Asymptotically Tight MLD Bounds and Minimum-Variance Importance Sampling Estimator for Linear Block Codes Over BSCs

In this paper, we re-examine the classical problem of efficiently evaluating the block and bit error rate performance of linear block codes over binary symmetric channels (BSCs). In communication systems, the maximum likelihood decoding (MLD) bounds are powerful tools to predict the error performanc...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.64785-64800
Main Authors: Pan, Jinzhe, Mow, Wai Ho
Format: Article
Language:English
Subjects:
Asymptotic properties
asymptotically tight bounds
Binary codes
binary symmetric channel
Bit error rate
Block codes
Codes
Communications systems
Computer simulation
Decoding
Encoding
Error probability
Errors
Importance sampling
Linear block codes
Lower bounds
Maximum likelihood decoding
Monte Carlo methods
Monte Carlo simulation
Signal to noise ratio
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Summary:In this paper, we re-examine the classical problem of efficiently evaluating the block and bit error rate performance of linear block codes over binary symmetric channels (BSCs). In communication systems, the maximum likelihood decoding (MLD) bounds are powerful tools to predict the error performance of the coded systems, especially in the asymptotic regime of low error probability (or high signal-to-noise ratio). Contrary to the conventional wisdom, we prove that for BSCs, all bounds based on Gallager's first bounding technique, including the famous union bound, are not asymptotically tight for all possible choices of the Gallager region. By proposing the so-called input demodulated-output weight enumerating function (IDWEF) of a code, asymptotically tight MLD upper and lower bounds for BSCs are then derived. In many practical scenarios where performance bounds are not applicable (e.g., due to the unavailability of the relevant coding parameters under a given decoder), the Monte Carlo simulation is commonly used despite its inefficiency, especially in the low error probability regime. We propose an efficient importance sampling (IS) estimator by deriving the optimal IS distribution of the Hamming weight of the error vector. In addition, the asymptotic relative saving on the required sample size of the proposed IS estimator over the state-of-the-art counterpart in the recent literature is characterized. Its accuracy in predicting the efficiency of the proposed IS estimator is verified by extensive computer simulation.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2022.3183203