arXiv subjects

Richard D. Wesel

Publications and source records attributed to Richard D. Wesel.

49 records · Page 3Linked to original sources

arXiv2014

Reliability-output Decoding of Tail-biting Convolutional Codes

We present extensions to Raghavan and Baum's reliability-output Viterbi algorithm (ROVA) to accommodate tail-biting convolutional codes. These tail-biting reliability-output algorithms compute the exact word-error probability of the decoded codeword after first calculating the posterior probability of the decoded tail-biting codeword's starting state. One approach employs a state-estimation algorithm that selects the maximum a posteriori state based on the posterior distribution of the starting states. Another approach is an approximation to the exact tail-biting ROVA that estimates the word-error probability. A comparison of the computational complexity of each approach is discussed in detail. The presented reliability-output algorithms apply to both feedforward and feedback tail-biting convolutional encoders. These tail-biting reliability-output algorithms are suitable for use in reliability-based retransmission schemes with short blocklengths, in which terminated convolutional codes would introduce rate loss.

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arXiv2013

Feedback Communication Systems with Limitations on Incremental Redundancy

This paper explores feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em finite-length} codes (with blocklength $N$) and decoding attempts only at {\em certain specified decoding times}, this paper presents the asymptotic expansion achieved by random coding, provides rate-compatible sphere-packing (RCSP) performance approximations, and presents simulation results of tail-biting convolutional codes. The information-theoretic analysis shows that values of $N$ relatively close to the expected latency yield the same random-coding achievability expansion as with $N = \infty$. However, the penalty introduced in the expansion by limiting decoding times is linear in the interval between decoding times. For binary symmetric channels, the RCSP approximation provides an efficiently-computed approximation of performance that shows excellent agreement with a family of rate-compatible, tail-biting convolutional codes in the short-latency regime. For the additive white Gaussian noise channel, bounded-distance decoding simplifies the computation of the marginal RCSP approximation and produces similar results as analysis based on maximum-likelihood decoding for latencies greater than 200. The efficiency of the marginal RCSP approximation facilitates optimization of the lengths of incremental transmissions when the number of incremental transmissions is constrained to be small or the length of the incremental transmissions is constrained to be uniform after the first transmission. Finally, an RCSP-based decoding error trajectory is introduced that provides target error rates for the design of rate-compatible code families for use in feedback communication systems.

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arXiv2013

Reliability-based Error Detection for Feedback Communication with Low Latency

This paper presents a reliability-based decoding scheme for variable-length coding with feedback and demonstrates via simulation that it can achieve higher rates than Polyanskiy et al.'s random coding lower bound for variable-length feedback (VLF) coding on both the BSC and AWGN channel. The proposed scheme uses the reliability output Viterbi algorithm (ROVA) to compute the word error probability after each decoding attempt, which is compared against a target error threshold and used as a stopping criterion to terminate transmission. The only feedback required is a single bit for each decoding attempt, informing the transmitter whether the ROVA-computed word-error probability is sufficiently low. Furthermore, the ROVA determines whether transmission/decoding may be terminated without the need for a rate-reducing CRC.

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arXiv2013

Variable-Length Coding with Feedback: Finite-Length Codewords and Periodic Decoding

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single-user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT) codes in the non-asymptotic regime. In that work, achievability is based on an infinite length random code and decoding is attempted at every symbol. The coding rate backoff from capacity due to channel dispersion is greatly reduced with feedback, allowing capacity to be approached with surprisingly small expected latency. This paper is mainly concerned with VLFT codes based on finite-length codes and decoding attempts only at certain specified decoding times. The penalties of using a finite block-length $N$ and a sequence of specified decoding times are studied. This paper shows that properly scaling $N$ with the expected latency can achieve the same performance up to constant terms as with $N = \infty$. The penalty introduced by periodic decoding times is a linear term of the interval between decoding times and hence the performance approaches capacity as the expected latency grows if the interval between decoding times grows sub-linearly with the expected latency.

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arXiv2012

A Rate-Compatible Sphere-Packing Analysis of Feedback Coding with Limited Retransmissions

Recent work by Polyanskiy et al. and Chen et al. has excited new interest in using feedback to approach capacity with low latency. Polyanskiy showed that feedback identifying the first symbol at which decoding is successful allows capacity to be approached with surprisingly low latency. This paper uses Chen's rate-compatible sphere-packing (RCSP) analysis to study what happens when symbols must be transmitted in packets, as with a traditional hybrid ARQ system, and limited to relatively few (six or fewer) incremental transmissions. Numerical optimizations find the series of progressively growing cumulative block lengths that enable RCSP to approach capacity with the minimum possible latency. RCSP analysis shows that five incremental transmissions are sufficient to achieve 92% of capacity with an average block length of fewer than 101 symbols on the AWGN channel with SNR of 2.0 dB. The RCSP analysis provides a decoding error trajectory that specifies the decoding error rate for each cumulative block length. Though RCSP is an idealization, an example tail-biting convolutional code matches the RCSP decoding error trajectory and achieves 91% of capacity with an average block length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how RCSP analysis can be used in cases where packets have deadlines associated with them (leading to an outage probability).

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arXiv2012

Chernoff Bounds for Analysis of Rate-Compatible Sphere-Packing with Numerous Transmissions

Recent results by Chen et al. and Polyanskiy et al. explore using feedback to approach capacity with short blocklengths. This paper explores Chernoff bounding techniques to extend the rate-compatible sphere-packing (RCSP) analysis proposed by Chen et al. to scenarios involving numerous retransmissions and different step sizes in each incremental retransmission. Williamson et al. employ exact RCSP computations for up to six transmissions. However, exact RCSP computation with more than six retransmissions becomes unwieldy because of joint error probabilities involving numerous chi-squared distributions. This paper explores Chernoff approaches for upper and lower bounds to provide support for computations involving more than six transmissions. We present two versions of upper and lower bounds for the two-transmission case. One of the versions is extended to the general case of $m$ transmissions where $m \geq 1$. Computing the general bounds requires minimization of exponential functions with the auxiliary parameters, but is less complex and more stable than multiple rounds of numerical integration. These bounds also provide a good estimate of the expected throughput and expected latency, which are useful for optimization purposes.

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arXiv2012

Coded Cooperative Data Exchange in Multihop Networks

Consider a connected network of n nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and exchanges coded packets with its neighbors. This paper provides necessary and sufficient conditions which characterize the set of all transmission schemes that permit every node to ultimately learn (recover) all k packets. When the network satisfies certain regularity conditions and packets are randomly distributed, this paper provides tight concentration results on the number of transmissions required to achieve universal recovery. For the case of a fully connected network, a polynomial-time algorithm for computing an optimal transmission scheme is derived. An application to secrecy generation is discussed.

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arXiv2011

Optimal Encoding Schemes for Several Classes of Discrete Degraded Broadcast Channels

Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which we call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each receiver) using the same single-letter function that adds distortion to the channel. The alphabet size of each NE codebook is bounded by that of the channel input. Inspired by Witsenhausen and Wyner, this paper defines the conditional entropy bound function $F^*$, studies its properties, and applies them to show that NE achieves the boundary of the capacity region for the multi-receiver broadcast Z channel. Then, this paper defines the input-symmetric DBC, introduces permutation encoding for the input-symmetric DBC, and proves its optimality. Because it is a special case of permutation encoding, NE is capacity achieving for the two-receiver group-operation DBC. Combining the broadcast Z channel and group-operation DBC results yields a proof that NE is also optimal for the discrete multiplication DBC. Along the way, the paper also provides explicit parametric expressions for the two-receiver binary-symmetric DBC and broadcast Z channel.

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arXiv2011

Minimizing weighted sum download time for one-to-many file transfer in peer-to-peer networks

This paper considers the problem of transferring a file from one source node to multiple receivers in a peer-to-peer (P2P) network. The objective is to minimize the weighted sum download time (WSDT) for the one-to-many file transfer. Previous work has shown that, given an order at which the receivers finish downloading, the minimum WSD can be solved in polynomial time by convex optimization, and can be achieved by linear network coding, assuming that node uplinks are the only bottleneck in the network. This paper, however, considers heterogeneous peers with both uplink and downlink bandwidth constraints specified. The static scenario is a file-transfer scheme in which the network resource allocation remains static until all receivers finish downloading. This paper first shows that the static scenario may be optimized in polynomial time by convex optimization, and the associated optimal static WSD can be achieved by linear network coding. This paper then presented a lower bound to the minimum WSDT that is easily computed and turns out to be tight across a wide range of parameterizations of the problem. This paper also proposes a static routing-based scheme and a static rateless-coding-based scheme which have almost-optimal empirical performances. The dynamic scenario is a file-transfer scheme which can re-allocate the network resource during the file transfer. This paper proposes a dynamic rateless-coding-based scheme, which provides significantly smaller WSDT than the optimal static scenario does.

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arXiv2009

The Single Source Two Terminal Network with Network Coding

We consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is demonstrated. We show by a simple graph-theoretic procedure that any such problem can be solved by performing network coding on the subset of messages that are requested by both the terminals and that routing is sufficient for transferring the remaining messages.

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arXiv2008

Analytical Framework for Optimizing Weighted Average Download Time in Peer-to-Peer Networks

This paper proposes an analytical framework for peer-to-peer (P2P) networks and introduces schemes for building P2P networks to approach the minimum weighted average download time (WADT). In the considered P2P framework, the server, which has the information of all the download bandwidths and upload bandwidths of the peers, minimizes the weighted average download time by determining the optimal transmission rate from the server to the peers and from the peers to the other peers. This paper first defines the static P2P network, the hierarchical P2P network and the strictly hierarchical P2P network. Any static P2P network can be decomposed into an equivalent network of sub-peers that is strictly hierarchical. This paper shows that convex optimization can minimize the WADT for P2P networks by equivalently minimizing the WADT for strictly hierarchical networks of sub-peers. This paper then gives an upper bound for minimizing WADT by constructing a hierarchical P2P network, and lower bound by weakening the constraints of the convex problem. Both the upper bound and the lower bound are very tight. This paper also provides several suboptimal solutions for minimizing the WADT for strictly hierarchical networks, in which peer selection algorithms and chunk selection algorithm can be locally designed.

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arXiv2008

Optimal Transmission Strategy and Explicit Capacity Region for Broadcast Z Channels

This paper provides an explicit expression for the capacity region of the two-user broadcast Z channel and proves that the optimal boundary can be achieved by independent encoding of each user. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two encoded streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that operates close to the optimal boundary.

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arXiv2007

Informed Dynamic Scheduling for Belief-Propagation Decoding of LDPC Codes

Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation, or message-passing, algorithm over the factor graph of the code. The traditional message-passing schedule consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling raises the problem of finding the best sequence of message updates. This paper presents practical scheduling strategies that use the value of the messages in the graph to find the next message to be updated. Simulation results show that these informed update sequences require significantly fewer iterations than standard sequential schedules. Furthermore, the paper shows that informed scheduling solves some standard trapping set errors. Therefore, it also outperforms traditional scheduling for a large numbers of iterations. Complexity and implementability issues are also addressed.

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