In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and output alphabets. This is the first bound of this type that explicitly uses the method of expurgation. It is shown that the exponent of this bound is greater than or equal to those of previously known bounds.
This work studies point-to-point, multiple access, and random access lossless source coding in the finite-blocklength regime. In each scenario, a random coding technique is developed and used to analyze third-order coding performance. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region with an improved converse that relies on a connection to composite hypothesis testing. For dependent sources, the result implies that the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The conce…
A new universal coding/decoding scheme for random access with collision detection is given in the case of two senders. The result is used to give an achievable joint source-channel coding error exponent for multiple access channels in the case of independent sources. This exponent is improved in a modified model that admits error free 0 rate communication between the senders.
Signature coding for multiple access OR channel is considered. We prove that in block asynchronous case the upper bound on the minimum code length asymptotically is the same as in the case of synchronous access.
Here we write in a unified fashion (using "R(P, Q, D)") the random coding exponents in channel coding and lossy source coding. We derive their explicit forms and show, that, for a given random codebook distribution Q, the channel decoding error exponent can be viewed as an encoding success exponent in lossy source coding, and the channel correct-decoding exponent can be viewed as an encoding failure exponent in lossy source coding. We then extend the channel exponents to arbitrary D, which corresponds for D > 0 to erasure decoding and for D < 0 to list decoding. For comparison, we also derive …
In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel decoding setting. We show that the random coding error exponent under optimum (i.e., maximum likelihood) PNC channel decoding can be achieved even under the sub-optimal XOR channel decoding. The derived achievability bounds provide us with valuable insight and can be used as a benchmark for the performance of practical channel-coded PNC systems employing low co…
In this paper we provide sufficient conditions for lossy transmission of functions of correlated data over a multiple access channel (MAC). The conditions obtained can be shown as generalized version of Yamamoto's result. We also obtain efficient joint source-channel coding schemes for transmission of discrete and continuous alphabet sources to recover the function values. Keywords: Joint source-channel coding, Graph coloring, Lipschitz functions, Correlated sources.
For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel coding problem and allows us to characterize the region of achievable rates when the receiver is able to decode each transmitted message at a different instant of time.We show an outer bound on this region and derive a simple coding scheme that can achieve, in particular settings, all rates within the region delimited by the outer bound. In addition, we propose a…
In this paper, we study the upper and the lower bounds on the joint source-channel coding error exponent with decoder side-information. The results in the paper are non-trivial extensions of the Csiszar's classical paper [5]. Unlike the joint source-channel coding result in [5], it is not obvious whether the lower bound and the upper bound are equivalent even if the channel coding error exponent is known. For a class of channels, including the symmetric channels, we apply a game-theoretic result to establish the existence of a saddle point and hence prove that the lower and upper bounds are th…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. Körner and Marton showed for distributed source coding that such function decoding can be achieved more efficiently than decoding the full information sources. Compute-and-forward has shown that function decoding, in combination with network coding ideas, is a useful building block for end-to-end communication. In both cases, good computation codes are the key component in the coding schemes. In this wo…
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent $α$. The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to $\frac{1}{4 α\log e} \log^2 n$. Then a coding strategy is proposed, with a Bayes redundancy equivalent to the maximin redundancy. At last, an adaptive algorithm is provided, whose redundancy is equivalent to the minimax redundancy
Leveraging recent progress in physical-layer network coding we propose a new approach to random access: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. The throughput of the proposed strategy is derived and shown to be significantly superior to the best known strategies, including multipacket reception.
This work contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both users. These universal decoders are certain variants of the maximum mutual information (MMI) universal decoder, which achieve the corresponding random coding exponents of optimal decoding. In addition, we introduce some lower bounds, which involve optimization over very few parameters, unlike the original, exact exponents, which involve minimizations over auxilia…
This paper studies the random-coding exponent of joint source-channel coding for the multiple-access channel with correlated sources. For each user, by defining a threshold, the messages of each source are partitioned into two classes. The achievable exponent for correlated sources with two message-dependent input distributions for each user is determined and shown to be larger than that achieved using only one input distribution for each user. A system of equations is presented to determine the optimal thresholds maximizing the achievable exponent. The obtained exponent is compared with the o…
In ALOHA-type packetized network, the transmission times of packets follow a stochastic process. In this paper, we advocate a deterministic approach for channel multiple-access. Each user is statically assigned a periodic protocol signal, which takes value either zero or one, and transmit packets whenever the value of the protocol signal is equal to one. On top of this multiple-access protocol, efficient channel coding and network coding schemes are devised. We illustrate the idea by constructing a transmission scheme for the tandem collision network, for both slot-synchronous and slot-asynchr…
We consider ensembles of channel codes that are partitioned into bins, and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs. Two main conclusions arise from this analysis: (i) for independent random selection of codewords within a given type class, the random coding exponent of optimal bin index decoding is given by the ordinary random coding exponent function, computed at the rate of the entire code, independently of the exponential rate of the size of the bin. (ii) for this ensemble of …
We consider the one helper source coding problem posed and investigated by Ahlswede, Körner and Wyner. In this system, the error probability of decoding goes to one as the source block length $n$ goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper we provide a much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.
Reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs) is considered. In MARCs, only the destination is interested in a reconstruction of the sources, while in MABRCs, both the relay and the destination want to reconstruct the sources. We allow an arbitrary correlation among the sources at the transmitters, and let both the relay and the destination have side information that are correlated with the sources. Two joint source-channel coding schemes are presented and the corresponding sets of suffi…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels a…
This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather …
In the traditional index coding problem, a server employs coding to send messages to $n$ clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation is that, learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each cl…
We consider the problem of transmission of several distributed sources over a multiple access channel (MAC) with side information at the sources and the decoder. Source-channel separation does not hold for this channel. Sufficient conditions are provided for transmission of sources with a given distortion. The source and/or the channel could have continuous alphabets (thus Gaussian sources and Gaussian MACs are special cases). Various previous results are obtained as special cases. We also provide several good joint source-channel coding schemes for a discrete/continuous source and discrete/co…
We analyze the optimal trade-off between the error exponent and the excess-rate exponent for variable-rate Slepian-Wolf codes. In particular, we first derive upper (converse) bounds on the optimal error and excess-rate exponents, and then lower (achievable) bounds, via a simple class of variable-rate codes which assign the same rate to all source blocks of the same type class. Then, using the exponent bounds, we derive bounds on the optimal rate functions, namely, the minimal rate assigned to each type class, needed in order to achieve a given target error exponent. The resulting excess-rate e…
We consider the problem of transmission of several distributed correlated sources over a multiple access channel (MAC) with side information at the sources and the decoder. Source-channel separation does not hold for this channel. Sufficient conditions are provided for transmission of sources with a given distortion. The source and/or the channel could have continuous alphabets (thus Gaussian sources and Gaussian MACs are special cases). Various previous results are obtained as special cases. We also provide several good joint source-channel coding schemes for discrete sources and discrete/con…
Due to the short and bursty incoming messages, channel access activities in a wireless random access system are often fractional. The lack of frequent data support consequently makes it difficult for the receiver to estimate and track the time varying channel states with high precision. This paper investigates random multiple access communication over a compound wireless channel where channel realization is known neither at the transmitters nor at the receiver. An achievable rate and error probability tradeoff bound is derived under the non-asymptotic assumption of a finite codeword length. Th…
In this paper a new method to construct zero cross correlation code with the help of Pascal's triangle pattern called Pascal's Triangle Matrix Code (PTMC) for Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA) system is successfully developed. The advantages of this code are simplicity of code construction, flexibility of choosing code weight and number of users. The numerical comparison shows that the newly constructed code is better in code length than the existing codes such as Optical Orthogonal Code (OOC), Hadamard, Modified Frequency Hopping (MFH) and Modified Do…
Index coding employs coding across clients within the same broadcast domain. This typically assumes that all clients learn the coding matrix so that they can decode and retrieve their requested data. However, learning the coding matrix can pose privacy concerns: it may enable clients to infer information about the requests and side information of other clients [1]. In this paper, we formalize the intuition that the achieved privacy can increase by decreasing the number of rows of the coding matrix that a client learns. Based on this, we propose the use of $k$-limited-access schemes: given an i…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the rate information among each other or with the receiver. The receiver will either decode the message or report a collision depending on whether reliable message recovery is possible. It was shown that, asymptotically as the codeword length goes to infinity, the set of communication rates supporting reliable message recovery can be characterized by an achievable …
This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding which extends to infinite and c…
In 1973, Gallager proved that the random-coding bound is exponentially tight for the random code ensemble at all rates, even below expurgation. This result explained that the random-coding exponent does not achieve the expurgation exponent due to the properties of the random ensemble, irrespective of the utilized bounding technique. It has been conjectured that this same behavior holds true for a random ensemble of linear codes. This conjecture is proved in this paper. Additionally, it is shown that this property extends to Poltyrev's random-coding exponent for a random ensemble of lattices.
We investigate the computation of Csiszar's bounds for the joint source-channel coding (JSCC) error exponent, E_J, of a communication system consisting of a discrete memoryless source and a discrete memoryless channel. We provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained. These equivalent representations can be readily computed for arbitrary source-channel pairs via Arimoto's algorithm. When the channel's distribution satisfies a symmetry property, the bounds admit closed-form parametric expressions. We then use our results…
The error exponent of Markov channels with feedback is studied in the variable-length block-coding setting. Burnashev's classic result is extended and a single letter characterization for the reliability function of finite-state Markov channels is presented, under the assumption that the channel state is causally observed both at the transmitter and at the receiver side. Tools from stochastic control theory are used in order to treat channels with intersymbol interference. In particular the convex analytical approach to Markov decision processes is adopted to handle problems with stopping time…
In this paper we address the problem of transmission of correlated sources over a fast fading multiple access channel (MAC) with partial channel state information available at both the encoders and the decoder. We provide sufficient conditions for transmission with given distortions. Next these conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal power allocation strategy and compare the strategy with various levels of channel state information. Keywords: Fading MAC, Power allocation, Partial channel state information, Correlated sources.
This work presents a polar coding scheme for fading channels, focusing primarily on fading binary symmetric and additive exponential noise channels. For fading binary symmetric channels, a hierarchical coding scheme is presented, utilizing polar coding both over channel uses and over fading blocks. The receiver uses its channel state information (CSI) to distinguish states, thus constructing an overlay erasure channel over the underlying fading channels. By using this scheme, the capacity of a fading binary symmetric channel is achieved without CSI at the transmitter. Noting that a fading AWGN…
The error exponent of a discrete memoryless channel is expressed in two forms. One is Gallager's expression with a positive slope parameter and the other is Csiszar and Korner's information-theoretic representation expressed using the mutual information and the relative entropy. They differ in appearance, and existing methods to prove their agreement are not elementary, as they require an evaluation of the KKT conditions that the optimal distribution must satisfy. Similarly, there are two types of expressions for the strong converse exponent. They are Arimoto's expression with a negative slope…
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. The former universally achieves corner points of the capacity region and the latter u…
We study the transmission of correlated sources over discrete memoryless (DM) multiple-access-relay channels (MARCs), in which both the relay and the destination have access to side information arbitrarily correlated with the sources. As the optimal transmission scheme is an open problem, in this work we propose a new joint source-channel coding scheme based on a novel combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding, and obtain the corresponding sufficient conditions. The proposed coding scheme is based on the decode-and-forward strategy, …
This work considers reliable transmission of general correlated sources over the multiple-access relay channel (MARC) and the multiple-access broadcast relay channel (MABRC). In MARCs only the destination is interested in a reconstruction of the sources, while in MABRCs both the relay and the destination want to reconstruct the sources. We assume that both the relay and the destination have correlated side information. We find sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rate. For correlated s…
Lossy coding of correlated sources over a multiple access channel (MAC) is studied. First, a joint source-channel coding scheme is presented when the decoder has correlated side information. Next, the optimality of separate source and channel coding, that emerges from the availability of a common observation at the encoders, or side information at the encoders and the decoder, is investigated. It is shown that separation is optimal when the encoders have access to a common observation whose lossless recovery is required at the decoder, and the two sources are independent conditioned on this co…
A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources. Specifically, the focus is on lossy compression of exponential and Laplacian sources, which is subsequently expanded using a finite alphabet prior to being quantized. Due to decomposability property of such sources, the resulting random variables post expansion are independent and discrete. Thus, each of the expanded levels corresponds to an independent discrete so…
We derive various error exponents in the bee identification problem under two different decoding rules. Under naïve decoding, which decodes each bee independently of the others, we analyze a general discrete memoryless channel and a relatively wide family of stochastic decoders. Upper and lower bounds to the random coding error exponent are derived and proved to be equal at relatively high coding rates. Then, we propose a lower bound on the error exponent of the typical random code, which improves upon the random coding exponent at low coding rates. We also derive a third bound, which is relat…
We analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in Wyner's wiretap channel setting using wiretap channel codes constructed from both i.i.d. and constant-composition random codes. Our analysis for those sampled from i.i.d. random coding ensemble shows that the previously-known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble. Furthermore, our analysis on wiretap channel codes constructed from the ensemble of constant-composition random codes leads to an exponent which, in a…
This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a …
Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal, and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler "separation" strategy where separate codebooks are used for the source coding and the channel coding tasks. In the present paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and …
We derive various error exponents for communication channels with random states, which are available non-causally at the encoder only. For both the finite-alphabet Gel'fand-Pinsker channel and its Gaussian counterpart, the dirty-paper channel, we derive random coding exponents, error exponents of the typical random codes (TRCs), and error exponents of expurgated codes. For the two channel models, we analyze some sub-optimal bin-index decoders, which turn out to be asymptotically optimal, at least for the random coding error exponent. For the dirty-paper channel, we show explicitly via a numeri…
In this paper, we propose a new polar coding scheme for the unsourced, uncoordinated Gaussian random access channel. Our scheme is based on sparse spreading, treat interference as noise and successive interference cancellation (SIC). On the transmitters side, each user randomly picks a code-length and a transmit power from multiple choices according to some probability distribution to encode its message, and an interleaver to spread its encoded codeword bits across the entire transmission block. The encoding configuration of each user is transmitted by compressive sensing, similar to some prev…
We study error exponents for source coding with side information. Both achievable exponents and converse bounds are obtained for the following two cases: lossless source coding with coded information (SCCSI) and lossy source coding with full side information (Wyner-Ziv). These results recover and extend several existing results on source-coding error exponents and are tight in some circumstances. Our bounds have a natural interpretation as a two-player game between nature and the code designer, with nature seeking to minimize the exponent and the code designer seeking to maximize it. In the Wy…
An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, an error-exponent is derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring the sequence's gap to capacity, using the new exponent, is demonstrated.
In this letter, we extend the sparse Kronecker-product (SKP) coding scheme, originally designed for the additive white Gaussian noise (AWGN) channel, to multiple input multiple output (MIMO) unsourced random access (URA). With the SKP coding adopted for MIMO transmission, we develop an efficient Bayesian iterative receiver design to solve the intended challenging trilinear factorization problem. Numerical results show that the proposed design outperforms the existing counterparts, and that it performs well in all simulated settings with various antenna sizes and active-user numbers.
This paper considers the Gaussian multiple-access channel (MAC) in the asymptotic regime where the number of users grows linearly with the code length. We propose efficient coding schemes based on random linear models with approximate message passing (AMP) decoding and derive the asymptotic error rate achieved for a given user density, user payload (in bits), and user energy. The tradeoff between energy-per-bit and achievable user density (for a fixed user payload and target error rate) is studied, and it is demonstrated that in the large system limit, a spatially coupled coding scheme with AM…
In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the number of other devices B having the same performance as one device A. In this paper, based on the concept of "representing the performance of one coding system A_n by the number of other coding systems B_n", we consider the merits of an encoder that can access the side information in the fixed-length source coding in general sources. The purpose of this pap…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For i.i.d. random coding…
This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel 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 i.i.d. random coding, and that the inclusion may be strict. The inner bound is e…
