On the Weight Enumerator and BER Bounds of Shortened Block and Product Codes

Code shortening is commonly performed in practice but its analytical decoding performance is not well understood. In this paper, we present tight expressions for estimating the weight enumerator and hence BER (bit error rate) performance of linear shortened and shortened-extended block/product codes operating in AWGN and Rayleigh fading channels. The expressions are easy to use as they are expressed in terms of the original (un-shortened) code properties, which are widely reported. Asymptotic coding loss expressions associated with code shortening are also derived.