The performance of a relatively simple two-dimensional (2-D) product code is considered. The row code is a short constraint length convolutional code, and the column code is a high-rate block code. Both the rows and columns are decoded with soft-decision maximum likelihood decoding. The soft output Viterbi algorithm (SOVA) is used to decode the rows. In one case, the same decoder may be used for the rows and the columns. It is shown that, depending on the rate of the row code, reliable signaling is achieved within about 1.0 to 1.5 dB of the R/sub 0/ limit. Results are given for a particular impulsive noise channel; it is seen that performance is robust over a wide range of channel conditions.

Use of the Viterbi decoder to decode the (63, 57) Hamming code is considered, Implementation and performance of systematic and nonsystematic codes are addressed. It is shown that a Viterbi decoder for the constraint length seven, rate- 1/2 convolutional code can be used to decode both systematic and nonsystematic (63, 57) Hamming codes, but an additional step is needed to complete the decoding of the systematic code. Bounds and simulation results for postdecoding bit-error probability are given and it is shown that the systematic code performs 0.4 dB better than the nonsystematic code. A heuristic explanation is provided.

A severely punctured version of the well known rate-1/2, constraint length 7 convolutional code is considered for transmission of short to moderate length messages. Transmissions are assumed to be truncated by use of tail bits. By severely punctured the authors mean that the only redundancy conveyed is contained in the tail. It is shown that the resulting codes are high rate distance-2 codes and for certain message lengths they are cyclic. The figure of merit assumed is the probability of not correctly decoding a message, and, with maximum likelihood decoding, significant coding gains are demonstrated. In one case, a Hamming code results and its performance is determined. The coding gains observed range from 3.8 dB for the Hamming code to 2.4 dB for the longest distance-2 code considered, a (5040, 5034) code.>

The problem of computing the probability of undetected error is considered for linear block codes used for error detection. The recent literature is first reviewed and several results are extended. It is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual. Using the dual code formulation, the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes. Several bounds on the undetected error probability are then presented. We conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained. An efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results.