Inclusion Criteria:

- Histologically, or cytologically documented diffuse large B-cell lymphoma, and other
aggressive CD20+ non-Burkitt non-Hodgkin B-cell lymphoma variants as defined by the
2008 WHO classification; rare aggressive CD20 negative B-cell lymphomas are also
eligible

- Subjects who are untreated or who received a maximum of one (1) cycle of chemotherapy
prior are eligible; the start of previous chemotherapy cycle must occur at least 21
days prior to beginning treatment under this protocol, and such cycle will count
towards the total maximum of 6 cycles under this study

- Documentation of HIV infection at any time prior to study entry; documentation may be
serologic (positive enzyme-linked immunosorbent assay [ELISA] and positive Western
blot), or other federally approved licensed HIV test; prior documentation of HIV
seropositivity is acceptable

- All stages of disease allowed

- Measurable or non-measurable tumor; non-measurable tumor parameters are defined as
not having bidimensional measurements (e.g., gastric or marrow involvement), but that
can be followed for response by other diagnostic tests such as gallium, positron
emission tomography (PET) imaging, and/or bone marrow biopsy

- Performance Status (PS) 0, 1, or 2 per the Eastern Cooperative Oncology Group (ECOG)
Performance Status Scale (Karnofsky Performance Score >= 50%)

- Able to provide informed consent

- Total bilirubin =< 1.5 institutional upper limit of normal (ULN), unless elevated
secondary to lymphomatous involvement of liver or biliary system, or due to other HIV
medications (e.g., indinavir, tenofovir, or atazanavir); for direct bilirubin > 1.2
due to hepatic involvement by tumor for the initial dose of EPOCH drug adjustment

- Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 times ULN
(unless elevated due to secondary lymphomatous involvement of the liver)

- Creatinine clearance >= 60 mL/min, unless secondary to renal involvement by lymphoma
(< 50 mL/min if due to kidney involvement by tumor)

- Absolute neutrophil count (ANC) >= 1,000/mm^3

- Platelet count >= 75,000/mm^3 (unless abnormal due to lymphomatous involvement of
bone marrow); All subjects must cease colony-stimulating factor therapy at least 24
hours prior to institution of Cycle 1 chemotherapy

- Left ventricular ejection fraction (LVEF) normal by multi gated acquisition scan
(MUGA) scan or echocardiogram (ECHO) within the past 6 weeks

- Concurrent radiation, with or without steroids, or steroids alone for emergency
conditions secondary to lymphoma (i.e. cord compression, etc.) will be permitted

- Female subjects must have a negative pregnancy test within 7 days of entering into
the study; both men and women of child bearing potential must agree to use adequate
methods of contraception for the duration of the treatment; women must avoid
pregnancy, and men must avoid fathering children while in the study and for 6 months
following the last study drug treatment

- Subjects on an antiretroviral regimen should be receiving treatment that is in
accordance with the current International AIDS Society guidelines; the specific
agents are at the discretion of the Investigator and use of agents currently
available on an expanded access basis is allowed but use of experimental
antiretroviral agents or those containing zidovudine (including Combivir and
Trizivir) are prohibited; changes to HAART therapy may be made if medically necessary
(toxicity, failure of regimen, etc.); antiretroviral naïve subjects: subjects who are
not on HAART at study entry MUST begin therapy (utilizing the above guidelines) AFTER
one cycle of chemotherapy has been completed under protocol; changes to HAART therapy
may be made if medically necessary (toxicity, failure of regimen, etc.); concurrent
therapy with zidovudine or a zidovudine-containing regimen (including Combivir and
Trizivir) will be prohibited until 2 months following the subject's completion of
chemotherapy as part of this protocol

- Subjects already receiving erythropoietin or colony-stimulating factor therapy are
eligible for participation, although the latter must be discontinued at least 24
hours prior to receiving chemotherapy

- Subjects must be able to swallow oral medications

Exclusion Criteria:

- Subjects may have received one prior cycle of chemotherapy similar to CHOP or EPOCH
with or without rituximab; subjects who received more than one (1) prior cycle of
chemotherapy are not allowed

- Absolute CD4 count of < 50 cells/ mm^3

- Presence of second active tumor, other than non-melanoma skin cancer, carcinoma in
situ of the cervix, or Kaposi's sarcoma (KS) that requires systemic therapy

- CNS involvement by lymphoma including parenchymal brain or spinal cord lymphoma or
known presence of leptomeningeal disease prior to registration

- Subjects who are Hepatitis B core antibody positive are eligible only if they start
or are on prophylactic therapy; subjects with known active Hepatitis B (surface
antigen, core antigen, or viral load positive) are ineligible; a hepatitis B viral
load should be confirmed negative on all patients who are hepatitis B core antibody
positive, but hepatitis B antigen negative

- Subjects with known chronic active Hepatitis C are ineligible; if Hepatitis C is
discovered after enrollment the patient must be evaluated by a specialist in order to
determine the need for treatment

- Pregnant women or nursing mothers

- ECOG Performance Score >= 3 (KPS < 50%)

- Expected survival < 2 months

- Unable to comply with the requirements of the protocol, or unable to provide adequate
informed consent in the opinion of the Principal Investigator

- Serious, ongoing, non-malignant disease or infection, which in the opinion of the
Investigator and/or the sponsor would compromise other protocol objectives; subjects
with active opportunistic infections are ineligible

- Major surgery, other than diagnostic surgery, occurring 4 weeks prior to study entry

- Rituximab therapy within the 12 months prior to study entry; patients treated with
rituximab within 12 months prior to study registration are eligible only if it was
given for indications other than the treatment of aggressive lymphoma

- Prior cytotoxic chemotherapy or radiotherapy for this lymphoma

- History of cutaneous or mucocutaneous reactions, or diseases in the past, due to any
cause, severe enough to cause hospitalization or an inability to eat or drink for > 2
days; this exclusion relates to the long-term possibility of severe cutaneous or
mucocutaneous reactions to rituximab that might occur at increased frequency in
patients who have had severe skin disease or reactions in the past

- Use of zidovudine as part of the HAART regimen (a drug substitution for zidovudine at
the time of study entry is allowed)

- Any acute, inter-current infection that may interfere with planned protocol
treatment; patients with mycobacterium avium will not be excluded from study entry;
chronic therapy with potentially myelosuppressive agents is allowed provided that
entry hematologic criteria are met

- Myocardial infarction (MI) within 6 months prior to study entry, New York Heart
Association (NYHA) Class II or greater heart failure, uncontrolled angina, severe
uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or
electrocardiographic evidence of acute ischemic or active conduction system
abnormalities

- Subjects should not have taken valproic acid or another histone deacetylase inhibitor
for at least 2 weeks prior to study enrollment