Capacity Achieving Forward Error Correcting Codes

Optical Link Optimization Using Embedded Forward Error Correcting Codes

The design of a single-chip optical transceiver to optimize the performance of a short-distance optical datalink is proposed. The transceiver includes an embedded hybrid automatic repeat request (ARQ) controller capable of operation at several gigahertz clock rates. The hybrid ARQ controller uses a combination of packet retransmission protocols and forward error correction (FEC) to minimize bit...

On decoding up to error correcting capacity of linear error-correcting codes with Gröbner bases

The problem of decoding up to error correcting capacity of arbitrary linear codes with the use of Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving some system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution e...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes

Statistical mechanics and capacity-approaching error-correcting codes

I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular, minimum error probability decoding is equivalent to (nding the ground state of the corresponding spin system. The most probable value of a symbol is related to the magnetisation at a di*erent temperature. Convolutional codes correspond to one-dimensional spin ...