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

Scalable Video Streaming with Prioritised Network Coding on End-System Overlays

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Progressive Source-Channel Coding for Multimedia Transmission over Noisy and Lossy Channels with and without Feedback

Rate-scalable or layered lossy source-coding is useful for progressive transmission of multimedia sources, where the receiver can reconstruct the source incrementally. This thesis considers ``joint source-channel'' schemes for such a progressive transmission, in the presence of noise or loss, with and without the use of a feedback link. First we design image communication schemes for memoryless and finite state channels using limited and explicitly constrained use of the feedback channel in the form of a variable incremental redundancy Hybrid ARQ protocol. Constraining feedback allows a direct comparison with schemes without feedback. Optimized feedback based systems are shown to have useful gains. Second, we develop a controlled Markov chain approach for constrained feedback Hybrid ARQ protocol design. The proposed methodology allows the protocol to be chosen from a collection of signal flow graphs, and also allows explicit control over the tradeoffs in throughput, reliability and complexity. Next we consider progressive image transmission in the absence of feedback. We assign unequal error protection to the bits of a rate-scalable source-coder using rate compatible channel codes. We show that, under the framework, the source and channel bits can be ``scheduled'' in a single bitstream in such a way that operational optimality is retained for different transmission budgets, creating a rate-scalable joint source-channel coder. Next we undertake the design of a joint source-channel decoder that uses ``distortion aware'' ACK/NACK feedback generation. For memoryless channels, and Type-I HARQ, the design of optimal ACK/NACK generation and decoding by packet combining is cast and solved as a sequential decision problem. We obtain dynamic programming based optimal solutions and also propose suboptimal, lower complexity distortion-aware decoders and feedback generation rules which outperform conventional BER based rules such as CRC-check. Finally we design operational rate-distortion optimal ACK/NACK feedback generation rules for transmitting a tree structured quantizer over a memoryless channel. We show that the optimal feedback generation rules are embedded, that is, they allow incremental switching to higher rates during the transmission. Also, we obtain the structure of the feedback generation rules in terms of a feedback threshold function that simplifies the implementation

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