Discrete Memoryless Multiple-access Channel Research Articles

Multiple Access Channel Resolvability Codes From Source Resolvability Codes

We show that the problem of code construction for multiple access channel (MAC) resolvability can be reduced to the simpler problem of code construction for source resolvability. Specifically, we propose a MAC resolvability code construction that relies on a combination of multiple source resolvability codes, used in a black-box manner, and leverages randomness recycling implemented via distributed hashing and block-Markov coding. Since explicit source resolvability codes are known, our results also yield the first explicit coding schemes that achieve the entire MAC resolvability region for any discrete memoryless multiple-access channel with binary input alphabets.

Error Exponents for Asynchronous Multiple Access Channels, Controlled Asynchronism May Outperform Synchronism

Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless multiple access channels with two senders, via the method of subtypes, a refinement of the method of types. An empirical entropy decoder is employed. A key tool is an improved packing lemma, that overcomes the technical difficulty caused by codeword repetitions via an induction based new argument. The asymptotic form of the bounds admits numerical evaluation. This demonstrates that error exponents achievable by synchronous transmission can be superseded via controlled asynchronism, i.e. a deliberate shift of the codewords.

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with “single-user” or sequential decoding can yield better achievable rates. For instance, the compute–forward problem examines the scenario of recovering $L \le K$ linear combinations of transmitted codewords over a $K$ -user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute–forward over a $K$ -user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.

Cooperative Resolvability and Secrecy in the Cribbing Multiple-Access Channel

We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.

Covert Communication Over a $K$ -User Multiple-Access Channel

We consider a scenario in which $K$ transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless multiple-access channel (MAC) while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the $K$ transmitters can transmit on the order of $\sqrt {n}$ reliable and covert bits per $n$ channel uses, exceeding which, the warden will be able to detect the communication. We identify the optimal pre-constants of the scaling, which leads to a complete characterization of the covert capacity region of the $K$ -user binary-input MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike the traditional MAC capacity region. We also characterize the channel conditions that have to be satisfied for the transmitters to operate without a secret key.

Towards an Algebraic Network Information Theory: Simultaneous Joint Typicality Decoding

Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering $L \le K$ linear combinations of transmitted codewords over a $K$-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. Here, we develop bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and apply them to obtain a larger achievable region for compute-forward over a $K$-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.

A Joint Typicality Approach to Compute–Forward

This paper presents a joint typicality framework for encoding and decoding nested linear codes in multi-user networks. This framework provides a new perspective on compute–forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing a linear combination over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute–forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, our framework provides some valuable insights on establishing the optimal decoding rate region for compute–forward by considering joint decoders, progressing beyond most previous works that consider successive cancellation decoding. Specifically, this paper establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from $K$ senders.

Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions.

The $K$ -User Vector Gaussian Multiple-Access Channel With General Messages Sets: Capacity, Polymatroidal Structure, and Efficient Computation

The capacity region of the $K$ -user vector Gaussian multiple-access channel with general message sets is established. Furthermore, due to the presence of convexity, both in the discrete and continuous senses, it is shown that this capacity region is efficiently computable. The capacity result is obtained by specializing recent results by the authors for the discrete memoryless multiple-access channel and demonstrating that it suffices to only consider jointly Gaussian input and auxiliary random variables. For this second conclusion, it is shown that jointly Gaussian random variables maximize entropy subject to lattice conditional independence and covariance constraints, a result that is of interest in its own right. Discrete convexity arises since the capacity region is a union of polymatroids . Over each polymatroid, computing the maximal weighted sum rates is simple due to submodularity—a discrete analog of concavity—of the set function associated with the linear inequalities that define the polymatroid. Continuous convexity arises as the set of admissible covariance matrices is convex and the polymatroidal bounds are concave in these covariances.

Multiuser Random Coding Techniques for Mismatched Decoding

This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensemble average, and positive within the interior of Lapidoth's achievable rate region. This exponent proves the ensemble tightness of the exponent of Liu and Hughes in the case of maximum-likelihood decoding. An equivalent dual form of Lapidoth's achievable rate region is given, and the latter is shown to extend immediately to channels with infinite and continuous alphabets. In the setting of single-user mismatched decoding, similar analysis techniques are applied to a refined version of superposition coding, which is shown to achieve rates at least as high as standard superposition coding for any set of random-coding parameters.

Impact of the relay on the coverage region of multiple‐access channels

From practical and theoretical viewpoints, performance analysis of communication systems by using information-theoretic results is important. In this study, first, the authors obtain a general achievable rate region for three-user discrete memoryless multiple-access relay channel (MARC) via partial decode and forward strategy and regular block Markov encoding/backward decoding. Also by extending the discrete alphabet results to the continuous alphabet channel, an inner bound for three-user Gaussian MARC (GMARC) is achieved. Next, based on the inner bound of three-user GMARC, they analyse the impact of a relay on the coverage region of MARC, as a basic model for uplink communications between a base station and users with the help of a relay. This analysis includes the coverage region for the multiple-access channel and two-user GMARC as special cases. Considering rate regions for the GMARC and fading GMARC, it is proved that in a fixed transmission rate, the relay extends coverage region of the MARC. Numerical illustrations confirm their theoretical results.

Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel (MAC) with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's combinatorial central limit theorem, an inner bound on the set of locally achievable second-order coding rates is given for each point on the boundary of the capacity region. It is shown that the inner bound for constant-composition random coding includes that recovered by independent identically distributed random coding, and that the inclusion may be strict. The inner bound is extended to the Gaussian MAC via an increasingly fine quantization of the inputs.

Feedback, Cribbing, and Causal State Information on the Multiple-Access Channel

The benefits afforded by feedback and/or causal state information (SI) on the state-dependent discrete memoryless multiple-access channel (SD-MAC) with cribbing encoder/s are studied. Capacity regions are derived for communication scenarios whose capacities without cribbing are still unknown. It is shown that when the encoders can crib, the SD-MAC behaves less like a MAC and more like a single-user channel: 1) feedback does not help; 2) strictly causal SI does not help; and 3) causal SI to both encoders is best utilized using Shannon strategies. However, in asymmetric settings, the single-user-like behavior may or may not occur. For example, the SD-MAC with only one cribbing encoder is single-user-like when the state is revealed to the cribbing encoder, but not if it is revealed to the noncribbing encoder.

Discrete Memoryless Multiple-Access Wiretap Channel with Non-Cooperative Encoders

In this paper, the discrete memoryless multiple-access wiretap channel (MAC-WT) with non-cooperative encoders is studied, where two users (cooperation between the users is not allowed) transmit their corresponding confidential messages (no common message) to a legitimate receiver, while an additional wiretapper wishes to obtain the messages via a wiretap channel. The inner and outer bounds on the capacity-equivocation region are provided forthis new model, and the result is further explained via a binary example.

Key Agreement over a Generalized Multiple Access Channel Using Noiseless and Noisy Feedback

A secret key agreement framework involving three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. There is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 where the three users receive outputs from the channel. Furthermore, there is a feedback channel from user 3 to users 1 and 2 through which user 3 sends information extracted from the received output from the GDMMAC to increase the key rates. We consider both noiseless and noisy feedback. In the case of noiseless feedback, a public channel of unlimited capacity from user 3 to users 1 and 2 is used only once. In the case of noisy feedback, a noisy broadcast channel (BC) from user 3 to users 1 and 2 can be repeatedly used, like GDMMAC. In both setups, inner bounds of the secret key capacity region are derived. The secret key capacity region is derived in some special cases where the channel inputs and outputs form Markov chains in certain orders. For illustration, the corresponding results are also derived and discussed for Gaussian channels. The cases with noiseless feedback, noisy feedback, and no feedback at all are compared with each other.

Multiple-access channel with correlated states and cooperating encoders

In this study, a two-user discrete memoryless multiple-access channel with two correlated states known non-causally at the corresponding encoder is considered. Each encoder transmits a message independent of the other encoder's and tries to cooperate with it. To consider cooperative encoders, it is assumed that each encoder strictly-causally receives and finds out the other encoder's transmitted signals and tries to cooperate with the other encoder by transmitting its message. A special case is also studied in which the common part of the states is known at the both encoders, resulting in a larger rate region. For these two scenarios, achievable rate regions are derived using a combination of block-Markov and Gel'fand-Pinsker coding techniques, and outer bounds are also established. For the second scenario, the achievable rate region of the Gaussian model is derived, and some implications of the results are discussed.

A New Achievable Rate Region for the Multiple-Access Channel With Noiseless Feedback

A new single-letter achievable rate region is proposed for the two-user discrete memoryless multiple-access channel(MAC) with noiseless feedback. The proposed region includes the Cover–Leung rate region <citerefgrp xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <citeref refid="ref1"/></citerefgrp> , and it is shown that the inclusion is strict. The proof uses a block-Markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback. The rates of transmission are too high for each encoder to decode the other's message directly using the feedback, so they transmit correlated information in the next block to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder. The coding scheme may be viewed as a natural generalization of the Cover–Leung scheme with a delay of one extra block and a pair of additional auxiliary random variables. We compute the proposed rate region for two different MACs and compare the results with other known rate regions for the MAC with feedback. Finally, we show how the coding scheme can be extended to obtain larger rate regions with more auxiliary random variables.

Coset Codes for Compound Multiple Access Channels With Common Information

Code construction is considered for arbitrary discrete memoryless compound multiple access channels (MACs) with common information. This class of channels includes MACs with/without common messages or with partially cooperating encoders. A construction method of code ensembles based on coset codes is proposed for these channels. Assuming joint maximum likelihood decoding, the performance of the proposed code ensemble is analyzed by deriving a lower bound on error exponents. A condition assuring that codes achieve the capacity region on average is given. It is seen that an elaborate combination of good linear codes gives capacity achieving codes for compound MACs with common messages or with partially cooperating encoders. The use of restricted ensembles with low-density parity check (LDPC) codes as component codes is also discussed. It is shown that a coset code ensemble based on nonbinary regular LDPC codes approaches the random coding exponent, and thus is capacity-achieving.

A Note on Capacity Computation for the Discrete Multiple Access Channel

This paper deals with computation of the capacity region of the discrete memoryless multiple-access channel (MAC), which is equivalent to solving a difficult nonconvex optimization problem. In the literature, it is claimed that for elementary MACs, i.e., MACs for which the size of output alphabet is greater or equal to the sizes of all input alphabets, the Karush-Kuhn-Tucker conditions provide a necessary and sufficient condition for sum-rate optimality. In this paper, we demonstrate that this claim does not hold, even for two-user channels with binary input and binary output alphabets. Consequently, the capacity computation problem for the discrete MAC remains an interesting and mostly unsolved problem.

Polynomial-Time Decodable Codes for Multiple Access Channels

A construction of polynomial-time decodable codes for discrete memoryless multiple access channels (MACs) is proposed based on concatenated codes. Concatenated codes, originally developed by Forney, can achieve any rate below capacity for the single-user discrete memoryless channel while requiring only polynomial-time decoding complexity in the code length. In this letter, Forney's construction together with multi-level concatenation is generalized to MACs. An error exponent for the constructed code is derived, and it is shown that the constructed code can achieve any rate in the capacity region.