A Recursive Single Parity Check Product Code with Non-Gaussian Fixed Weight Distribution

In iterated product of single parity check (SPC) codes, weight distribution is an important factor for the performance against transmission errors. A product code with Gaussian weight distribution should have a good performance. We present a closed-form solution for the weight distribution of a recursive SPC product code. We show that the code weights for this code are symmetrically distributed at (N plusmn radic(N)/2), where N is the full-length of a codeword. Though this code does not have a Gaussian weight distribution, it has better performance than conventional product codes. When soft-output iterative decoding is applied, the performance is away from the Shannon capacity limit by only 0.95 dB. Hence, we conclude that Gaussian weight distribution is not a necessary condition for a good performance.