Block Coding with Interleaving
Block codes are typically combined with block interleaving to spread out burst errors from fading.
- A block interleaver is an array with d rows and n columns, as shown in Figure 1
- The interleaver contents are read out by columns into the modulator for subsequent transmission over the channel.
- During transmission codeword symbols in the same codeword are separated by d − 1 other symbols, so symbols in the same codeword experience approximately independent fading if their separation in time is greater than the channel coherence time: i.e. if dTs>Tc ≈ 1/Bd, where Ts is the codeword symbol duration, Tc is the channel coherence time, and Bd is the channel Doppler.
- An interleaver is called a deep interleaver if the condition dTs>Tcis satisfied.
- The de interleaver is an array identical to the interleaver.The de interleaver output is read into the decoder by rows, i.e. one codeword at a time
- Figure 1 shows the ability of coding and interleaving to correct for bursts of errors
- Performance analysis of coding and interleaving requires pairwide-error probability analysis or application of the Chernoff or union bounds.The union bound provides a simple approximation to performanceAssume a Rayleigh fading channel with deep interleaving such that each coded symbol fades independently.Then the union bound for an (n, k) block code with soft-decision decoding under non-coherent FSK modulation yields a codeword error given as
Where dmin is the minimum Hamming distance of the code and
- Similarly, for slowly fading channels where a coherent phase reference can be obtained, the union bound on codeword error probability an (n, k) block code with soft-decision decoding and BPSK modulation yields
- Designs for block coding and interleaving over fading channels optimize their performance by maximizing the Hamming distance of the code
- Coding and interleaving is a suboptimal coding technique, since the correlation of the fading which affects subsequent bits contains information about the channel which could be used in a true maximum-likelihood decoding scheme