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.
Paolini, E., Liva, G. (2019). A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel. Piscataway, USA : IEEE [10.1109/ISIT.2019.8849509].
A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel
Paolini, E
;
2019
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
