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Error Exponents for Joint Source-Channel Coding with Delay-Constraints



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Error Exponents for Joint Source Channel Coding with Delay Constraints Cheng Chang Anant Sahai Wireless Foundations Dept of EECS University of California at Berkeley Email cchang eecs berkeley edu Wireless Foundations Dept of EECS University of California at Berkeley Email sahai eecs berkeley edu Abstract Traditionally joint source channel coding is viewed in the block coding context all the source symbols are known in advance by the encoder Here we consider source symbols to be revealed to the encoder in real time and require that they be reconstructed at the decoder within a certain fixed end to end delay We derive upper and lower bounds on the reliability function with delay for cases with and without channel feedback For erasure channels with feedback the upper bound is shown to be achievable and the resulting scheme shows that from a delay perspective nearly separate source and channel coding is optimal I I NTRODUCTION The block length story for error exponents is particularly seductive when upper and lower bounds agree as they do for both lossless source coding and for point to point channel coding in the high rate regime 1 2 However the block code setting conflates a particular style of implementation with the problem statement itself Recently it has become clear that fixed block codes may indeed incur unnecessarily poor performance with respect to end to end delay even when the required delay is fixed In 3 we show that despite the block channel coding reliability functions not changing with feedback in the high rate regime the reliability function with respect to fixed delay can in fact improve dramatically with feedback 1 For fixed rate lossless source coding 5 showed similarly that the reliability function with fixed delay is much better than the reliability with fixed block length An example given in 5 6 illustrated how sometimes an extremely simple and clearly suboptimal nonblock code can dramatically outperform the best possible fixed length block code



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