another carrier wave, i.e., the carriers interfere with each other through amplitude-to-phase conversion. For the case of two carriers, a new technique called interference focusing is proposed where each carrier achieves the capacity pre-log 1, thereby doubling the pre-log of 1/2 achieved by using conventional methods. The technique requires neither channel time variations nor global channel state information. Generalizations to more than two carriers are outlined.

The focus is on noise-free half-duplex line networks with two sources where the first node and either the second node or the second-last node in the cascade act as sources. In both cases, we establish the capacity region of rates at which both sources can transmit independent information to a common sink. The achievability scheme presented for the first case is constructive while the achievability scheme for the second case is based on a random coding argument.

The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.

The “Japanese” theorem is extended to multiple multicast sessions in an arbitrary network to characterize the routing capacity region by the intersection of an infinite collection of halfspaces. An elimination technique is developed to simplify this infinite description into a finite one based upon the shortest routing paths and trees in the network graph. This result is used as a step in providing the capacity regions for two multimessage multicast problems on undirected ring networks; in the first case only unicast and broadcast sessions are considered, and in the second case multicast sessions where the source and destination vertices form lines of adjacent vertices are studied. Network coding is generally necessary to achieve network capacity, but for our multimessage multicast problems, new arguments are used to demonstrate that routing can achieve network coding bounds.

The Marton-Gelfand-Pinsker inner bound on the capacity region of broadcast channels was extended by Han-Costa to include arbitrarily correlated sources where the capacity region is replaced by an admissible source region. The main arguments of Han-Costa are correct but unfortunately the authors overlooked an inequality in their derivation. The corrected region is presented and the absence of the omitted inequality is shown to sometimes admit sources that are not admissible.

This paper considers an interference network composed of K half-duplex single-antenna pairs of users who wish to establish bi-directional communication with the aid of a multi-input-multi-output (MIMO) half-duplex relay node. This channel is referred to as the ¿MIMO wireless switch¿ since, for the sake of simplicity, our model assumes no direct link between the two end nodes of each pair implying that all communication must go through the relay node (i.e., the MIMO switch). Assuming a delay-limited scenario, the fundamental limits in the high signal-to-noise ratio (SNR) regime is analyzed using the diversity-multiplexing tradeoff (DMT) framework. Our results sheds light on the structure of optimal transmission schemes and the gain offered by the relay node in two distinct cases, namely reciprocal and non-reciprocal channels (between the relay and end-users). In particular, the existence of a relay node, equipped with a sufficient number of antennas, is shown to increase the multiplexing gain; as compared with the traditional fully connected K-pair interference channel. To the best of our knowledge, this is the first known example where adding a relay node results in enlarging the pre-log factor of the sum rate. Moreover, for the case of reciprocal channels, it is shown that, when the relay has a number of antennas at least equal to the sum of antennas of all the users, static time allocation of decode and forward (DF) type schemes is optimal. On the other hand, in the non-reciprocal scenario, we establish the optimality of dynamic decode and forward in certain relevant scenarios.

The sum-rate capacity of the parallel Gaussian interference channel is studied. Sufficient conditions are derived in terms of channel coefficients and power constraints such that the sum-rate capacity can be achieved by: 1) independent transmission across sub-channels, and 2) treating interference as noise in each sub-channel. The optimal power allocation is characterized for such parallel channels.

We study the three-user multi-antenna Gaussian multiple-access channel (MAC) where prior to the transmission over the MAC the transmitters can communicate with each other over noise-free broadcast pipes of given capacities. We present the capacity region of this channel. Additionally, we also study the three-user multi-antenna Gaussian MAC with common messages and present its capacity region. The main step in deriving these two capacity results consists in proving that Gaussian distributions maximize certain mutual information expressions under multiple Markov constraints. Towards this end, a tool previously used is extended to the vector case and to multiple Markov conditions.

Cooperative communications refers to network communication where nodes cooperate, rather than compete, to transmit data for themselves and others. The main goal of this talk is to review basic strategies for cooperative communications with particular emphasis on a method called “compress-and-forward”. This method has recently been used successfully to treat a variety of theoretical problems concerning relaying, e.g., determining antenna-clustering capacities, the diversity-multiplexing tradeoff, scaling laws of networks, oblivious communication rates, and suggesting problems for which cut-set bounds can be improved. Some of these results are reviewed in detail.

A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this paper. Specifically, it is shown that if the channel crosstalk coefficient magnitudes lie below thresholds defined by the power constraints then single-user detection at each receiver is sum-rate optimal, i.e., treating the interference as noise incurs no loss in performance. This is the first capacity result for the Gaussian interference channel with weak to moderate interference. Furthermore, for certain mixed (weak and strong) interference scenarios, the new outer bounds give a corner point of the capacity region.

In this paper, we study the optimal transceiver structure for achieving sum-rate capacity of a parallel Gaussian symmetric interference channel. Specifically, we derive a set of channel and power constraint conditions such that the total sum-rate capacity can be achieved by treating interference as noise in each sub-channel. The property of the optimal power allocation is also characterized for such parallel channels.

Rapid acquisition of accurate crosstalk estimates is a core requirement for effective preceding in digital subscriber line (DSL) systems. It is shown that signal-to-noise ratio (SNR) reports provided by customer premises equipment (CPE) can be used to perform this task by "tuning" the precoder, i.e., iterating alternate steps of estimation and precoder adaptation. Such an approach has the advantage that it can be applied to legacy CPEs. Estimation algorithms are designed using techniques from stochastic control.

The problem of sending a pair of correlated sources through a broadcast channel with correlated side information at the receivers is studied from a joint source-channel coding perspective. Sufficient and necessary conditions are provided for reliable transmission. The two conditions are identical except for the left-hand side of one of three inequalities. For two special cases the problem is solved completely: when one side information is a function of the sources, and when a certain Markov property is satisfied on the sources and side information.

An outer bound on the capacity region of the two-user Gaussian interference channel is derived. The bound shows that for low power and small crosstalk coefficients the sum-rate capacity is achieved by treating interference as noise. The results are generalized to multiuser channels.

We consider the problem of source coding with receiver side information for the simple network proposed by R. Gray and A. Wyner in 1974. In this network, a transmitter must reliably transport the output of two correlated information sources to two receivers using three noiseless channels: a public channel which connects the transmitter to both receivers, and two private channels which connect the transmitter directly to each receiver. We extend Gray and Wyner's original problem by permitting side information to be present at each receiver. We derive inner and outer bounds for the achievable rate region and, for three special cases, we show that the outer bound is tight.

We investigate network coding in star networks with multiple unicast sessions. We use entropy arguments to upper bound the simultaneous rates of communication among the different nodes in the network and prove that in many cases, the optimal network code is related to the combinatorial optimization problem of finding the maximum number of edge disjoint cycles in the demand graph of the network. Finally, we propose a polynomial time algorithm with linear binary operations that achieves the capacity in many cases.

Outer bounds on the capacity region of broadcast channels are reviewed and a new outer bound is presented.

The compound wire-tap channel is studied, which is based on Wynerpsilas wire-tap model with both the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states. No matter which states occur for the two channels, the source wishes to guarantee that the destination decodes its message successfully and that the wire-tapper does not obtain the source message. The semideterministic compound wire-tap channel is first studied, in which the channel from the source to the destination is deterministic and has only one state. The secrecy capacity is obtained. An example parallel Gaussian compound wire-tap channel is then studied, in which both channels have two states. Three schemes are studied, and it is shown that introducing randomness either into the source message or into the encoder achieves the maximal secrecy degree of freedom. Both channels studied in this paper demonstrate that creating an auxiliary input, and hence adding a prefix channel from this auxiliary input to the actual channel input, improves the secrecy rate.

The problem of a nomadic terminal sending information to a remote destination via agents with lossless connections to the destination is investigated. Such a setting suits, e.g., access points of a wireless network where each access point is connected by a wire to a wireline-based network. The Gaussian codebook capacity for the case where the agents do not have any decoding ability is characterized for the Gaussian channel. This restriction is demonstrated to be severe, and allowing the nomadic transmitter to use other signaling improves the rate. For both general and degraded discrete memoryless channels, lower and upper bounds on the capacity are derived. An achievable rate with unrestricted agents, which are capable of decoding, is also given and then used to characterize the capacity for the deterministic channel.

Binary message-passing decoders for LDPC codes are analyzed using EXIT charts. For the analysis, the variable node decoder performs all computations in the L-value domain. For the special case of a hard decision channel, this leads to the well-know Gallager B algorithm, while the analysis can be extended to channels with larger output alphabets. By increasing the output alphabet from hard decisions to four symbols, a gain of more than 1.0 dB is achieved using optimized codes. For this code optimization, the mixing property of EXIT functions has to be modified to the case of binary message-passing decoders.

An achievable region, outer bounds and a capacity result are established for two-sender two-receiver interference channels with one cognitive transmitter. Specifically, we assume that one transmitter knows either the full or, more realistically, the partial message of the other transmitter due to its cognitive capabilities. The achievable region is obtained by a rate-splitting strategy, which generalizes prior strategies under both weak and strong interference conditions. The outer bounds are based on an extension of the Nair-El Gamal outer bound for the broadcast channel capacity. When only the partial message is known to the cognitive user, the capacity region in strong interference is established. In this regime, the interference is such that both receivers can decode both messages with no rate penalty.

We develop an extension of the Japanese theorem to multiple multicast sessions and interpret the result in terms of the collection of minimal length routing trees for the various multicast sessions. We use this result as a step in providing the capacity region for multiple unicast and broadcast sessions on an undirected ring network via a simple characterization of the family of bounds needed. We further demonstrate that routing is rate-optimal using new extensions to progressive d-separating edge set bounds.

The thirty-four papers in this special issue are devoted to models, theories, and codes for relaying and cooperation in communication networks. The demand for large, more efficient, reliable, and cost effective communication networks is motivating new network architectures for cellular and wireless communications as well as cognitive radio and sensor networks.

A rate distortion problem is solved that is motivated by a quantum data compression problem. The goal is to send information about a source string x so that a receiver can construct a second string y for which the joint empirical probability distribution of x and y is close to some desired distribution. The problem differs from the usual rate distortion problems in that one must consider both remote sources and distortion functions that are not averages of per-letter distortion functions

A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner bound reduces to an inner bound on the capacity region of broadcast channels that includes an inner bound of Marton, and Gel'fand and Pinsker. The outer bound reduces to a new outer bound on the capacity region of broadcast channels that generalizes an outer bound of Marton to include a common message, and that generalizes an outer bound of Gel'fand and Pinsker to apply to general discrete memoryless broadcast channels. The proof for the outer bound simplifies the proof of Gel'fand and Pinsker that was based on a recursive approach. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels.

Capacity regions are established for several two-sender, two-receiver channels with partial transmitter cooperation. First, the capacity regions are determined for compound multiple- access channels (MACs) with common information and compound MACs with conferencing. Next, two interference channel models are considered: an interference channel with common information (ICCI) and an interference channel with unidirectional cooperation (ICUC) in which the message sent by one of the encoders is known to the other encoder. The capacity regions of both of these channels are determined when there is strong interference, i.e., the interference is such that both receivers can decode all messages with no rate penalty. The resulting capacity regions coincide with the capacity region of the compound MAC with common information.

An offset encoding technique is presented that improves sliding-window decoding with decode-and-forward for K-user multiple-access relay channels. The technique offsets user transmissions by one block per user and achieves the corner points of the destination's backward decoding rate regions but with a smaller delay. As a result, one achieves boundary points of the best known decode-and-forward rate regions with a smaller delay than with backward decoding.

The capacity region for multiple unicast sessions on a bidirectional ring network is established and is shown to be achieved by routing. The proof uses recently developed progressive d-separating edge set bounds, new extensions of these bounds, as well as tools from the literature on the multicommodity flow problem

Dependence balance bounds of Hekstra and Willems are generalized and refined. The new bounds are applied to the K-user multiaccess channel (MAC) with output feedback, and they are shown to establish the feedback sum-rate capacity for the Gaussian MAC when all users have the same per-symbol power constraints. The sum-rate capacity is achieved by Fourier modulated estimate correction. The feedback sum-rate capacity is shown to improve the no-feedback capacity by only log log K nats per use for large K. The new bounds also improve on cut-set bounds for asymmetric powers and rates.

The multicast capacity is determined for networks that have deterministic channels with broadcasting at the transmitters and no interference at the receivers. The multicast capacity is shown to have a cut-set interpretation. It is further shown that one cannot always layer channel and network coding in such networks. The proof of the latter result partially generalizes to discrete memoryless broadcast channels and is used to bound the common rate for problems where one achieves a cut bound on throughput.

The capacity of additive white Gaussian noise relay channels under Gaussian fading is investigated. The transmitter, the relay, and the receiver are all considered to be ignorant of the fading realizations. Capacity upper and lower bounds are derived with focus on the capacity pre-log, i.e., the limiting ratio of the capacity to the logarithm of the signal-to-noise ratio. Conditions are presented under which the upper and lower bounds on the capacity pre-log coincide

A bound on network coding rates is developed that generalizes an edge-cut bound on routing rates. The bound involves progressively removing edges from a network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound, and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature

A multi-access problem is considered where two encoders wish to communicate their messages to two decoders. The encoders can further cooperate via a conference, as introduced by Willems for multi-access channels. The capacity region of this channel is shown to be the intersection of the capacity regions of two multi-access channels with partially cooperating encoders

It is shown that one cannot always layer, or separate, channel and network coding for multicasting in deterministic relay networks with no interference. We call such networks Aref networks. The suboptimality of such layering in Aref networks is in contrast to the optimality of a similar layering in networks of discrete memoryless channels and certain networks of two-way channels

The common problem of a nomadic terminal sending information to a remote destination via agents with lossless connections is investigated. Such a setting suits, e.g. access points of a wireless network, where each access point is equipped with a different connection bandwidth. The case where these agents do not have any decoding ability is fully characterized for the Gaussian channel, when the transmitter uses "typical" codewords. For general discrete memoryless channels, lower and upper bounds are derived. An achievable rate with unrestricted agents, which are capable of decoding, is also given and then demonstrated by a numerical example for the Gaussian channel

The performance of source-cooperation in a multi-access network is compared to that of using a wireless relay. The former network is modeled as a multi-access channel with generalized feedback and the latter as a multi-access relay channel. Using power as the cost metric, achievable rates and outage probabilities for the two networks are compared under a total transmit power constraint and a specified geometry. The use of a relay is shown to be advantageous for a variety of wireless fading channels

Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.

A network of two way channels (TWCs) is specified by a graph having an edge between vertex u and vertex v if there is a TWC between these vertices. A new cut-set bound is determined for such networks when network coding is permitted, and some implications of this bound are discussed.

Low-delay decoding schemes based on window decoding are developed for the multiaccess channel with generalized feedback (MAC-GF). It is shown that window decoding sometimes incurs a rate loss as compared to backward decoding. Wireless cases are found for which the achievable rates with backward or window decoding give the capacity region.

A three-tier hierarchical wireless sensor network is considered that consists of a cluster of sensors, an intermediate relay with better computing and communication capabilities than the sensors, and a central server or access point. Such a network can be modeled as a multiple-access relay channel (MARC) with additive white Gaussian noise and fading. Capacity bounds for this network are presented with and without constraints on simultaneous reception and transmission by the relay. The results identify cooperative strategies between the relay and sensors for increasing network capacity. These strategies also preserve limited battery resources by eliminating the need for cooperation between sensors.

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.

Two outer bounds on the capacity region of the two-user Gaussian interference channel (IFC) are derived. The idea of the first bound is to let a genie give each receiver just enough information to decode both messages. This bound unifies and improves the best known outer bounds of Sato and Carleial. Furthermore, the bound extends to discrete memoryless IFCs and is shown to be equivalent to another bound of Carleial. The second bound follows directly from existing results of Costa and Sato and possesses certain optimality properties for weak interference.

A discrete memoryless network (DMN) is a memoryless multiterminal channel with discrete inputs and outputs. A sequence of inner bounds to the DMN capacity region is derived by using code trees. Capacity expressions are given for three classes of DMNs: (1) a single-letter expression for a class with a common output, (2) a two-letter expression for a binary-symmetric broadcast channel (BC) with partial feedback, and (3) a finite-letter expression for push-to-talk DMNs. The first result is a consequence of a new capacity outer bound for common output DMNs. The third result demonstrates that the common practice of using a time-sharing random variable does not include all time-sharing possibilities, namely, time sharing of channels. Several techniques for improving the bounds are developed: (1) causally conditioned entropy and directed information simplify the inner bounds, (2) code trellises serve as simple code trees, (3) superposition coding and binning with code trees improves rates. Numerical computations show that the last technique enlarges the best known rate regions for a multiple-access channel (MAC) and a BC, both with feedback. In addition to the rate bounds, a sequence of inner bounds to the DMN reliability function is derived. A numerical example for a two-way channel illustrates the behavior of the error exponents.

An achievable region for the L-channel multiple description coding problem is presented. This region generalizes two-channel results of El Gamal and Cover (1982) and of Zhang and Berger (1987). It further generalizes three-channel results of Gray and Wyner (1974) and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the rate-distortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.

A white Gaussian interference network is a channel with T transmitters and R receivers where the received symbols are linear combinations of the transmitted symbols and white Gaussian noise. This paper considers the case where K messages are transmitted through the network in a point-to-point manner, i.e., each message is encoded by exactly one transmitter and is destined for exactly one receiver. It is further assumed that feedback is available so that each transmitter sees the outputs of the receivers to which it is sending messages. Communication strategies based on the discrete Fourier transform (DFT) are developed that perform well for such networks. For multiple-access channels (K=T, R=1) with equal transmitter powers the strategies achieve the feedback sum-rate capacity if the powers are beyond some threshold. For the same channels with fixed transmitter powers and large K, the achievable sum-rate is approximately (log log K)/2 larger than the sum-rate capacity without feedback. For broadcast channels (T=1, K=R) with strong symmetries, the strategies achieve a monotonically increasing sum-rate with K. For interference channels (K=T=R) with strong interference, the strategies significantly enlarge the no-feedback capacity region by "correlation routing.".

New achievability results for the L-stage successive refinement problem with L>2 are presented. These are derived from a recent achievability result for the more general problem of multiple description (MD) coding with L>2 channels. It is shown that successive refinability on chains implies successive refinability on trees and that memoryless Gaussian sources are successively refinable on chains and trees.

Feedback strategies are presented for the class of two-user discrete memoryless multiple-access channels for which one of the inputs to the channel is determined by the second input and the channel output. The strategies achieve any rate point inside the capacity region of these channels.