Ordered-statistic decoding of linear block codes utilizing hash and syndrome

Abstract EN

The Order Statistics Decoding (OSD) algorithm is an efficient soft input hard output decoder that uses a list of most likely error patterns.

OSD uses a hard decision decoder after correcting the most reliable bits by a long list of the test error patterns.

In this paper, the original OSD was developed with hash and syndrome (OSD-HSD) decoder where the low complexity hard decision decoder is integrated as component decoder.

The main idea was to create the error pattern list using the hash techniques by storing each error pattern in short list with equal decimal value of its syndrome and correcting the most reliable bits.

It was observed that when the receiver receives a sequence, it accesses directly to the error patterns corresponding to the decimal value of its syndrome without the need to access all error patterns for certain weigh as in OSD.

For this scenario, the simulation results and complexity analysis show that the proposed solution yields to good error correcting performances and complexity reduction compared to original OSD and many other decoding algorithms utilizing hash syndrome decoding such as the chase algorithms with hash soft decision decoder (Chase-HSDec) and soft decision decoder by hash technique (SDHT).

The proposed decoder has shown a good performance in terms of BER up to with reduced temporal complexity by reducing the length of test errors patterns specially for long linear block codes with high code rate (K/N>0.5) and small values of .

Also the proposed algorithm OSD-HSD yields to the same or slightly less error correcting performance (less than 1 dB) compared to original OSD and better performance than other competitors for medium to long linear block codes with high code rate (K/N>0.5) and large in terms of BER.

But by significant reduction in complexity in term of coding list.ُ