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<p>This paper examines error control coding (ECC) use in wireless sensor networks (WSNs) to determine the energy efficiency of specific ECC implementations in WSNs. ECC provides coding gain, resulting in transmitter energy savings, at the cost of added decoder power consumption. This paper derives an expression for the critical distance <mml:math>   <mml:msub>    <mml:mi>d</mml:mi>    <mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi>    </mml:mrow>   </mml:msub> </mml:math>, the distance at which the decoder's energy consumption per bit equals the transmit energy savings per bit due to coding gain, compared to an uncoded system. Results for several decoder implementations, both analog and digital, are presented for <mml:math>   <mml:msub>    <mml:mi>d</mml:mi>    <mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi>    </mml:mrow>   </mml:msub> </mml:math> in different environments over a wide frequency range. In free space, <mml:math>   <mml:msub>    <mml:mi>d</mml:mi>    <mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi>    </mml:mrow>   </mml:msub> </mml:math> is very large at lower frequencies, suitable only for widely spaced outdoor sensors. In crowded environments and office buildings, <mml:math>   <mml:msub>    <mml:mi>d</mml:mi>    <mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi>    </mml:mrow>   </mml:msub> </mml:math> drops significantly, to 3 m or greater at 10 GHz. Interference is not considered; it would lower <mml:math>   <mml:msub>    <mml:mi>d</mml:mi>    <mml:mrow><mml:mi>C</mml:mi><mml:mi>R</mml:mi>    </mml:mrow>   </mml:msub> </mml:math>. Analog decoders are shown to be the most energy-efficient decoders in this study.</p

Error Control Coding in Low-Power Wireless Sensor Networks: When Is ECC Energy-Efficient?