New Short Constraint Length, Rate 1/N Convolutional Codes Which Minimize the Required SNR for Given Desired Bit Error Rates

Abstract

New, good ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K, 1/N</tex> ) convolutional codes are tabulated for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3 \leq K \leq 7</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 \leq N \leq 8</tex> , which were selected based on the criterion of minimizing the required signal-to-noise ratio (SNR) for given desired bit error rates (BER). A transfer function upper bound was used to find the BER performance. Partial searches were performed using the idea that "good codes generate good lower rate codes." The new codes save signal energy up to 0.4 dB compared to previously reported codes of the same parameters.