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Register a new userCapacity Results for the Noisy Shuffling Channel
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Added by
Ilan Shomorony
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel, which breaks the data block into small pieces and shuffles them. This channel models a DNA storage system, by capturing two of its key aspects: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the molecules are corrupted by noise at synthesis, sequencing, and during storage. For the BSC-shuffling channel we characterize the capacity exactly (for a large set of parameters), and show that a simple index-based coding scheme is optimal.
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The relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay. Based on different degradation orders among the relay and the receivers outputs, three types of physically degraded RBCs (PDRBCs) are introduced. Inner bounds and outer bounds are derived on the capacity region of the presented three types. The bounds are tight for two types of PDRBCs: 1) one receivers output is a degraded form of the other receivers output, and the relays output is a degraded form of the weaker receivers output; 2) one receivers output is a degraded form of the relays output, and the other receivers output is a degraded form of the relays output. For the Gaussian PDRBC, the bounds match, i.e., establish its capacity region.
This work considers a communication scenario where the transmitter chooses a list of size K from a total of M messages to send over a noisy communication channel, the receiver generates a list of size L and communication is considered successful if the intersection of the lists at two terminals has cardinality greater than a threshold T. In traditional communication systems K=L=T=1. The fundamental limits of this setup in terms of K, L, T and the Shannon capacity of the channel between the terminals are examined. Specifically, necessary and/or sufficient conditions for asymptotically error free communication are provided.
This paper studies the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $Delta$. It is shown that the capacity of this channel tends to that of the unquantized Gaussian channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity. In the low signal-to-noise ratio (SNR) regime, it is shown that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of $Delta$. Furthermore, an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios is given and evaluated in the low- and high-resolution limit. It is demonstrated that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity. Comparing these results with achievability results for (undithered) 1-bit quantization, it is observed that the dither reduces capacity in the low-precision limit, and it reduces the low-SNR asymptotic capacity unless the peak-to-average-power ratio is unbounded.
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 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 Martons 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 ranges of bit-pipe capacities.
Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.
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