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On Decoder Ties for the Binary Symmetric Channel with Arbitrarily Distributed Input.

Ling-Hua Chang1, Po-Ning Chen2, Fady Alajaji3

  • 1Department of Electrical Engineering, Yuan Ze University, Taoyuan 32003, Taiwan.

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|May 16, 2023
PubMed
Summary
This summary is machine-generated.

Investigating block codes over a binary symmetric channel (BSC) with non-uniform input, this study shows maximum a posteriori (MAP) decoder ties do not impact the error exponent. This finding extends previous research on uniform input distributions.

Keywords:
binary symmetric channelblock codesdecoder tieserror exponenterror probabilityjoint source-channel codingmaximum a posteriori (MAP) decodingnon-uniformly distributed channel inputs

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Area of Science:

  • Information Theory
  • Coding Theory
  • Digital Communications

Background:

  • Block codes are fundamental in digital communication for error detection and correction.
  • The binary symmetric channel (BSC) is a standard model for noisy communication channels.
  • Maximum a posteriori (MAP) decoding is an optimal decoding strategy aiming to minimize error probability.

Purpose of the Study:

  • To analyze the error probability of block codes transmitted over a memoryless BSC.
  • To investigate the impact of non-uniform input distributions on decoder performance.
  • To determine the effect of MAP decoder ties on the error exponent of block codes.

Main Methods:

  • Mathematical analysis of error probabilities for block codes.
  • Investigation of MAP decoding rule under non-uniform input distributions.
  • Derivation of the relationship between decoder ties and error probability growth with blocklength.

Main Results:

  • The ratio of MAP decoder ties to error probability grows linearly with blocklength when ties do not occur.
  • Decoder ties do not influence the error exponent of the block codes.
  • The findings generalize previous results obtained for uniform input distributions.

Conclusions:

  • MAP decoder ties do not affect the fundamental error performance (error exponent) of block codes.
  • The analysis provides a generalized understanding of error probability in block-coded systems under various input conditions.
  • This research contributes to the theoretical understanding of coding over noisy channels.