Cord Blood Fucosylation to Enhance Homing and Engraftment in Patients With Hematologic Malignancies

Inclusion Criteria: 1. Patients must have one of the following hematologic malignancies: Acute Myelogenous Leukemia (AML), induction failure, high-risk for relapse first remission (with intermediate-risk or high-risk cytogenetics, flt3 mutation positive and/or evidence of minimal residual disease by flow cytometry), secondary leukemia from prior chemotherapy and/or arising from MDS, Langerhan's cell histiocytosis, any disease beyond first remission; or, 2. Myelodysplastic Syndrome (MDS): Primary or therapy related; or, 3. Acute Lymphoblastic Leukemia (ALL): induction failure, primary refractory to treatment (do not achieve complete remission after first course of therapy) or are beyond first remission including second or greater remission or active disease. Patients in first remission are eligible if they are considered high risk, defined as any of the following detected at any time: with translocations 9;22 or 4;11, hypodiploidy, complex karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or evidence of minimal residual disease, or acute biphenotypic leukemia, or double hit non-Hodgkin's lymphoma; or, 4. Non-Hodgkin's Lymphoma (NHL) in primary induction failure, second or third complete remission, refractory disease, or relapse (including relapse post autologous hematopoietic stem cell transplant). Double hit lymphomas in first remission or more advanced disease; or, 5. Small Lymphocytic Lymphoma (SLL), or Chronic Lymphocytic Leukemia (CLL) with progressive disease following standard therapy; or, 6. CML second chronic phase or accelerated phase; or, 7. Hodgkin's Disease (HD): Induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant). 8. Patients Age Criteria: Age \>/= 1 and \</= 80 years old. Eligibility for pediatric patients will be determined in conjunction with an MDACC pediatrician. 9. Performance score of at least 80% by Karnofsky or PS \< 3 (ECOG) (age \>/= 12 years), or Lansky Play-Performance Scale of at least 60% or greater (age \<12 years). 10. Adequate major organ system function as demonstrated by: a. Left ventricular ejection fraction of at least 40-45% b. Pulmonary function test (PFT) demonstrating a diffusion capacity of least 50% predicted. For children \</= 7 years of age who are unable to perform PFT, oxygen saturation \>/= 92% on room air by pulse oximetry. c. Creatinine \< 1.6 mg/dL. d. SGPT/bilirubin \</= to 2.0 x normal. 11. Negative Beta HCG test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization and willing to use an effective contraceptive measure while on study. 12. Patients must have two CB units available which are matched with the patient at 4, 5, or 6/6 HLA class I (serological) and II (molecular) antigens. Each cord must contain at least 1.5 x 10\^7 total nucleated cells/Kg recipient body weight (pre-thaw). 13. Have identified a back-up cell source in case of engraftment failure. The source can be autologous, related or unrelated. Exclusion Criteria: 1. Patients with known history of HIV/AIDS. 2. Active CNS disease in patient with history of CNS malignancy. 3. Patients with chronic active hepatitis or cirrhosis. If positive hepatitis serology, the Study Chair may deem the patient eligible based on the results of liver biopsy. 4. Patients with uncontrolled serious medical condition such as persistent septicemia despite adequate antibiotic therapy, decompensated congestive heart failure despite cardiac medications or pulmonary insufficiency requiring intubation (excluding primary disease for which CB transplantation is proposed), or psychiatric condition that would limit informed consent. 5. Positive beta HCG in female of child-bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization or breast-feeding.