On the Error Exponents of ARQ Channels with Deadlines

We consider communication over Automatic Repeat reQuest (ARQ) memoryless channels with deadlines. In particular, an upper bound L is imposed on the maximum number of ARQ transmission rounds. In this setup, it is shown that incremental redundancy ARQ outperforms Forney's memoryless decoding in terms of the achievable error exponents.Comment: 16 pages, 6 figures, Submitted to the IEEE Trans. on Information Theor

Error-and-Erasure Decoding for Block Codes with Feedback

Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then an outer bound is derived using a generalization of the straight-line bound to errors-and-erasures decoders and the optimal error exponent trade off of a feedback encoder with two messages. In addition upper and lower bounds are derived, for the optimal erasure exponent of error free block codes in terms of the rate. Finally we present a proof of the fact that the optimal trade off between error exponents of a two message code does not increase with feedback on DMCs.Comment: 33 pages, 1 figure

Exponential bounds on error probability with Feedback

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 95-97).Feedback is useful in memoryless channels for decreasing complexity and increasing reliability; the capacity of the memoryless channels, however, can not be increased by feedback. For fixed length block codes even the decay rate of error probability with block length does not increase with feedback for most channel models. Consequently for making the physical layer more reliable for higher layers one needs go beyond the framework of fixed length block codes and consider relaxations like variable-length coding, error- erasure decoding. We strengthen and quantify this observation by investigating three problems. 1. Error-Erasure Decoding for Fixed-Length Block Codes with Feedback: Error-erasure codes with communication and control phases, introduced by Yamamoto and Itoh, are building blocks for optimal variable-length block codes. We improve their performance by changing the decoding scheme and tuning the durations of the phases, and establish inner bounds to the tradeoff between error exponent, erasure exponent and rate. We bound the loss of performance due to the encoding scheme of Yamamoto-Itoh from above by deriving outer bounds to the tradeoff between error exponent, erasure exponent and rate both with and without feedback. We also consider the zero error codes with erasures and establish inner and outer bounds to the optimal erasure exponent of zero error codes. In addition we present a proof of the long known fact that, the error exponent tradeoff between two messages is not improved with feedback. 2. Unequal Error Protection for Variable-Length Block Codes with Feedback: We use Kudrayashov's idea of implicit confirmations and explicit rejections in the framework of unequal error protection to establish inner bounds to the achievable pairs of rate vectors and error exponent vectors. Then we derive an outer bound that matches the inner bound using a new bounding technique. As a result we characterize the region of achievable rate vector and error exponent vector pairs for bit-wise unequal error protection problem for variable-length block codes with feedback. Furthermore we consider the single message message-wise unequal error protection problem and determine an analytical expression for the missed detection exponent in terms of rate and error exponent, for variable-length block codes with feedback. 3. Feedback Encoding Schemes for Fixed-Length Block Codes: We modify the analysis technique of Gallager to bound the error probability of feedback encoding schemes. Using the encoding schemes suggested by Zigangirov, D'yachkov and Burnashev we recover or improve all previously known lower bounds on the error exponents of fixedlength block codes.by Bariş Nakiboḡlu.Ph.D

Network coding for delay challenged environments

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 191-196).Delay is a fundamental problem of data communication and networks, a problem that is not usually addressed in classical coding, information or networking theory. We focus on the general problem of delay challenged networks. This delay challenge may be related to different reasons, for example, 1) large latency, which can affect the performance of the system in delay, throughput or energy efficiency, 2) half-duplex constraints on the nodes, which precludes a node to receive and transmit at the same time, and/or 3) application-level requirements for reliable, fast and efficient dissemination of information. We consider three main problems of study and the role of network coding on solving these problems. The first is related to the problem of reliable communication in time-division duplexing channels, also known as half-duplex channels, in the presence of large latency. In large latency channels, feedback about received packets may lag considerably the transmission of the original packets, limiting the feedback's usefulness. Moreover, the time duplex constraints may entail that receiving feedback may be costly. In this work, we consider tailoring feedback and (network) coding jointly in such settings to reduce the mean delay for successful in order reception of packets. We find that, in certain applications, judicious choices provide results that are close to those that would be obtained with a full-duplex system. The second part of this thesis studies the problem of data dissemination in arbitrary networks. In particular, we study the problem of minimizing the delay incurred in disseminating a finite number of data packets. We show that the optimal solution to the problem can be thought of as a scheduling problem, which is hard to solve. Thus, we consider the use of a greedy linear network coding algorithm that only takes into account the current state of the system to make a decision. The proposed algorithm tries to maximize the impact on the network at each slot, i.e., maximize the number of nodes that will benefit from the coded packet sent by each active transmitter. We show that our scheme is considerably better, in terms of the number of slots to complete transmission, than schemes that choose the node with more information as the transmitter The third part of this work studies the case of underwater acoustic networks as an example of delay challenged networks. We consider the use of network coding under two different lights. First, as a means to obtain a lower bound on the transmission power of multicast connections in underwater networks. Second, to develop practical schemes useful in such networks. Finally, we study upper bounds on the transport capacity of underwater acoustic networks under unicast connections. We show that the amount of information that can be exchanged by each source-destination pair in underwater acoustic networks goes to zero as the number of nodes n goes to infinity. This occurs at least at a rate n-1/Qe-Wo(O(n-k)) where Wo represents the branch zero of the Lambert W function, and a path loss exponent of a. Note that typical values of the path loss exponent are a E [1, 2] for underwater acoustic networks. This is significantly different to the a > 2 of radio wireless applications.by Daniel Enrique Lucani.Ph.D