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Dan Piponi
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affects Effects of shortening and puncturing on codes

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affects of shortening and puncturing on codes

Given a binary block code $C=[n,k]$ of codeword length $n$, and dimension $k$. Suppose I've determined these properties for it : $d_{min}$ (minimum distance), $N_{dmin}$ (number of codewords at $d_{min}$), $G_{min}$ (minimum girth), and $N_{four}$ (number of 4-cylces in its Tanner graph). These are all commonly defined properties so I won't redefine them here. Now suppose that I have a new code derived from $C$ by shortening $N_s$ bits and puncturing $N_p$ bits resulting in a new $C'=[n-N_s-N_p,k-N_s]$ code what can be said about this new code? How would $d_{min}$,$G_{min}$,...change? Bounds are fine if no exact treatment is known. Any reference or survey articles would be really appreciated.