Performance of Reed-Solomon coded M-ary modulation systems with overlapped symbols

We analyzed the bit error probability of a single RS codeword with symbol overlapping. By symbol overlapping, we mean that the bits in each modulation symbol can belong to 2 or more RS symbols and vice versa. We propose two novel designs for Reed-Solomon (RS) coded modulation with symbol overlapping. For an RS code with symbol size GF(2ⁿ), the information bits are first RS coded. For the first strategy, the coded bits are matrix interleaved prior to modulation and for the second strategy, the RS symbols are matrix interleaved and the resulting coded symbols are shifted circularly by n/2 bits prior to modulation. In this paper, we considered a M = 2ⁿ-ary modulation scheme. The received signal is demodulated appropriately, de-interleaved and RS decoded. The decoded symbols are interleaved and sent to the demodulator where it makes use of the decoded symbols from other codewords to re-demodulate the signals. This process is repeated until there is no improvement in the bit error rate. It is observed that this simple coded modulation design scheme has about 0.5 dB better performance than one that does not employ symbol overlapping over an AWGN channel at bit error rate of 10^-3. An improvement of 1 dB is observed over a Rayleigh fading channel