A Family of Low Complexity Adaptive Binary Linear Block Codes
Pavel Loskot, Norman C. Beaulieu · 2006
A family of linear binary block codes is constructed from ordinary block repetition codes using cyclic shifts of the input information vector which greatly simplifies encoding. These codes have variable block length and variable minimum Ham- ming distance. Several sets of cyclic shifts are defined to constrain the search for good codes. Codeword enumeration strategies are discussed. The proposed codes are shown to be good candi- dates for adaptive coding, turbo product coding, retransmission schemes and multihop routing, and block differential encoding. A generic parallel encoder structure well suited to OFDM systems, and a non-recursive block differential encoder capable of arbitrarily increasing the code rate with the block length, for given minimum Hamming distance, are proposed. Numerical examples compare the bit-error rate assuming iterative soft- decision decoding and the union bound. (13). The LDPC codes based on circulant matrices, and the repeat accumulate codes are designed to optimize soft-decision decoding to approach channel capacity (14). The BBRC's discussed in this paper are designed for a desired minimum Hamming distance while the block length can vary. Such a design criterion supports numerous applications. In this paper, we extend the results reported in (5) and (6). In Section II, the BBRC's are defined and their properties are examined. The applications of BBRC's are investigated in Section III. We consider BBRC's for adaptive coding schemes, for iteratively decoded turbo product codes, for retransmission and multihop routing schemes, and for block differential encoding. Conclusions are given in Section IV.