QUANTIZATION LOSS IN CONVOLUTIONAL DECODING

We study the loss in quantizing coded symbols from the AWGN channel wi th BPSK or QPSK modulation. A new quantization scheme and branch metri c calculation method are presented. For the uniformly quantized AWGN c hannel, cutoff rate is used to determine the stepsize and the smallest number of quantization bits needed for a given bit signal-to-noise ra tio (E(b)/N0) loss. A 9-level quantizer is presented, along with 3-bit branch metrics for a rate 1/2 code, which causes an E(b)/N0 loss of o nly 0.14 dB. These results also apply to soft-decision decoding of blo ck codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the new memory 14, rate 1/4 or 1/6 codes used by the big Viterbi decoders at JPL.