This document addresses several aspects of block turbo codes (BTC) and higher order modulations, selected as the optional coding scheme for the burst modes of the IEEE 802.16.1, air interface draft standard. Compatibility, with mandatory burst modes (MODE B downstream and upstream transmissions), includes the same processes for the transmission convergence (TC) layer and physical media dependent (PMD) layer. However, the PMD sublayer is enhanced to allow for the replacement the FEC schemes based on RS variants with BTC.

Several additive codes of odd length over Z/sub 2//sup 2/ are introduced. These codes are cyclic and reversible. Furthermore, they are self-dual under an appropriately selected binary-valued inner product. Some binary derivatives of these codes have good parameters. All cyclic and reversible [5,2.5,3] additive codes over Z/sub 2//sup 2/ are isomorphic and possess interesting properties.

A [6,3,4] code E/sub 6/ over an Abelian group A/sub 4/ with four elements is presented. E/sub 6/ is cyclic, unlike the [6,3,4] hexacode H/sub 6/ over GF(4). However, E/sub 6/ and H/sub 6/ are isomorphic when the latter is viewed as a group code. Differences and similarities between E/sub 6/ and H/sub 6/ are discussed. A dual code of E/sub 6/ is presented. Some binary codes, among them the [24,12,8] Golay, are derived with the aid of E/sub 6/. A related cyclic [4,2,3] code E/sub 4/* is applied to construct the Nordstrom-Robinson code. E/sub 6/ is the smallest member of a class of [2k,k,4] cyclic and reversible codes over A/sub 4/. Another class of cyclic and reversible codes of length 2l+1; l/spl ges/2 and minimum distance 3 over A/sub 4/ is also presented.

We present algorithms for maximum likelihood soft decoding of the second order Reed-Muller codes RM(2,m) and the extended (24,12,8) Golay code. The decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered. Such representation enables application of certain elimination rules. A structure, called constrained design, is established to support the elimination procedures. Remarkably efficient algorithms are obtainable by this approach. The method of elimination is applicable also in combination with existing coset decoding schemes.>

Efficient algorithms are derived for maximum likelihood (ML) soft-decision decoding of some binary self-dual codes. A family of easily decodable self-dual codes is derived by modifying a known F/sub 24/, which has a weight distribution resembling that of the (24, 12, 8) Golay code G/sub 24/. The ML decoding of F/sub 24/ is accomplished by only 227 real additions, compared to 651 required for G/sub 24/, yet the error rates of the two decoders are similar for moderate noise conditions.>