Flexible physical layer design subject to delay and energy constraints

One of the main problem in transmitting coded data is that the decoder does not know the real number of errors to correct. This issue is critical since it means that the decoders spend much more iterations for correcting them. A paradigmatic case of this is the Bose-Chaudhuri-Hocquenghem (BCH) code. This type of code generally resorts to the Berlekamp-Massey algorithm to estimate the Error Locator Polynomial (ELP) in an iterative manner. The number of iterations of this algorithm is fixed by the maximum error capability of the BCH code. This constraint is a drawback when the real number of errors in the codeword is small and the maximum error capability is high. However, if the number of errors in a codeword is small, it is possible to obtain closed-expressions for the ELP of amenable complexity. By doing so, it is feasible to apply a combined strategy between the closed-solution of the ELP and the Berlekamp-Massey algorithm to correct noisy codewords. Finally, we also show how to design the codeword length, rate and maximum error correction capability of BCH code under delay and energy constraints. Indeed, the proposed cross-layer design of the code parameters is valid for any linear block code.