Error-and-Erasure Decoding for Block Codes with Feedback

Abstract

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.

33 pages, 1 figures

References in corpus (5)

• Variations on a theme by Schalkwijk and Kailath
• A Simple Converse of Burnashev's Reliability
• Error Exponents of Erasure/List Decoding Revisited via Moments of Distance Enumerators
• On the Error Exponents of ARQ Channels with Deadlines
• Error Exponents for Variable-length Block Codes with Feedback and Cost Constraints

Cited by in corpus (7)

• Active sequential hypothesis testing
• The Zero-Undetected-Error Capacity Approaches the Sperner Capacity
• The Sphere Packing Bound via Augustin's Method
• On the Listsize Capacity with Feedback
• A Large Deviations Approach to Secure Lossy Compression
• Bit-wise Unequal Error Protection for Variable Length Block Codes with Feedback
• On Error Exponents of Almost-Fixed-Length Channel Codes and Hypothesis Tests