2016/07/22 by Rahul Devassy, Devassy, Rahul, Giuseppe Durisi +7
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1607.06837
openalex publication_date 2016/07/22 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We present nonasymptotic achievability and converse bounds on the maximum\ncoding rate (for a fixed average error probability and a fixed average\nblocklength) of variable-length full-feedback (VLF) and variable-length\nstop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For\nthe VLF setup, the achievability bound relies on a scheme that maps each\nmessage onto a variable-length Huffman codeword and then repeats each bit of\nthe codeword until it is received correctly. The converse bound is inspired by\nthe meta-converse framework by Polyanskiy, Poor, and Verd 'u (2010) and relies\non binary sequential hypothesis testing. For the case of zero error\nprobability, our achievability and converse bounds match. For the VLSF case, we\nprovide achievability bounds that exploit the following feature of BEC: the\ndecoder can assess the correctness of its estimate by verifying whether the\nchosen codeword is the only one that is compatible with the erasure pattern.\nOne of these bounds is obtained by analyzing the performance of a\nvariable-length extension of random linear fountain codes. The gap between the\nVLSF achievability and the VLF converse bound, when number of messages is\nsmall, is significant: 23 % for 8 messages on a BEC with erasure probability\n0.5. The absence of a tight VLSF converse bound does not allow us to assess\nwhether this gap is fundamental.\n