Processing Gain in a Recursive Single Parity Check Product Code with Non-Gaussian Weight Distribution

We present a recursive single parity check product code, which was originally introduced as a constant amplitude multi-code CDMA. The proposed code has two advantageous features over conventional parity check product codes. First, the proposed code does not have any low-weight codewords. We derived a closed-form solution for the weight distribution. The code weights are symmetrically distributed at (N plusmn radic(N))/2, where N is the full-length of a codeword. Second, the processing gain in the despreading process after the iterative decoding provides additional improvement in BER performance. As a result, the proposed scheme has excellent error correcting capability. When soft-output iterative decoding is applied, the performance is away from the Shannon capacity limit by only 0.95 dB. Hence, the proposed code is a simple coding scheme with a good error correction performance.