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Paper Detail

Paper Title A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel
Paper IdentifierWE2.R9.1
Authors Enrico Paolini, University of Bologna, Italy; Gianluigi Liva, German Aerospace Center, Germany
Session Bounds on Codes
Location Pontoise, Level 5
Session Time Wednesday, 10 July, 11:40 - 13:20
Presentation Time Wednesday, 10 July, 11:40 - 12:00
Manuscript  Click here to download the manuscript
Abstract A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble-specific interval of erasure probabilities, when the ensemble weight spectral shape function tends to a negative value as the fractional codeword weight tends to zero. For these ensembles we can therefore lower bound the block-wise ML decoding threshold. Two examples are presented, namely, linear random parity-check codes and fixed-rate Raptor codes with linear random precoders. While for the former a full analytical solution is possible, for the latter we can lower bound the ML decoding threshold on the erasure channel by simply solving a 2 x 2 system of nonlinear equations.