List Decoding—Random Coding Exponents and Expurgated Exponents

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES List Decoding − Random Coding Exponents and Expurgated Exponents

Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size L. Two asymptotic regimes are considered, the fixed list–size regime, where L is fixed independently of the block length n, and the exponential list–size, where L grows exponentially with n. We first derive a general upper bound on the list–decoding ave...

On list size exponents in rate-distortion coding

We charactrize and investigate the highest achievable exponential growth rate of the expected number of rate-distortion codewords that are within a certain distance from a given source vector. Current address: Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, U.S.A. Email: [email protected]. Permanent address: HP Israel Science Center, Technion City, Haifa 32000, Israel. E...

Coding exponents for ( some )

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Expurgated Random-Coding Ensembles: Exponents, Refinements and Connections

This paper studies expurgated random-coding bounds and exponents with a given (possibly suboptimal) decoding rule. Variations of Gallager’s analysis are presented, yielding new asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent which coincides with that of Csiszár and Körner for discr...

Error exponents in scalable source coding

The characterization of the set of achievable rate and distortion values for scalable source coding is extended to additionally account for error exponents, namely, the negative normalized asymptotic log likelihood of error events at different layers. The “error” at each layer is defined as the event that the source block is not reproduced within the prespecified fidelity at the corresponding d...