Improvements in Block-Retransmission Schemes

Consider the case where an
n
-digit block encoded word cannot be decoded reliably and a second block of
n
redundant digits is sent to allow the receiver to make a new try based on the combined information received. Two classes of schemes are proposed and analyzed which give significantly better performance than is obtained by sending a repeat of the first block, yet do not require excessive decoding complexity. One approach is to consider small sub-blocks of the original
n
-digit code as the data digits of a short rate one-half code. The other approach is to treat the first sending as the data digits of a systematic convolutional code of short constraint length. Comparisons are made for the white Gaussian noise channel and the erasure channel. The comparisons are limited to an assessment of the improvement gained after two sendings. Procedures using length 4 sub-blocks and using convolutional codes with constraint lengths as short as 2 or 3 digits yield considerable improvement over block retransmission. For the case of the erasure channel, a very simple decoding rule is devised for the convolutional code case.