A five-parameter Lagrange-dual lower bound is derived for the typical random code error exponent for i.i.d. ensembles and mismatched likelihood decoding.
Error Exponents of Typical Random Trellis Codes
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abstract
In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time-varying trellis codes for general discrete memoryless channels, focusing on a certain range of low rates. By analyzing an upper bound to the error probability of the typical random trellis code, using the method of types, we first derive a Csiszar-style error exponent formula (with respect to the constraint length), which allows to easily identify and characterize properties of good codes and dominant error events. We also derive a Gallager-style form of this error exponent, which turns out to be related to the expurgated error exponent. The main result is further extended to channels with memory and mismatch.
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2019 1verdicts
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A Lagrange-Dual Lower Bound to the Error Exponent Function of the Typical Random Code
A five-parameter Lagrange-dual lower bound is derived for the typical random code error exponent for i.i.d. ensembles and mismatched likelihood decoding.