This paper studies the detection problem for the Gaussian random access channels, in which only a randomly chosen αK out of K senders wish to convey their messages to a receiver that has the side information of which sender is actively transmitting. A novel coding scheme, referred to as L-interleaved block coding, based on interleaving L single-user codes and successive cancellation decoding is proposed for the symmetric rate tuples in the capacity region of this channel. L-interleaved block coding with L sufficiently large is shown to achieve arbitrarily close to the symmetric capacity. Therefore, it replaces the efforts of finding capacity achieving codes for the Gaussian random access channels with selecting L off-the-shelf codes for Gaussian point-to-point channels for L sufficiently large. An example illustrates that this scheme with a small number of blocks (L = 16) achieves more than 0.95 of the symmetric capacity when two senders are active.

In the celebrated coded caching problem studied by Maddah-Ali and Niesen, the peak-traffic network load is to be reduced by first caching some information about contents into individual memories of end users during the off-peak hours and then upon user requests broadcasting some other information about the contents, which, combined with cached information, can let each user recover their requested content. Thus, information-theoretic studies of coded caching involve the optimal tradeoff among communication rates for the two phases of cache placement and content delivery, and the optimal construction of codes for cache placement and content delivery. In order to allow better utilization of network resources, this paper introduces a new caching model in which user requests can arise at any point of time during the cache placement phase, and proposes a successive refinement approach as an answer to this dynamic caching problem. For uniformly random file requests, the optimal tradeoff among average-case delivery rates are characterized when the cache rate is above a well-defined threshold. For arbitrary file requests, a successive caching algorithm is developed to simultaneously reduce worst-case delivery rates at every request time, which are uniformly within a constant multiplicative factor of their respective optima.

Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies the potential of structured coset coding as a complete replacement for random coding in network information theory. The roles of two techniques used in coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping via nested coset codes of the same generator matrix (which we refer to as homologous codes) and channel transformation is shown to achieve the same performance as traditional random codes for the general two-sender multiple access channel. The achievability proof of the capacity region is extended to multiple access channels with more than two senders, and with one or more receivers. A quantization argument adapted to the proposed combination of two techniques is presented to establish the achievability proof for their Gaussian counterparts. It is illustrated by an example that combining shaping and channel transformation is useful even when the goal of transmission for a subset of the receivers is to recover a linear combination of messages. These results open up new possibilities of utilizing homologous codes for a broader class of applications.

The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random ensembles of homologous codes, namely, structured nested coset codes from the same generator matrix and individual shaping functions, but when decoding is optimized with respect to the realization of the encoders. For the special case in which the desired linear combination is “matched” to the structure of the multiple access channel in a natural sense, these inner and outer bounds coincide. This result indicates that most, if not all, coding schemes for computation in the literature that rely on random construction of nested coset codes cannot be improved by using more powerful decoders such as the maximum likelihood decoder. The proof techniques are adapted to characterize the rate region for broadcast channels achieved by Marton's (random) coding scheme under maximum likelihood decoding. By generalizing some of the techniques, a single-letter outer bound for the capacity region of the computation problem is presented and compared with the inner bound achieved by homologous codes.

To reduce the network load during peak hours, servers deliver partial data to users during the off-peak time of the network before the actual requests are known, which is known as caching. This paper studies a single user caching problem in which the file contents are subject to dynamic modifications with respect to a certain probability distribution. To cope with the dynamical nature of the file contents, a successive refinement approach to caching is presented: partial information of the original data is cached first and then if there is a modification, a refinement to the previously cached data is delivered to the user. Given a fixed cache memory, there is a tension between the rates of two cache descriptions. The problem of optimal caching strategies is formulated through a successive Gray-Wyner network, the optimal rate region of which is characterized. Some lower and upper bounds on the performance of optimal caching strategies are developed and shown to actually yield closed form solutions for certain classes of file contents.

Recent studies by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar built the framework of nested coset codes for the computation problem, namely, computing a desired linear combination of sources over a multiple access channel. This paper presents an outer bound on the optimal rate region for the computation problem when the encoding strategy is restricted to random ensembles of homologous codes, namely, structured nested coset codes from the same generator matrix and individual shaping functions based on joint typicality encoding. The optimal rate region is characterized when the desired linear combination and the channel structure are matched. Under this condition, a suboptimal joint typicality decoding rule is shown to achieve the optimal rate region. This result implies that the performance of random homologous code ensembles cannot be improved by using the optimal maximum likelihood decoder for the aforementioned class of computation problems.

The Liu-Cuff-Verdu lemma states that in estimating a source X from an observation Y, making a random guess X' from the posterior p(xly) can go wrong at most twice as often as the optimal answer. Several variations of this fundamental, yet rather arcane, result are explored for detection, decoding, and estimation problems.

Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies the potential of structured coding as a complete replacement for random coding in network information theory. The roles of two techniques used in nested coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping and channel transformation is shown to achieve the same performance as traditional random codes for this channel model, which opens up new possibilities of utilizing nested coset codes with the same generator matrix for a broader class of applications.

In this paper, we propose a low complexity graph-based linear minimum mean-square-error (LMMSE) equalizer in order to remove inter-symbol and inter-stream interference in a multiple input multiple output (MIMO) communication. The proposed state space representation inflicted on the graph provides linearly increasing computational complexity with block length. In addition, owing to the Gaussian assumption used in the presented cycle-free factor graph, the complexity of the suggested equalizer structure is not affected by the size of the signaling space. In addition, we introduce an efficient way of computing extrinsic bit log-likelihood ratio values for the LMMSE estimation compatible with higher order alphabets, which is shown to perform better than the other methods in the literature. Overall, we provide an efficient receiver structure reaching high data rates in frequency selective MIMO systems, whose performance is shown to be very close to a genie-aided matched filter bound through extensive simulations.

We propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer which considers both the intersymbol interference (ISI) and the effect of non-white noise inherent in Faster-than-Nyquist (FTN) signaling. In order to incorporate the statistics of noise signal into the factor graph over which the LMMSE algorithm is implemented, we suggest a method that models it as an autoregressive (AR) process. Furthermore, we develop a new mechanism for exchange of information between the proposed equalizer and the channel decoder through turbo iterations. Based on these improvements, we show that the proposed low complexity receiver structure performs close to the optimal decoder operating in ISI-free ideal scenario without FTN signaling through simulations.

We propose a reduced complexity, graph based linear minimum mean square error (LMMSE) filter in which the non-white statistics of a random noise process are taken into account. Our method corresponds to block LMMSE filtering, and has the advantage of complexity linearly increasing with the block length and the ease of incorporating the a priori information of the input signals whenever possible. The proposed method can be used with any random process with a known autocorrelation function by use of an approximation to an autoregressive (AR) process. We show through extensive simulations that our method performs identical with the optimal block LMMSE filtering for Gaussian input signals.