Efficient codeword recovery architecture for low-complexity Chase Reed-Solomon decoding

Compared to other soft-decision decoding algorithms of Reed-Solomon (RS) codes, the low-complexity Chase (LCC) algorithm can achieve better performance-complexity tradeoff. In order to reduce the complexity of the LCC decoding, the re-encoding and coordinate transformation techniques can be applied for high-rate codes. In this case, to recover a codeword for an (n, k) RS code, an erasure decoding needs to be employed after the errors in the k most reliable symbols are corrected by making use of the interpolation output. Alternatively, it can be done by reversing the coordinate transformation at the interpolation output followed by evaluating a polynomial of degree k over finite field elements. These approaches lead to significant overhead. A novel scheme and efficient architectures are proposed in this paper for codeword recovery in the LCC decoding. Our scheme computes the codeword symbols consecutively by applying the Chien search over the interpolation output and a polynomial of degree n-k. The Chien search can be implemented by constant multipliers, which cost much less area than general multipliers required by previous approaches. For the LCC decoding with eight test vectors for a (255, 239) RS code, adopting the proposed codeword recovery architecture can lead to 15% area reduction without sacrificing the throughput.